Question

When I try to execute

StandardDeviation[{1}]

I get an error

StandardDeviation::shlen: "The argument {1} should have at least two elements"

But std of one element is 0, isn’t it?

Answer 1

The standard deviation is commonly defined as the square-root of the unbiased estimator of the variance:

You can easily see that for a single sample, N=1 and you get 0/0, which is undefined. Hence your standard deviation is undefined for a single sample in Mathematica.

Now depending on your conventions, you might want to define a standard deviation for a single sample (either return Null or some value or 0). Here’s an example that shows you how to define it for a single sample.

std[x_List] := Which[(Length[x] == 1), 0, True, StandardDeviation[x]]
std[{1}]
Out[1]= 0