# Pooled standard deviation

34,202pages on
this wiki

### Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.

Pooled standard deviation is a way to find a better estimate of the true standard deviation given several different samples taken in different circumstances where the mean may vary between samples but the true standard deviation (precision) is assumed to remain the same. It is calculated by

$s_p=\sqrt{\frac{\sum_{i=1}^k((n_i - 1)s_i^2)}{\sum_{i=1}^k(n_i - 1)}}$

or with simpler notation,

$s_p=\sqrt{\frac{(n_1 - 1)s_1^2+(n_2 - 1)s_2^2+\cdots+(n_k - 1)s_k^2)}{n_1+n_2+\cdots+n_k - k}}$

where sp is the pooled standard deviation, ni is the sample size of the i'th sample, si is the standard deviation of the i'th sample, and k is the number of samples being combined. n−1 is used instead of n for the same reason it may be used in calculating standard deviations from samples.