DOC: sample variance -> population variance

[kwhkim]

Pandas version checks

• I have checked that the issue still exists on the latest versions of the docs on main here

Location of the documentation

https://pandas.pydata.org/docs/dev/user_guide/gotchas.html

Documentation problem

Differences with NumPy
For Series and DataFrame objects, var() normalizes by
N-1 to produce unbiased estimates of the sample variance, while NumPy’s numpy.var() normalizes by N, which measures the variance of the sample.

"unbiased estimates of the sample variance" needs to be corrected to 'the population variance'

Suggested fix for documentation

"unbiased estimates of the sample variance" needs to be corrected to 'the population variance'

[phofl]

Could you elaborate why you would make this change?

[kwhkim]

https://en.wikipedia.org/wiki/Bias_of_an_estimator

note that sample variance can be either biased or unbiased.

Note that the usual definition of sample variance is

and this is an unbiased estimator of the population variance.

The phrase above is quoted as it is in wikipedia. $S^2$ is a random variable so it is called estimator. If we have concrete numbers and calculated using the same formula, the result should be called estimate.

[phofl]

Thanks, would you be interested in submitting a pr?

[kwhkim]

sure

[kwhkim]

@jreback sorry this pull request is for issue #46440. Would you help me move this PR to that issue? I thought trailing (#...) would be sufficient but it appears not.