diff --git a/stdlib/Statistics/src/Statistics.jl b/stdlib/Statistics/src/Statistics.jl
index 19e73e6ab13bf..d16340aaa4d30 100644
--- a/stdlib/Statistics/src/Statistics.jl
+++ b/stdlib/Statistics/src/Statistics.jl
@@ -645,8 +645,8 @@ function corm(x::AbstractVector, mx, y::AbstractVector, my)
 
     @inbounds begin
         # Initialize the accumulators
-        xx = zero(sqrt(abs2(x[1])))
-        yy = zero(sqrt(abs2(y[1])))
+        xx = zero(sqrt(abs2(one(x[1]))))
+        yy = zero(sqrt(abs2(one(y[1]))))
         xy = zero(x[1] * y[1]')
 
         @simd for i in eachindex(x, y)
diff --git a/stdlib/Statistics/test/runtests.jl b/stdlib/Statistics/test/runtests.jl
index 1f1020970a5ae..fb77c535c299f 100644
--- a/stdlib/Statistics/test/runtests.jl
+++ b/stdlib/Statistics/test/runtests.jl
@@ -460,6 +460,8 @@ end
     @test cor(repeat(1:17, 1, 17))[2] <= 1.0
     @test cor(1:17, 1:17) <= 1.0
     @test cor(1:17, 18:34) <= 1.0
+    @test cor(Any[1, 2], Any[1, 2]) == 1.0
+    @test isnan(cor([0], Int8[81]))
     let tmp = range(1, stop=85, length=100)
         tmp2 = Vector(tmp)
         @test cor(tmp, tmp) <= 1.0