Standardize the Samples (Compute the z-Score) Given a list of floating point numbers, standardize it.
Details

A list \$x_1,x_2,\ldots,x_n\$ is standardized if the mean of all values is 0, and the standard deviation is 1. One way to compute this is by first computing the mean \$\mu\$ and the standard deviation \$\sigma\$ as
$$ \mu = \frac1n\sum_{i=1}^n x_i \qquad \sigma = \sqrt{\frac{1}{n}\sum_{i=1}^n (x_i -\mu)^2} ,$$
and then computing the standardization by replacing every \$x_i\$ with \$\frac{x_i-\mu}{\sigma}\$.
You can assume that the input contains at least two distinct entries (which implies \$\sigma \neq 0\$).
Note that some implementations use the sample standard deviation, which is not equal to the population standard deviation \$\sigma\$ we are using here.
There is a CW answer for all trivial solutions.

Examples
[1,2,3] -&gt; [-1.224744871391589,0.0,1.224744871391589]
[1,2] -&gt; [-1,1]
[-3,1,4,1,5] -&gt; [-1.6428571428571428,-0.21428571428571433,0.8571428571428572,-0.21428571428571433,1.2142857142857144]

(These examples have been generated with this script.)
R, 51 45 38 37 bytes

Thanks to Giuseppe and J.Doe!


function(x)scale(x)/(1-1/sum(x|1))^.5


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