To calculate standard deviation of an array or chunked array.

I would prefer two pass algorithm [1] as a balance of numerical stability and performance. Numpy uses this method to calculate variance [2].
Welford's online algorithm [3] is more stable, but also more expensive in computation.

[1] https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Two-pass_algorithm
[2] https://github.com/numpy/numpy/blob/92ebe1e9a6aeb47a881a1226b08218175776f9ea/numpy/core/_methods.py#L176
[3] https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Welford's_online_algorithm

Reporter: Yibo Cai / @cyb70289
Assignee: Yibo Cai / @cyb70289

Related issues:

• [C++] Incremental Variance, Standard Deviation aggregators (is duplicated by)

PRs and other links:

• GitHub Pull Request #8269

_{Note: This issue was originally created as ARROW-10070. Please see the migration documentation for further details.}