From 2771d5835cdfd49de9ee17a00117b9d90749e821 Mon Sep 17 00:00:00 2001 From: Philipp Burckhardt Date: Tue, 7 Mar 2023 21:00:01 -0500 Subject: [PATCH] docs: render equations via math code blocks --- .../@stdlib/stats/base/dmean/README.md | 8 +++- .../@stdlib/stats/base/dmeankbn/README.md | 8 +++- .../@stdlib/stats/base/dmeankbn2/README.md | 8 +++- .../@stdlib/stats/base/dmeanli/README.md | 8 +++- .../@stdlib/stats/base/dmeanlipw/README.md | 8 +++- .../@stdlib/stats/base/dmeanors/README.md | 8 +++- .../@stdlib/stats/base/dmeanpn/README.md | 8 +++- .../@stdlib/stats/base/dmeanpw/README.md | 8 +++- .../@stdlib/stats/base/dmeanstdev/README.md | 32 +++++++++---- .../@stdlib/stats/base/dmeanstdevpn/README.md | 32 +++++++++---- .../@stdlib/stats/base/dmeanvar/README.md | 32 +++++++++---- .../@stdlib/stats/base/dmeanvarpn/README.md | 32 +++++++++---- .../@stdlib/stats/base/dmeanwd/README.md | 8 +++- .../@stdlib/stats/base/dnanmean/README.md | 8 +++- .../@stdlib/stats/base/dnanmeanors/README.md | 8 +++- .../@stdlib/stats/base/dnanmeanpn/README.md | 8 +++- .../@stdlib/stats/base/dnanmeanpw/README.md | 8 +++- .../@stdlib/stats/base/dnanmeanwd/README.md | 8 +++- .../@stdlib/stats/base/dnanstdev/README.md | 32 +++++++++---- .../@stdlib/stats/base/dnanstdevch/README.md | 32 +++++++++---- .../@stdlib/stats/base/dnanstdevpn/README.md | 32 +++++++++---- .../@stdlib/stats/base/dnanstdevtk/README.md | 32 +++++++++---- .../@stdlib/stats/base/dnanstdevwd/README.md | 32 +++++++++---- .../@stdlib/stats/base/dnanstdevyc/README.md | 32 +++++++++---- .../@stdlib/stats/base/dnanvariance/README.md | 32 +++++++++---- .../stats/base/dnanvariancech/README.md | 32 +++++++++---- .../stats/base/dnanvariancepn/README.md | 32 +++++++++---- .../stats/base/dnanvariancetk/README.md | 32 +++++++++---- .../stats/base/dnanvariancewd/README.md | 32 +++++++++---- .../stats/base/dnanvarianceyc/README.md | 32 +++++++++---- .../@stdlib/stats/base/dsem/README.md | 16 +++++-- .../@stdlib/stats/base/dsemch/README.md | 16 +++++-- .../@stdlib/stats/base/dsempn/README.md | 16 +++++-- .../@stdlib/stats/base/dsemtk/README.md | 16 +++++-- .../@stdlib/stats/base/dsemwd/README.md | 16 +++++-- .../@stdlib/stats/base/dsemyc/README.md | 16 +++++-- .../@stdlib/stats/base/dsmean/README.md | 8 +++- .../@stdlib/stats/base/dsmeanors/README.md | 8 +++- .../@stdlib/stats/base/dsmeanpn/README.md | 8 +++- .../@stdlib/stats/base/dsmeanpw/README.md | 8 +++- .../@stdlib/stats/base/dsmeanwd/README.md | 8 +++- .../@stdlib/stats/base/dsnanmean/README.md | 8 +++- .../@stdlib/stats/base/dsnanmeanors/README.md | 8 +++- .../@stdlib/stats/base/dsnanmeanpn/README.md | 8 +++- .../@stdlib/stats/base/dsnanmeanwd/README.md | 8 +++- .../@stdlib/stats/base/dstdev/README.md | 32 +++++++++---- .../@stdlib/stats/base/dstdevch/README.md | 32 +++++++++---- .../@stdlib/stats/base/dstdevpn/README.md | 32 +++++++++---- .../@stdlib/stats/base/dstdevtk/README.md | 32 +++++++++---- .../@stdlib/stats/base/dstdevwd/README.md | 32 +++++++++---- .../@stdlib/stats/base/dstdevyc/README.md | 32 +++++++++---- .../@stdlib/stats/base/dsvariance/README.md | 32 +++++++++---- .../@stdlib/stats/base/dsvariancepn/README.md | 32 +++++++++---- .../@stdlib/stats/base/dvariance/README.md | 32 +++++++++---- .../@stdlib/stats/base/dvariancech/README.md | 32 +++++++++---- .../@stdlib/stats/base/dvariancepn/README.md | 32 +++++++++---- .../@stdlib/stats/base/dvariancetk/README.md | 48 ++++++++++++++----- .../@stdlib/stats/base/dvariancewd/README.md | 32 +++++++++---- .../@stdlib/stats/base/dvarianceyc/README.md | 32 +++++++++---- .../@stdlib/stats/base/dvarm/README.md | 32 +++++++++---- .../@stdlib/stats/base/dvarmpn/README.md | 32 +++++++++---- .../@stdlib/stats/base/dvarmtk/README.md | 32 +++++++++---- .../@stdlib/stats/base/mean/README.md | 8 +++- .../@stdlib/stats/base/meankbn/README.md | 8 +++- .../@stdlib/stats/base/meankbn2/README.md | 8 +++- .../@stdlib/stats/base/meanors/README.md | 8 +++- .../@stdlib/stats/base/meanpn/README.md | 8 +++- .../@stdlib/stats/base/meanpw/README.md | 8 +++- .../@stdlib/stats/base/meanwd/README.md | 8 +++- .../@stdlib/stats/base/nanmean/README.md | 8 +++- .../@stdlib/stats/base/nanmeanors/README.md | 8 +++- .../@stdlib/stats/base/nanmeanpn/README.md | 8 +++- .../@stdlib/stats/base/nanmeanwd/README.md | 8 +++- .../@stdlib/stats/base/nanstdev/README.md | 32 +++++++++---- .../@stdlib/stats/base/nanstdevch/README.md | 32 +++++++++---- .../@stdlib/stats/base/nanstdevpn/README.md | 32 +++++++++---- .../@stdlib/stats/base/nanstdevtk/README.md | 32 +++++++++---- .../@stdlib/stats/base/nanstdevwd/README.md | 32 +++++++++---- .../@stdlib/stats/base/nanstdevyc/README.md | 32 +++++++++---- .../@stdlib/stats/base/nanvariance/README.md | 32 +++++++++---- .../stats/base/nanvariancech/README.md | 32 +++++++++---- .../stats/base/nanvariancepn/README.md | 32 +++++++++---- .../stats/base/nanvariancetk/README.md | 32 +++++++++---- .../stats/base/nanvariancewd/README.md | 32 +++++++++---- .../stats/base/nanvarianceyc/README.md | 32 +++++++++---- .../@stdlib/stats/base/sdsmean/README.md | 8 +++- .../@stdlib/stats/base/sdsmeanors/README.md | 8 +++- .../@stdlib/stats/base/sdsnanmean/README.md | 8 +++- .../stats/base/sdsnanmeanors/README.md | 8 +++- .../@stdlib/stats/base/smean/README.md | 8 +++- .../@stdlib/stats/base/smeankbn/README.md | 8 +++- .../@stdlib/stats/base/smeankbn2/README.md | 8 +++- .../@stdlib/stats/base/smeanli/README.md | 8 +++- .../@stdlib/stats/base/smeanlipw/README.md | 8 +++- .../@stdlib/stats/base/smeanors/README.md | 8 +++- .../@stdlib/stats/base/smeanpn/README.md | 8 +++- .../@stdlib/stats/base/smeanpw/README.md | 8 +++- .../@stdlib/stats/base/smeanwd/README.md | 8 +++- .../@stdlib/stats/base/snanmean/README.md | 8 +++- .../@stdlib/stats/base/snanmeanors/README.md | 8 +++- .../@stdlib/stats/base/snanmeanpn/README.md | 8 +++- .../@stdlib/stats/base/snanmeanwd/README.md | 8 +++- .../@stdlib/stats/base/snanstdev/README.md | 32 +++++++++---- .../@stdlib/stats/base/snanstdevch/README.md | 32 +++++++++---- .../@stdlib/stats/base/snanstdevpn/README.md | 32 +++++++++---- .../@stdlib/stats/base/snanstdevtk/README.md | 32 +++++++++---- .../@stdlib/stats/base/snanstdevwd/README.md | 32 +++++++++---- .../@stdlib/stats/base/snanstdevyc/README.md | 32 +++++++++---- .../@stdlib/stats/base/snanvariance/README.md | 32 +++++++++---- .../stats/base/snanvariancech/README.md | 32 +++++++++---- .../stats/base/snanvariancepn/README.md | 32 +++++++++---- .../stats/base/snanvariancetk/README.md | 32 +++++++++---- .../stats/base/snanvariancewd/README.md | 32 +++++++++---- .../stats/base/snanvarianceyc/README.md | 32 +++++++++---- .../@stdlib/stats/base/sstdev/README.md | 32 +++++++++---- .../@stdlib/stats/base/sstdevch/README.md | 32 +++++++++---- .../@stdlib/stats/base/sstdevpn/README.md | 32 +++++++++---- .../@stdlib/stats/base/sstdevtk/README.md | 32 +++++++++---- .../@stdlib/stats/base/sstdevwd/README.md | 32 +++++++++---- .../@stdlib/stats/base/sstdevyc/README.md | 32 +++++++++---- .../@stdlib/stats/base/stdev/README.md | 36 +++++++++----- .../@stdlib/stats/base/stdevch/README.md | 32 +++++++++---- .../@stdlib/stats/base/stdevpn/README.md | 32 +++++++++---- .../@stdlib/stats/base/stdevtk/README.md | 32 +++++++++---- .../@stdlib/stats/base/stdevwd/README.md | 32 +++++++++---- .../@stdlib/stats/base/stdevyc/README.md | 32 +++++++++---- .../@stdlib/stats/base/svariance/README.md | 32 +++++++++---- .../@stdlib/stats/base/svariancech/README.md | 32 +++++++++---- .../@stdlib/stats/base/svariancepn/README.md | 32 +++++++++---- .../@stdlib/stats/base/svariancetk/README.md | 48 ++++++++++++++----- .../@stdlib/stats/base/svariancewd/README.md | 32 +++++++++---- .../@stdlib/stats/base/svarianceyc/README.md | 32 +++++++++---- .../@stdlib/stats/base/variance/README.md | 32 +++++++++---- .../@stdlib/stats/base/variancech/README.md | 32 +++++++++---- .../@stdlib/stats/base/variancepn/README.md | 32 +++++++++---- .../@stdlib/stats/base/variancetk/README.md | 32 +++++++++---- .../@stdlib/stats/base/variancewd/README.md | 32 +++++++++---- .../@stdlib/stats/base/varianceyc/README.md | 32 +++++++++---- 138 files changed, 2346 insertions(+), 786 deletions(-) diff --git a/lib/node_modules/@stdlib/stats/base/dmean/README.md b/lib/node_modules/@stdlib/stats/base/dmean/README.md index dd8bdb6a4ef3..52a771ce16a3 100644 --- a/lib/node_modules/@stdlib/stats/base/dmean/README.md +++ b/lib/node_modules/@stdlib/stats/base/dmean/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dmeankbn/README.md b/lib/node_modules/@stdlib/stats/base/dmeankbn/README.md index 931d65d7ba29..bfd03ff5c837 100644 --- a/lib/node_modules/@stdlib/stats/base/dmeankbn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dmeankbn/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dmeankbn2/README.md b/lib/node_modules/@stdlib/stats/base/dmeankbn2/README.md index 5d421591f138..79ba581a937c 100644 --- a/lib/node_modules/@stdlib/stats/base/dmeankbn2/README.md +++ b/lib/node_modules/@stdlib/stats/base/dmeankbn2/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dmeanli/README.md b/lib/node_modules/@stdlib/stats/base/dmeanli/README.md index e580b5cceaab..e27e0cf2fec3 100644 --- a/lib/node_modules/@stdlib/stats/base/dmeanli/README.md +++ b/lib/node_modules/@stdlib/stats/base/dmeanli/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dmeanlipw/README.md b/lib/node_modules/@stdlib/stats/base/dmeanlipw/README.md index 9dc8edaafc70..c2f21a70aff2 100644 --- a/lib/node_modules/@stdlib/stats/base/dmeanlipw/README.md +++ b/lib/node_modules/@stdlib/stats/base/dmeanlipw/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dmeanors/README.md b/lib/node_modules/@stdlib/stats/base/dmeanors/README.md index d89ec2d96585..ef5b9edb6552 100644 --- a/lib/node_modules/@stdlib/stats/base/dmeanors/README.md +++ b/lib/node_modules/@stdlib/stats/base/dmeanors/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dmeanpn/README.md b/lib/node_modules/@stdlib/stats/base/dmeanpn/README.md index 2940c84e1cef..73eda8656b1c 100644 --- a/lib/node_modules/@stdlib/stats/base/dmeanpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dmeanpn/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dmeanpw/README.md b/lib/node_modules/@stdlib/stats/base/dmeanpw/README.md index 5fc9bd884fb5..42648a1c1c87 100644 --- a/lib/node_modules/@stdlib/stats/base/dmeanpw/README.md +++ b/lib/node_modules/@stdlib/stats/base/dmeanpw/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dmeanstdev/README.md b/lib/node_modules/@stdlib/stats/base/dmeanstdev/README.md index 6fe1f1e75bd2..f6dd03f07602 100644 --- a/lib/node_modules/@stdlib/stats/base/dmeanstdev/README.md +++ b/lib/node_modules/@stdlib/stats/base/dmeanstdev/README.md @@ -30,10 +30,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -41,10 +45,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -52,10 +60,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -63,10 +75,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dmeanstdevpn/README.md b/lib/node_modules/@stdlib/stats/base/dmeanstdevpn/README.md index f6b63e268a3b..091296125973 100644 --- a/lib/node_modules/@stdlib/stats/base/dmeanstdevpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dmeanstdevpn/README.md @@ -30,10 +30,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -41,10 +45,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -52,10 +60,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -63,10 +75,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dmeanvar/README.md b/lib/node_modules/@stdlib/stats/base/dmeanvar/README.md index c01ebd1bc0bd..fd61fc07abbd 100644 --- a/lib/node_modules/@stdlib/stats/base/dmeanvar/README.md +++ b/lib/node_modules/@stdlib/stats/base/dmeanvar/README.md @@ -30,10 +30,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -41,10 +45,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -52,10 +60,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -63,10 +75,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dmeanvarpn/README.md b/lib/node_modules/@stdlib/stats/base/dmeanvarpn/README.md index f57d1d317295..60abf2661988 100644 --- a/lib/node_modules/@stdlib/stats/base/dmeanvarpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dmeanvarpn/README.md @@ -30,10 +30,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -41,10 +45,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -52,10 +60,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -63,10 +75,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dmeanwd/README.md b/lib/node_modules/@stdlib/stats/base/dmeanwd/README.md index 9d5616c39f5a..323b3a45fcdb 100644 --- a/lib/node_modules/@stdlib/stats/base/dmeanwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/dmeanwd/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanmean/README.md b/lib/node_modules/@stdlib/stats/base/dnanmean/README.md index ff8f27ec348e..17ce4a303f3a 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanmean/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanmean/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanmeanors/README.md b/lib/node_modules/@stdlib/stats/base/dnanmeanors/README.md index 4e50129228de..18124db12981 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanmeanors/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanmeanors/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanmeanpn/README.md b/lib/node_modules/@stdlib/stats/base/dnanmeanpn/README.md index 98774005a2f9..9a9a2344a962 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanmeanpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanmeanpn/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanmeanpw/README.md b/lib/node_modules/@stdlib/stats/base/dnanmeanpw/README.md index 453ce40ae9ed..64b1e5cc791c 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanmeanpw/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanmeanpw/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanmeanwd/README.md b/lib/node_modules/@stdlib/stats/base/dnanmeanwd/README.md index 67de0d64460a..8392e1999459 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanmeanwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanmeanwd/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanstdev/README.md b/lib/node_modules/@stdlib/stats/base/dnanstdev/README.md index 6fd6ebb1190a..71b7adbac231 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanstdev/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanstdev/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanstdevch/README.md b/lib/node_modules/@stdlib/stats/base/dnanstdevch/README.md index bcbbc13012b5..485302bdc7cc 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanstdevch/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanstdevch/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanstdevpn/README.md b/lib/node_modules/@stdlib/stats/base/dnanstdevpn/README.md index 52c9f5436a1d..be1b74321aff 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanstdevpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanstdevpn/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanstdevtk/README.md b/lib/node_modules/@stdlib/stats/base/dnanstdevtk/README.md index 348934c009b6..677899ab93e4 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanstdevtk/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanstdevtk/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanstdevwd/README.md b/lib/node_modules/@stdlib/stats/base/dnanstdevwd/README.md index 857e70fc42ad..7a2d1b8b66eb 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanstdevwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanstdevwd/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanstdevyc/README.md b/lib/node_modules/@stdlib/stats/base/dnanstdevyc/README.md index 5f47641bd2d2..566b1f30d7af 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanstdevyc/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanstdevyc/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanvariance/README.md b/lib/node_modules/@stdlib/stats/base/dnanvariance/README.md index 7dfbcf2f7041..9b125e03d9c2 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanvariance/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanvariance/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanvariancech/README.md b/lib/node_modules/@stdlib/stats/base/dnanvariancech/README.md index 807470748078..0deb506a3836 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanvariancech/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanvariancech/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanvariancepn/README.md b/lib/node_modules/@stdlib/stats/base/dnanvariancepn/README.md index 88c4d40fc288..a096d2bcc40d 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanvariancepn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanvariancepn/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanvariancetk/README.md b/lib/node_modules/@stdlib/stats/base/dnanvariancetk/README.md index 171de1997759..a180fcd4b753 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanvariancetk/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanvariancetk/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanvariancewd/README.md b/lib/node_modules/@stdlib/stats/base/dnanvariancewd/README.md index 555fe534c503..71a7c2eb6f25 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanvariancewd/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanvariancewd/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dnanvarianceyc/README.md b/lib/node_modules/@stdlib/stats/base/dnanvarianceyc/README.md index 484df0c36676..48d27c59b488 100644 --- a/lib/node_modules/@stdlib/stats/base/dnanvarianceyc/README.md +++ b/lib/node_modules/@stdlib/stats/base/dnanvarianceyc/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsem/README.md b/lib/node_modules/@stdlib/stats/base/dsem/README.md index 92f44e73371e..129b5d6e40b7 100644 --- a/lib/node_modules/@stdlib/stats/base/dsem/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsem/README.md @@ -28,10 +28,14 @@ The [standard error of the mean][standard-error] of a finite size sample of size -
+```math +\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} +``` + + @@ -41,10 +45,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +\sigma_{\bar{x}} \approx \frac{s}{\sqrt{n}} +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsemch/README.md b/lib/node_modules/@stdlib/stats/base/dsemch/README.md index d7225f1a3ffb..041f4cca147b 100644 --- a/lib/node_modules/@stdlib/stats/base/dsemch/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsemch/README.md @@ -28,10 +28,14 @@ The [standard error of the mean][standard-error] of a finite size sample of size -
+```math +\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} +``` + + @@ -41,10 +45,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +\sigma_{\bar{x}} \approx \frac{s}{\sqrt{n}} +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsempn/README.md b/lib/node_modules/@stdlib/stats/base/dsempn/README.md index e7651d5d4541..28c17d007b31 100644 --- a/lib/node_modules/@stdlib/stats/base/dsempn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsempn/README.md @@ -28,10 +28,14 @@ The [standard error of the mean][standard-error] of a finite size sample of size -
+```math +\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} +``` + + @@ -41,10 +45,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +\sigma_{\bar{x}} \approx \frac{s}{\sqrt{n}} +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsemtk/README.md b/lib/node_modules/@stdlib/stats/base/dsemtk/README.md index d4fb7e67cbf5..ab6c894ee1e7 100644 --- a/lib/node_modules/@stdlib/stats/base/dsemtk/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsemtk/README.md @@ -28,10 +28,14 @@ The [standard error of the mean][standard-error] of a finite size sample of size -
+```math +\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} +``` + + @@ -41,10 +45,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +\sigma_{\bar{x}} \approx \frac{s}{\sqrt{n}} +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsemwd/README.md b/lib/node_modules/@stdlib/stats/base/dsemwd/README.md index 1f22c99c3736..ea94c1ec11a2 100644 --- a/lib/node_modules/@stdlib/stats/base/dsemwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsemwd/README.md @@ -28,10 +28,14 @@ The [standard error of the mean][standard-error] of a finite size sample of size -
+```math +\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} +``` + + @@ -41,10 +45,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +\sigma_{\bar{x}} \approx \frac{s}{\sqrt{n}} +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsemyc/README.md b/lib/node_modules/@stdlib/stats/base/dsemyc/README.md index e5d0c10fbb38..c9cdcc5014b0 100644 --- a/lib/node_modules/@stdlib/stats/base/dsemyc/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsemyc/README.md @@ -28,10 +28,14 @@ The [standard error of the mean][standard-error] of a finite size sample of size -
+```math +\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} +``` + + @@ -41,10 +45,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +\sigma_{\bar{x}} \approx \frac{s}{\sqrt{n}} +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsmean/README.md b/lib/node_modules/@stdlib/stats/base/dsmean/README.md index 940be76cdf67..8343c4b95c04 100644 --- a/lib/node_modules/@stdlib/stats/base/dsmean/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsmean/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsmeanors/README.md b/lib/node_modules/@stdlib/stats/base/dsmeanors/README.md index 3b3081b9affe..47c4ca5ee399 100644 --- a/lib/node_modules/@stdlib/stats/base/dsmeanors/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsmeanors/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsmeanpn/README.md b/lib/node_modules/@stdlib/stats/base/dsmeanpn/README.md index 77a63286c494..53fd8f36ebde 100644 --- a/lib/node_modules/@stdlib/stats/base/dsmeanpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsmeanpn/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsmeanpw/README.md b/lib/node_modules/@stdlib/stats/base/dsmeanpw/README.md index ef8ca7676951..08cb8e5b71c2 100644 --- a/lib/node_modules/@stdlib/stats/base/dsmeanpw/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsmeanpw/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsmeanwd/README.md b/lib/node_modules/@stdlib/stats/base/dsmeanwd/README.md index 4d2aad9b41d9..977729836d8f 100644 --- a/lib/node_modules/@stdlib/stats/base/dsmeanwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsmeanwd/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsnanmean/README.md b/lib/node_modules/@stdlib/stats/base/dsnanmean/README.md index 115282ce0c59..43b8daaa1671 100644 --- a/lib/node_modules/@stdlib/stats/base/dsnanmean/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsnanmean/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsnanmeanors/README.md b/lib/node_modules/@stdlib/stats/base/dsnanmeanors/README.md index 12888501b6e8..2075fa4df919 100644 --- a/lib/node_modules/@stdlib/stats/base/dsnanmeanors/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsnanmeanors/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsnanmeanpn/README.md b/lib/node_modules/@stdlib/stats/base/dsnanmeanpn/README.md index 80998a36dc03..34331e207e4d 100644 --- a/lib/node_modules/@stdlib/stats/base/dsnanmeanpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsnanmeanpn/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsnanmeanwd/README.md b/lib/node_modules/@stdlib/stats/base/dsnanmeanwd/README.md index 1bc366c6b7e3..93d13d5a9f6e 100644 --- a/lib/node_modules/@stdlib/stats/base/dsnanmeanwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsnanmeanwd/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dstdev/README.md b/lib/node_modules/@stdlib/stats/base/dstdev/README.md index 911ed9fd51a7..e0bf39b41633 100644 --- a/lib/node_modules/@stdlib/stats/base/dstdev/README.md +++ b/lib/node_modules/@stdlib/stats/base/dstdev/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dstdevch/README.md b/lib/node_modules/@stdlib/stats/base/dstdevch/README.md index addf4b8e20ce..0e57659268a2 100644 --- a/lib/node_modules/@stdlib/stats/base/dstdevch/README.md +++ b/lib/node_modules/@stdlib/stats/base/dstdevch/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dstdevpn/README.md b/lib/node_modules/@stdlib/stats/base/dstdevpn/README.md index 551ce1a504f8..fc9b1260667a 100644 --- a/lib/node_modules/@stdlib/stats/base/dstdevpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dstdevpn/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dstdevtk/README.md b/lib/node_modules/@stdlib/stats/base/dstdevtk/README.md index 6b86313f2c26..bdaf224d6b67 100644 --- a/lib/node_modules/@stdlib/stats/base/dstdevtk/README.md +++ b/lib/node_modules/@stdlib/stats/base/dstdevtk/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dstdevwd/README.md b/lib/node_modules/@stdlib/stats/base/dstdevwd/README.md index 01e20e21b01d..6c59790179e0 100644 --- a/lib/node_modules/@stdlib/stats/base/dstdevwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/dstdevwd/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dstdevyc/README.md b/lib/node_modules/@stdlib/stats/base/dstdevyc/README.md index ba80fe4b3895..768af0905646 100644 --- a/lib/node_modules/@stdlib/stats/base/dstdevyc/README.md +++ b/lib/node_modules/@stdlib/stats/base/dstdevyc/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsvariance/README.md b/lib/node_modules/@stdlib/stats/base/dsvariance/README.md index c7269eabafb5..d57fb40a07e6 100644 --- a/lib/node_modules/@stdlib/stats/base/dsvariance/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsvariance/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dsvariancepn/README.md b/lib/node_modules/@stdlib/stats/base/dsvariancepn/README.md index a9893b487100..4757d2c3b39b 100644 --- a/lib/node_modules/@stdlib/stats/base/dsvariancepn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dsvariancepn/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dvariance/README.md b/lib/node_modules/@stdlib/stats/base/dvariance/README.md index 5a11002d5e72..44fe52bc6680 100644 --- a/lib/node_modules/@stdlib/stats/base/dvariance/README.md +++ b/lib/node_modules/@stdlib/stats/base/dvariance/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dvariancech/README.md b/lib/node_modules/@stdlib/stats/base/dvariancech/README.md index a13e9604419f..8de7fb0ffa42 100644 --- a/lib/node_modules/@stdlib/stats/base/dvariancech/README.md +++ b/lib/node_modules/@stdlib/stats/base/dvariancech/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dvariancepn/README.md b/lib/node_modules/@stdlib/stats/base/dvariancepn/README.md index 99314b3c5792..a2c83064d151 100644 --- a/lib/node_modules/@stdlib/stats/base/dvariancepn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dvariancepn/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dvariancetk/README.md b/lib/node_modules/@stdlib/stats/base/dvariancetk/README.md index 9573ea5d65e7..548089be3223 100644 --- a/lib/node_modules/@stdlib/stats/base/dvariancetk/README.md +++ b/lib/node_modules/@stdlib/stats/base/dvariancetk/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ After rearranging terms, the population [variance][variance] can be equivalently -
+```math +\sigma^2 = \frac{1}{N}\biggl(\ \sum_{i=0}^{N-1} x_i^2 - \frac{1}{N}\biggl(\ \sum_{i=0}^{N-1} x_i \ \biggr)^2\ \biggr) +``` + + @@ -61,10 +73,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -72,10 +88,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + @@ -83,10 +103,14 @@ Similar to the population [variance][variance], after rearranging terms, the **u -
+```math +s^2 = \frac{1}{n-1}\biggl(\ \sum_{i=0}^{n-1} x_i^2 - \frac{1}{n}\biggl(\ \sum_{i=0}^{n-1} x_i \ \biggr)^2\ \biggr) +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dvariancewd/README.md b/lib/node_modules/@stdlib/stats/base/dvariancewd/README.md index f29778c5862b..9e11e1a8c15f 100644 --- a/lib/node_modules/@stdlib/stats/base/dvariancewd/README.md +++ b/lib/node_modules/@stdlib/stats/base/dvariancewd/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dvarianceyc/README.md b/lib/node_modules/@stdlib/stats/base/dvarianceyc/README.md index 88531013c0d6..ba7635b8d142 100644 --- a/lib/node_modules/@stdlib/stats/base/dvarianceyc/README.md +++ b/lib/node_modules/@stdlib/stats/base/dvarianceyc/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dvarm/README.md b/lib/node_modules/@stdlib/stats/base/dvarm/README.md index 2b487b6fff2f..b0a5e8fbe696 100644 --- a/lib/node_modules/@stdlib/stats/base/dvarm/README.md +++ b/lib/node_modules/@stdlib/stats/base/dvarm/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dvarmpn/README.md b/lib/node_modules/@stdlib/stats/base/dvarmpn/README.md index 5a32e7180fe9..0095e5a671d0 100644 --- a/lib/node_modules/@stdlib/stats/base/dvarmpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/dvarmpn/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/dvarmtk/README.md b/lib/node_modules/@stdlib/stats/base/dvarmtk/README.md index 84a4aeff43eb..0e5c661833ee 100644 --- a/lib/node_modules/@stdlib/stats/base/dvarmtk/README.md +++ b/lib/node_modules/@stdlib/stats/base/dvarmtk/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/mean/README.md b/lib/node_modules/@stdlib/stats/base/mean/README.md index d2d7a05cb562..2b887ff25993 100644 --- a/lib/node_modules/@stdlib/stats/base/mean/README.md +++ b/lib/node_modules/@stdlib/stats/base/mean/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/meankbn/README.md b/lib/node_modules/@stdlib/stats/base/meankbn/README.md index 7447e6fd0801..ef4eeed9e605 100644 --- a/lib/node_modules/@stdlib/stats/base/meankbn/README.md +++ b/lib/node_modules/@stdlib/stats/base/meankbn/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/meankbn2/README.md b/lib/node_modules/@stdlib/stats/base/meankbn2/README.md index 1ea506a91ce1..52ca1aa12dda 100644 --- a/lib/node_modules/@stdlib/stats/base/meankbn2/README.md +++ b/lib/node_modules/@stdlib/stats/base/meankbn2/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/meanors/README.md b/lib/node_modules/@stdlib/stats/base/meanors/README.md index 936b16ed5968..26406d5cea17 100644 --- a/lib/node_modules/@stdlib/stats/base/meanors/README.md +++ b/lib/node_modules/@stdlib/stats/base/meanors/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/meanpn/README.md b/lib/node_modules/@stdlib/stats/base/meanpn/README.md index 1a2b534438dd..2d6091bd86d7 100644 --- a/lib/node_modules/@stdlib/stats/base/meanpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/meanpn/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/meanpw/README.md b/lib/node_modules/@stdlib/stats/base/meanpw/README.md index e84812c2a7a1..25e62e162631 100644 --- a/lib/node_modules/@stdlib/stats/base/meanpw/README.md +++ b/lib/node_modules/@stdlib/stats/base/meanpw/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/meanwd/README.md b/lib/node_modules/@stdlib/stats/base/meanwd/README.md index f1acb0d92b34..80008c4df7dd 100644 --- a/lib/node_modules/@stdlib/stats/base/meanwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/meanwd/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanmean/README.md b/lib/node_modules/@stdlib/stats/base/nanmean/README.md index 6ab2089dd7c7..a13ed07dd001 100644 --- a/lib/node_modules/@stdlib/stats/base/nanmean/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanmean/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanmeanors/README.md b/lib/node_modules/@stdlib/stats/base/nanmeanors/README.md index dc8c18fef4ef..505e77d0369d 100644 --- a/lib/node_modules/@stdlib/stats/base/nanmeanors/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanmeanors/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanmeanpn/README.md b/lib/node_modules/@stdlib/stats/base/nanmeanpn/README.md index 5c7fe5cdc08c..4a48a17f883d 100644 --- a/lib/node_modules/@stdlib/stats/base/nanmeanpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanmeanpn/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanmeanwd/README.md b/lib/node_modules/@stdlib/stats/base/nanmeanwd/README.md index 15dbc39e3177..e9002dab41f0 100644 --- a/lib/node_modules/@stdlib/stats/base/nanmeanwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanmeanwd/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanstdev/README.md b/lib/node_modules/@stdlib/stats/base/nanstdev/README.md index a3eb59d6f81c..cd869ae063b8 100644 --- a/lib/node_modules/@stdlib/stats/base/nanstdev/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanstdev/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanstdevch/README.md b/lib/node_modules/@stdlib/stats/base/nanstdevch/README.md index 52c83b5ba433..aa8abc3a0653 100644 --- a/lib/node_modules/@stdlib/stats/base/nanstdevch/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanstdevch/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanstdevpn/README.md b/lib/node_modules/@stdlib/stats/base/nanstdevpn/README.md index f5f25a1ee2c1..d4d071c1e6b7 100644 --- a/lib/node_modules/@stdlib/stats/base/nanstdevpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanstdevpn/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanstdevtk/README.md b/lib/node_modules/@stdlib/stats/base/nanstdevtk/README.md index 3e2be4c5b9c2..7c4d7a997f7f 100644 --- a/lib/node_modules/@stdlib/stats/base/nanstdevtk/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanstdevtk/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanstdevwd/README.md b/lib/node_modules/@stdlib/stats/base/nanstdevwd/README.md index e9a501bccc31..2c091fd267b7 100644 --- a/lib/node_modules/@stdlib/stats/base/nanstdevwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanstdevwd/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanstdevyc/README.md b/lib/node_modules/@stdlib/stats/base/nanstdevyc/README.md index e77ec76eeb56..035d8a165c74 100644 --- a/lib/node_modules/@stdlib/stats/base/nanstdevyc/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanstdevyc/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanvariance/README.md b/lib/node_modules/@stdlib/stats/base/nanvariance/README.md index f27beb45f077..1cf829ea218a 100644 --- a/lib/node_modules/@stdlib/stats/base/nanvariance/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanvariance/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanvariancech/README.md b/lib/node_modules/@stdlib/stats/base/nanvariancech/README.md index 5206ba19d74d..479cf68094bd 100644 --- a/lib/node_modules/@stdlib/stats/base/nanvariancech/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanvariancech/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanvariancepn/README.md b/lib/node_modules/@stdlib/stats/base/nanvariancepn/README.md index d851725f79c1..fbefab955fef 100644 --- a/lib/node_modules/@stdlib/stats/base/nanvariancepn/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanvariancepn/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanvariancetk/README.md b/lib/node_modules/@stdlib/stats/base/nanvariancetk/README.md index 20917f4d3a1a..48ef01f74076 100644 --- a/lib/node_modules/@stdlib/stats/base/nanvariancetk/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanvariancetk/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanvariancewd/README.md b/lib/node_modules/@stdlib/stats/base/nanvariancewd/README.md index cdd8e5c823f7..35df01d49a2b 100644 --- a/lib/node_modules/@stdlib/stats/base/nanvariancewd/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanvariancewd/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/nanvarianceyc/README.md b/lib/node_modules/@stdlib/stats/base/nanvarianceyc/README.md index 8a566c043126..f49d0ef84510 100644 --- a/lib/node_modules/@stdlib/stats/base/nanvarianceyc/README.md +++ b/lib/node_modules/@stdlib/stats/base/nanvarianceyc/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/sdsmean/README.md b/lib/node_modules/@stdlib/stats/base/sdsmean/README.md index 75d5002da676..c7a74022dd77 100644 --- a/lib/node_modules/@stdlib/stats/base/sdsmean/README.md +++ b/lib/node_modules/@stdlib/stats/base/sdsmean/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/sdsmeanors/README.md b/lib/node_modules/@stdlib/stats/base/sdsmeanors/README.md index af20345b4cec..b6735cf153ed 100644 --- a/lib/node_modules/@stdlib/stats/base/sdsmeanors/README.md +++ b/lib/node_modules/@stdlib/stats/base/sdsmeanors/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/sdsnanmean/README.md b/lib/node_modules/@stdlib/stats/base/sdsnanmean/README.md index 0096eebcc647..cc496e85f3da 100644 --- a/lib/node_modules/@stdlib/stats/base/sdsnanmean/README.md +++ b/lib/node_modules/@stdlib/stats/base/sdsnanmean/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/sdsnanmeanors/README.md b/lib/node_modules/@stdlib/stats/base/sdsnanmeanors/README.md index 2c03d9f58300..4e3b564c181a 100644 --- a/lib/node_modules/@stdlib/stats/base/sdsnanmeanors/README.md +++ b/lib/node_modules/@stdlib/stats/base/sdsnanmeanors/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/smean/README.md b/lib/node_modules/@stdlib/stats/base/smean/README.md index 2a23f45b9a0b..bc851c0b90ee 100644 --- a/lib/node_modules/@stdlib/stats/base/smean/README.md +++ b/lib/node_modules/@stdlib/stats/base/smean/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/smeankbn/README.md b/lib/node_modules/@stdlib/stats/base/smeankbn/README.md index 47275b5b554f..dabfac1a840d 100644 --- a/lib/node_modules/@stdlib/stats/base/smeankbn/README.md +++ b/lib/node_modules/@stdlib/stats/base/smeankbn/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/smeankbn2/README.md b/lib/node_modules/@stdlib/stats/base/smeankbn2/README.md index bf996e64f6be..4dda1cd483d5 100644 --- a/lib/node_modules/@stdlib/stats/base/smeankbn2/README.md +++ b/lib/node_modules/@stdlib/stats/base/smeankbn2/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/smeanli/README.md b/lib/node_modules/@stdlib/stats/base/smeanli/README.md index 518c2515eb82..a784871351ac 100644 --- a/lib/node_modules/@stdlib/stats/base/smeanli/README.md +++ b/lib/node_modules/@stdlib/stats/base/smeanli/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/smeanlipw/README.md b/lib/node_modules/@stdlib/stats/base/smeanlipw/README.md index a098877e40e9..57a3fe2d765b 100644 --- a/lib/node_modules/@stdlib/stats/base/smeanlipw/README.md +++ b/lib/node_modules/@stdlib/stats/base/smeanlipw/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/smeanors/README.md b/lib/node_modules/@stdlib/stats/base/smeanors/README.md index c195903c2b0b..562c8b729a38 100644 --- a/lib/node_modules/@stdlib/stats/base/smeanors/README.md +++ b/lib/node_modules/@stdlib/stats/base/smeanors/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/smeanpn/README.md b/lib/node_modules/@stdlib/stats/base/smeanpn/README.md index f7297f0c56d8..fff97c6bbfc4 100644 --- a/lib/node_modules/@stdlib/stats/base/smeanpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/smeanpn/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/smeanpw/README.md b/lib/node_modules/@stdlib/stats/base/smeanpw/README.md index 1aa5002d0e7e..299dbd72be49 100644 --- a/lib/node_modules/@stdlib/stats/base/smeanpw/README.md +++ b/lib/node_modules/@stdlib/stats/base/smeanpw/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/smeanwd/README.md b/lib/node_modules/@stdlib/stats/base/smeanwd/README.md index cd746291c8c9..a66534f117e4 100644 --- a/lib/node_modules/@stdlib/stats/base/smeanwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/smeanwd/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanmean/README.md b/lib/node_modules/@stdlib/stats/base/snanmean/README.md index 89ec8990ffca..bcff56d4ee58 100644 --- a/lib/node_modules/@stdlib/stats/base/snanmean/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanmean/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanmeanors/README.md b/lib/node_modules/@stdlib/stats/base/snanmeanors/README.md index 9e868f7cca8e..fcb3edbeca24 100644 --- a/lib/node_modules/@stdlib/stats/base/snanmeanors/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanmeanors/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanmeanpn/README.md b/lib/node_modules/@stdlib/stats/base/snanmeanpn/README.md index bc34ca783798..a99794c0331f 100644 --- a/lib/node_modules/@stdlib/stats/base/snanmeanpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanmeanpn/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanmeanwd/README.md b/lib/node_modules/@stdlib/stats/base/snanmeanwd/README.md index 3510a343f990..0ba6cc043fab 100644 --- a/lib/node_modules/@stdlib/stats/base/snanmeanwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanmeanwd/README.md @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as -
+```math +\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanstdev/README.md b/lib/node_modules/@stdlib/stats/base/snanstdev/README.md index 970730f2e694..be2fd408d6c0 100644 --- a/lib/node_modules/@stdlib/stats/base/snanstdev/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanstdev/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanstdevch/README.md b/lib/node_modules/@stdlib/stats/base/snanstdevch/README.md index 4d08b6eb9466..cffeee917341 100644 --- a/lib/node_modules/@stdlib/stats/base/snanstdevch/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanstdevch/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanstdevpn/README.md b/lib/node_modules/@stdlib/stats/base/snanstdevpn/README.md index b9dbaccc593c..490a7b3456df 100644 --- a/lib/node_modules/@stdlib/stats/base/snanstdevpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanstdevpn/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanstdevtk/README.md b/lib/node_modules/@stdlib/stats/base/snanstdevtk/README.md index 0e7b4ec2938e..4a8229b743f2 100644 --- a/lib/node_modules/@stdlib/stats/base/snanstdevtk/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanstdevtk/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanstdevwd/README.md b/lib/node_modules/@stdlib/stats/base/snanstdevwd/README.md index c00b8c7f909a..15b39df6f55b 100644 --- a/lib/node_modules/@stdlib/stats/base/snanstdevwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanstdevwd/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanstdevyc/README.md b/lib/node_modules/@stdlib/stats/base/snanstdevyc/README.md index 8e76408fc801..358b8299fcff 100644 --- a/lib/node_modules/@stdlib/stats/base/snanstdevyc/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanstdevyc/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanvariance/README.md b/lib/node_modules/@stdlib/stats/base/snanvariance/README.md index e5f2850b3171..3e152a17494c 100644 --- a/lib/node_modules/@stdlib/stats/base/snanvariance/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanvariance/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanvariancech/README.md b/lib/node_modules/@stdlib/stats/base/snanvariancech/README.md index 7f05a5544fd2..ddfb129489e7 100644 --- a/lib/node_modules/@stdlib/stats/base/snanvariancech/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanvariancech/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanvariancepn/README.md b/lib/node_modules/@stdlib/stats/base/snanvariancepn/README.md index d0d108d969f8..5dc2b610a058 100644 --- a/lib/node_modules/@stdlib/stats/base/snanvariancepn/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanvariancepn/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanvariancetk/README.md b/lib/node_modules/@stdlib/stats/base/snanvariancetk/README.md index fd979fb1e6c8..1a6d06d92acb 100644 --- a/lib/node_modules/@stdlib/stats/base/snanvariancetk/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanvariancetk/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanvariancewd/README.md b/lib/node_modules/@stdlib/stats/base/snanvariancewd/README.md index 27f2796b7443..3bfb237d57e9 100644 --- a/lib/node_modules/@stdlib/stats/base/snanvariancewd/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanvariancewd/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/snanvarianceyc/README.md b/lib/node_modules/@stdlib/stats/base/snanvarianceyc/README.md index b67670eb49fb..b7ce9c93311b 100644 --- a/lib/node_modules/@stdlib/stats/base/snanvarianceyc/README.md +++ b/lib/node_modules/@stdlib/stats/base/snanvarianceyc/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/sstdev/README.md b/lib/node_modules/@stdlib/stats/base/sstdev/README.md index 7a8ca8f50a89..1c296336602c 100644 --- a/lib/node_modules/@stdlib/stats/base/sstdev/README.md +++ b/lib/node_modules/@stdlib/stats/base/sstdev/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/sstdevch/README.md b/lib/node_modules/@stdlib/stats/base/sstdevch/README.md index 249a67337d96..24a8bf737b56 100644 --- a/lib/node_modules/@stdlib/stats/base/sstdevch/README.md +++ b/lib/node_modules/@stdlib/stats/base/sstdevch/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/sstdevpn/README.md b/lib/node_modules/@stdlib/stats/base/sstdevpn/README.md index 2a7e08622ac5..30b5db737050 100644 --- a/lib/node_modules/@stdlib/stats/base/sstdevpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/sstdevpn/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/sstdevtk/README.md b/lib/node_modules/@stdlib/stats/base/sstdevtk/README.md index 3df4eaaf21af..86674e29aff4 100644 --- a/lib/node_modules/@stdlib/stats/base/sstdevtk/README.md +++ b/lib/node_modules/@stdlib/stats/base/sstdevtk/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/sstdevwd/README.md b/lib/node_modules/@stdlib/stats/base/sstdevwd/README.md index d1041e57b441..e7fbf8a54a40 100644 --- a/lib/node_modules/@stdlib/stats/base/sstdevwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/sstdevwd/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/sstdevyc/README.md b/lib/node_modules/@stdlib/stats/base/sstdevyc/README.md index f027224e41e5..5907eff1f536 100644 --- a/lib/node_modules/@stdlib/stats/base/sstdevyc/README.md +++ b/lib/node_modules/@stdlib/stats/base/sstdevyc/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/stdev/README.md b/lib/node_modules/@stdlib/stats/base/stdev/README.md index f3f6e4476796..1ddf01b10995 100644 --- a/lib/node_modules/@stdlib/stats/base/stdev/README.md +++ b/lib/node_modules/@stdlib/stats/base/stdev/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + @@ -234,10 +250,6 @@ console.log( v ); [mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray -[@stdlib/stats/base/dstdev]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dstdev - -[@stdlib/stats/base/sstdev]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/sstdev - [@stdlib/stats/base/dstdev]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/stats/base/dstdev diff --git a/lib/node_modules/@stdlib/stats/base/stdevch/README.md b/lib/node_modules/@stdlib/stats/base/stdevch/README.md index 27a0a025b6f8..ea75e4bdb1b4 100644 --- a/lib/node_modules/@stdlib/stats/base/stdevch/README.md +++ b/lib/node_modules/@stdlib/stats/base/stdevch/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/stdevpn/README.md b/lib/node_modules/@stdlib/stats/base/stdevpn/README.md index 91094e0b6a32..83655d3abc52 100644 --- a/lib/node_modules/@stdlib/stats/base/stdevpn/README.md +++ b/lib/node_modules/@stdlib/stats/base/stdevpn/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/stdevtk/README.md b/lib/node_modules/@stdlib/stats/base/stdevtk/README.md index d5efd911c0f5..927988055cd5 100644 --- a/lib/node_modules/@stdlib/stats/base/stdevtk/README.md +++ b/lib/node_modules/@stdlib/stats/base/stdevtk/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/stdevwd/README.md b/lib/node_modules/@stdlib/stats/base/stdevwd/README.md index 52a5525b6c23..cf40262beb09 100644 --- a/lib/node_modules/@stdlib/stats/base/stdevwd/README.md +++ b/lib/node_modules/@stdlib/stats/base/stdevwd/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/stdevyc/README.md b/lib/node_modules/@stdlib/stats/base/stdevyc/README.md index 400bb07bd266..2ddfad8004fa 100644 --- a/lib/node_modules/@stdlib/stats/base/stdevyc/README.md +++ b/lib/node_modules/@stdlib/stats/base/stdevyc/README.md @@ -28,10 +28,14 @@ The population [standard deviation][standard-deviation] of a finite size populat -
+```math +\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [standard deviation][standard -
+```math +s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/svariance/README.md b/lib/node_modules/@stdlib/stats/base/svariance/README.md index 5352e22e3862..fa71a5a99ffc 100644 --- a/lib/node_modules/@stdlib/stats/base/svariance/README.md +++ b/lib/node_modules/@stdlib/stats/base/svariance/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/svariancech/README.md b/lib/node_modules/@stdlib/stats/base/svariancech/README.md index 0822a3daae67..5ce6463a8869 100644 --- a/lib/node_modules/@stdlib/stats/base/svariancech/README.md +++ b/lib/node_modules/@stdlib/stats/base/svariancech/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/svariancepn/README.md b/lib/node_modules/@stdlib/stats/base/svariancepn/README.md index fb82969fe618..2e8f965b47d8 100644 --- a/lib/node_modules/@stdlib/stats/base/svariancepn/README.md +++ b/lib/node_modules/@stdlib/stats/base/svariancepn/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/svariancetk/README.md b/lib/node_modules/@stdlib/stats/base/svariancetk/README.md index 2d7de820839f..4b894f4dc155 100644 --- a/lib/node_modules/@stdlib/stats/base/svariancetk/README.md +++ b/lib/node_modules/@stdlib/stats/base/svariancetk/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ After rearranging terms, the population [variance][variance] can be equivalently -
+```math +\sigma^2 = \frac{1}{N}\biggl(\ \sum_{i=0}^{N-1} x_i^2 - \frac{1}{N}\biggl(\ \sum_{i=0}^{N-1} x_i \ \biggr)^2\ \biggr) +``` + + @@ -61,10 +73,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -72,10 +88,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + @@ -83,10 +103,14 @@ Similar to the population [variance][variance], after rearranging terms, the **u -
+```math +s^2 = \frac{1}{n-1}\biggl(\ \sum_{i=0}^{n-1} x_i^2 - \frac{1}{n}\biggl(\ \sum_{i=0}^{n-1} x_i \ \biggr)^2\ \biggr) +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/svariancewd/README.md b/lib/node_modules/@stdlib/stats/base/svariancewd/README.md index a085b0227813..3c0591778073 100644 --- a/lib/node_modules/@stdlib/stats/base/svariancewd/README.md +++ b/lib/node_modules/@stdlib/stats/base/svariancewd/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/svarianceyc/README.md b/lib/node_modules/@stdlib/stats/base/svarianceyc/README.md index 5b537af8f704..b10f32fc6bbb 100644 --- a/lib/node_modules/@stdlib/stats/base/svarianceyc/README.md +++ b/lib/node_modules/@stdlib/stats/base/svarianceyc/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/variance/README.md b/lib/node_modules/@stdlib/stats/base/variance/README.md index 6cce04b3940e..916d85c4a011 100644 --- a/lib/node_modules/@stdlib/stats/base/variance/README.md +++ b/lib/node_modules/@stdlib/stats/base/variance/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/variancech/README.md b/lib/node_modules/@stdlib/stats/base/variancech/README.md index 5d38f7ad60bc..0ea0e96fc214 100644 --- a/lib/node_modules/@stdlib/stats/base/variancech/README.md +++ b/lib/node_modules/@stdlib/stats/base/variancech/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/variancepn/README.md b/lib/node_modules/@stdlib/stats/base/variancepn/README.md index 476d5fb473ea..5775585ee772 100644 --- a/lib/node_modules/@stdlib/stats/base/variancepn/README.md +++ b/lib/node_modules/@stdlib/stats/base/variancepn/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/variancetk/README.md b/lib/node_modules/@stdlib/stats/base/variancetk/README.md index 117626916805..6d7e2c24e243 100644 --- a/lib/node_modules/@stdlib/stats/base/variancetk/README.md +++ b/lib/node_modules/@stdlib/stats/base/variancetk/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/variancewd/README.md b/lib/node_modules/@stdlib/stats/base/variancewd/README.md index 5ee63e47a0a1..636deff359a0 100644 --- a/lib/node_modules/@stdlib/stats/base/variancewd/README.md +++ b/lib/node_modules/@stdlib/stats/base/variancewd/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + + diff --git a/lib/node_modules/@stdlib/stats/base/varianceyc/README.md b/lib/node_modules/@stdlib/stats/base/varianceyc/README.md index 46a80625d67b..aa2f84f74d2f 100644 --- a/lib/node_modules/@stdlib/stats/base/varianceyc/README.md +++ b/lib/node_modules/@stdlib/stats/base/varianceyc/README.md @@ -28,10 +28,14 @@ The population [variance][variance] of a finite size population of size `N` is g -
+```math +\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2 +``` + + @@ -39,10 +43,14 @@ where the population mean is given by -
+```math +\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i +``` + + @@ -50,10 +58,14 @@ Often in the analysis of data, the true population [variance][variance] is not k -
+```math +s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 +``` + + @@ -61,10 +73,14 @@ where the sample mean is given by -
+```math +\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i +``` + +