# Pooled Standard Deviation

-

The pooled standard deviation is a quantity that is used to measure the combined standard deviations for two or more samples.

Applications of Pooled Standard Deviation:

1. The pooled standard deviation is calculated whenever we perform two sample T test to check for equality of means.
2. Also, the pooled sample variance is used as an unbiased estimator for the combined population variance for two or more populations.

How to calculate Pooled Standard Deviation?

Suppose you have ‘k’ number of samples with each having standard deviation Si. The formula for pooled standard deviation is given as,

The denominator in the above formula represents the combined degrees of freedom of the test statistic.

Example: Suppose we are given the following data about four samples. Calculate the pooled standard deviation.

Solution: We calculate the quantities required as below,

Substituting all this in the above formula we get,

Pooled Standard Deviation = √(221/17) = √13 = 3.61

Hey 👋

I have always been passionate about statistics and mathematics education.

I created this website to explain mathematical and statistical concepts in the simplest possible manner.

If you've found value from reading my content, feel free to support me in even the smallest way you can.

Previous article
Next article