stddev missmatches postgres'

[surister]

Context

In standard deviation calculation there is the Bessel's correction this mean that there are 'two ways' of calculating a deviation: population standard deviation and sample standard deviation, they are very similar but the formula and result varies a little bit.

population stddev

$\sqrt{Σxi - u}\over{N}$

sample stddev

$\sqrt{Σxi - u}\over{N-1}$

The problem.

Our stddev is a population stddev but postgres's is sample stddev so crate and postgres cannot equate stddev results.

you can quickly check this in here and running

crate:
select stddev(a) from unnest([1.0, 2.0, 3.0, 4.0, 5.0]) as a; -> 1.4142135623730951

postgres:
select stddev(a) from unnest(array[1.0, 2.0, 3.0, 4.0, 5.0]) as a; -> 1.5811388300841897

Possible Solutions

Change the implementation of stddev to match postgres' or keep it the same and add stddev_pop and stddev_samp? so we can at least polyfill/overload stddev calls.

Most databases seem to implement both functions in one way or another:
postgres -> stddev (default sample), stddev_pop and stddev_samp
mongodb -> stdDevPop and stdDevSamp
mysql -> sstdev (default pop), stddev_pop, stddev_samp
influxdb -> stddev(..., mode: 'sample' or 'population' = 'sample')

Considered Alternatives

No response

[surister]

This is pretty much also the case with variance, the formula varies depending on sample vs population.

crate:
select variance(a) from unnest([1, 2, 3, 4, 5]) as a; -> 2

postgres:
select variance(a) from unnest(array[1.0, 2.0, 3.0, 4.0, 5.0]) as a; -> 2.5