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docs: render equations via math code blocks
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Planeshifter committed Mar 8, 2023
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8 changes: 6 additions & 2 deletions lib/node_modules/@stdlib/stats/base/dmean/README.md
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Expand Up @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as

<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
```math
\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bc3f9a977a19bdac15d08515d55073e20ad38e9e/lib/node_modules/@stdlib/stats/base/dmean/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

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8 changes: 6 additions & 2 deletions lib/node_modules/@stdlib/stats/base/dmeankbn/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as

<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
```math
\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@195c6d0df4074a7fb40f55cc6bc541f7b70125e7/lib/node_modules/@stdlib/stats/base/dmeankbn/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

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8 changes: 6 additions & 2 deletions lib/node_modules/@stdlib/stats/base/dmeankbn2/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as

<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
```math
\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@4bf02936365dcd2e9d3cbd3d606450bc9646d382/lib/node_modules/@stdlib/stats/base/dmeankbn2/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

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8 changes: 6 additions & 2 deletions lib/node_modules/@stdlib/stats/base/dmeanli/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as

<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
```math
\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@2f444e66f5cd85766019efeaf24447d1e0f1a491/lib/node_modules/@stdlib/stats/base/dmeanli/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

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8 changes: 6 additions & 2 deletions lib/node_modules/@stdlib/stats/base/dmeanlipw/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as

<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
```math
\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@4415a930fcdcfd8c5ff6a8781a93d88b40ab0e18/lib/node_modules/@stdlib/stats/base/dmeanlipw/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

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8 changes: 6 additions & 2 deletions lib/node_modules/@stdlib/stats/base/dmeanors/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as

<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
```math
\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@31813f0075e020c41f607780a0a8646db7d050fc/lib/node_modules/@stdlib/stats/base/dmeanors/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

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8 changes: 6 additions & 2 deletions lib/node_modules/@stdlib/stats/base/dmeanpn/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as

<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
```math
\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d13eec599263c9a3b3e4b458e5f79182459edeed/lib/node_modules/@stdlib/stats/base/dmeanpn/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

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8 changes: 6 additions & 2 deletions lib/node_modules/@stdlib/stats/base/dmeanpw/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -28,10 +28,14 @@ The [arithmetic mean][arithmetic-mean] is defined as

<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
```math
\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@656f7f68149fb4a1b69495608fadfc54b1248e80/lib/node_modules/@stdlib/stats/base/dmeanpw/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

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32 changes: 24 additions & 8 deletions lib/node_modules/@stdlib/stats/base/dmeanstdev/README.md
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Expand Up @@ -30,43 +30,59 @@ The population [standard deviation][standard-deviation] of a finite size populat

<!-- <equation class="equation" label="eq:population_standard_deviation" align="center" raw="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" alt="Equation for the population standard deviation."> -->

<div class="equation" align="center" data-raw-text="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" data-equation="eq:population_standard_deviation">
```math
\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}
```

<!-- <div class="equation" align="center" data-raw-text="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" data-equation="eq:population_standard_deviation">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@fc1d35912f15aaa6bfb58aadc07a842b1239c98c/lib/node_modules/@stdlib/stats/base/dmeanstdev/docs/img/equation_population_standard_deviation.svg" alt="Equation for the population standard deviation.">
<br>
</div>
</div> -->

<!-- </equation> -->

where the population mean is given by

<!-- <equation class="equation" label="eq:population_mean" align="center" raw="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" alt="Equation for the population mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" data-equation="eq:population_mean">
```math
\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" data-equation="eq:population_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@fc1d35912f15aaa6bfb58aadc07a842b1239c98c/lib/node_modules/@stdlib/stats/base/dmeanstdev/docs/img/equation_population_mean.svg" alt="Equation for the population mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

Often in the analysis of data, the true population [standard deviation][standard-deviation] is not known _a priori_ and must be estimated from a sample drawn from the population distribution. If one attempts to use the formula for the population [standard deviation][standard-deviation], the result is biased and yields an **uncorrected sample standard deviation**. To compute a **corrected sample standard deviation** for a sample of size `n`,

<!-- <equation class="equation" label="eq:corrected_sample_standard_deviation" align="center" raw="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" alt="Equation for computing a corrected sample standard deviation."> -->

<div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" data-equation="eq:corrected_sample_standard_deviation">
```math
s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}
```

<!-- <div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" data-equation="eq:corrected_sample_standard_deviation">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@fc1d35912f15aaa6bfb58aadc07a842b1239c98c/lib/node_modules/@stdlib/stats/base/dmeanstdev/docs/img/equation_corrected_sample_standard_deviation.svg" alt="Equation for computing a corrected sample standard deviation.">
<br>
</div>
</div> -->

<!-- </equation> -->

where the sample mean is given by

<!-- <equation class="equation" label="eq:sample_mean" align="center" raw="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the sample mean."> -->

<div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:sample_mean">
```math
\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:sample_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@fc1d35912f15aaa6bfb58aadc07a842b1239c98c/lib/node_modules/@stdlib/stats/base/dmeanstdev/docs/img/equation_sample_mean.svg" alt="Equation for the sample mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

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32 changes: 24 additions & 8 deletions lib/node_modules/@stdlib/stats/base/dmeanstdevpn/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -30,43 +30,59 @@ The population [standard deviation][standard-deviation] of a finite size populat

<!-- <equation class="equation" label="eq:population_standard_deviation" align="center" raw="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" alt="Equation for the population standard deviation."> -->

<div class="equation" align="center" data-raw-text="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" data-equation="eq:population_standard_deviation">
```math
\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}
```

<!-- <div class="equation" align="center" data-raw-text="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" data-equation="eq:population_standard_deviation">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@8467ec3de1244d48205fbf95404ac53f957b4c5b/lib/node_modules/@stdlib/stats/base/dmeanstdevpn/docs/img/equation_population_standard_deviation.svg" alt="Equation for the population standard deviation.">
<br>
</div>
</div> -->

<!-- </equation> -->

where the population mean is given by

<!-- <equation class="equation" label="eq:population_mean" align="center" raw="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" alt="Equation for the population mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" data-equation="eq:population_mean">
```math
\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" data-equation="eq:population_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@8467ec3de1244d48205fbf95404ac53f957b4c5b/lib/node_modules/@stdlib/stats/base/dmeanstdevpn/docs/img/equation_population_mean.svg" alt="Equation for the population mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

Often in the analysis of data, the true population [standard deviation][standard-deviation] is not known _a priori_ and must be estimated from a sample drawn from the population distribution. If one attempts to use the formula for the population [standard deviation][standard-deviation], the result is biased and yields an **uncorrected sample standard deviation**. To compute a **corrected sample standard deviation** for a sample of size `n`,

<!-- <equation class="equation" label="eq:corrected_sample_standard_deviation" align="center" raw="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" alt="Equation for computing a corrected sample standard deviation."> -->

<div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" data-equation="eq:corrected_sample_standard_deviation">
```math
s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}
```

<!-- <div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" data-equation="eq:corrected_sample_standard_deviation">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@8467ec3de1244d48205fbf95404ac53f957b4c5b/lib/node_modules/@stdlib/stats/base/dmeanstdevpn/docs/img/equation_corrected_sample_standard_deviation.svg" alt="Equation for computing a corrected sample standard deviation.">
<br>
</div>
</div> -->

<!-- </equation> -->

where the sample mean is given by

<!-- <equation class="equation" label="eq:sample_mean" align="center" raw="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the sample mean."> -->

<div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:sample_mean">
```math
\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:sample_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@8467ec3de1244d48205fbf95404ac53f957b4c5b/lib/node_modules/@stdlib/stats/base/dmeanstdevpn/docs/img/equation_sample_mean.svg" alt="Equation for the sample mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

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32 changes: 24 additions & 8 deletions lib/node_modules/@stdlib/stats/base/dmeanvar/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -30,43 +30,59 @@ The population [variance][variance] of a finite size population of size `N` is g

<!-- <equation class="equation" label="eq:population_variance" align="center" raw="\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2" alt="Equation for the population variance."> -->

<div class="equation" align="center" data-raw-text="\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2" data-equation="eq:population_variance">
```math
\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2
```

<!-- <div class="equation" align="center" data-raw-text="\sigma^2 = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2" data-equation="eq:population_variance">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@f85af87fd916af053698e5c33740948c95161155/lib/node_modules/@stdlib/stats/base/dmeanvar/docs/img/equation_population_variance.svg" alt="Equation for the population variance.">
<br>
</div>
</div> -->

<!-- </equation> -->

where the population mean is given by

<!-- <equation class="equation" label="eq:population_mean" align="center" raw="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" alt="Equation for the population mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" data-equation="eq:population_mean">
```math
\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" data-equation="eq:population_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@f85af87fd916af053698e5c33740948c95161155/lib/node_modules/@stdlib/stats/base/dmeanvar/docs/img/equation_population_mean.svg" alt="Equation for the population mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

Often in the analysis of data, the true population [variance][variance] is not known _a priori_ and must be estimated from a sample drawn from the population distribution. If one attempts to use the formula for the population [variance][variance], the result is biased and yields a **biased sample variance**. To compute an **unbiased sample variance** for a sample of size `n`,

<!-- <equation class="equation" label="eq:unbiased_sample_variance" align="center" raw="s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2" alt="Equation for computing an unbiased sample variance."> -->

<div class="equation" align="center" data-raw-text="s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2" data-equation="eq:unbiased_sample_variance">
```math
s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2
```

<!-- <div class="equation" align="center" data-raw-text="s^2 = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2" data-equation="eq:unbiased_sample_variance">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@f85af87fd916af053698e5c33740948c95161155/lib/node_modules/@stdlib/stats/base/dmeanvar/docs/img/equation_unbiased_sample_variance.svg" alt="Equation for computing an unbiased sample variance.">
<br>
</div>
</div> -->

<!-- </equation> -->

where the sample mean is given by

<!-- <equation class="equation" label="eq:sample_mean" align="center" raw="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the sample mean."> -->

<div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:sample_mean">
```math
\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i
```

<!-- <div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:sample_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@f85af87fd916af053698e5c33740948c95161155/lib/node_modules/@stdlib/stats/base/dmeanvar/docs/img/equation_sample_mean.svg" alt="Equation for the sample mean.">
<br>
</div>
</div> -->

<!-- </equation> -->

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