Question

What is a pooled variance?

Answer 1

Hint: In this problem, we are going to see about pooled variance. We should know in statistics, pooled variance is the method of estimating variance of several different populations when the mean of each population may differ, but one may assume that the variance of each population is the same. The numerical estimate resulting from the use of this method is also called the pooled variance. We can now see it with its formula.

Complete step by step answer:
Here we can see about pooled variance.
We should know in statistics, pooled variance is the method of estimating variance of several different populations when the mean of each population may differ, but one may assume that the variance of each population is the same. The numerical estimate resulting from the use of this method is also called the pooled variance.
It is also called combined variance, composite variance and overall variance.
The formula of pooled variance is,
\[s_{i}^{2}=\dfrac{1}{{{n}_{i}}-1}\sum\limits_{j=1}^{{{n}_{i}}}{{{\left( {{y}_{j}}-{{\overline{y}}_{i}} \right)}^{2}}}\]
Where,
\[s_{i}^{2}\] is sample variance.
\[{{n}_{i}}\] is sample size.
\[{{y}_{i}}\] is \[{{i}^{th}}\] observation.
\[{{y}_{j}}\] sample means of group j.

Note: We should know in statistics, pooled variance is the method of estimating variance of several different populations when the mean of each population may differ, but one may assume that the variance of each population is the same. The numerical estimate resulting from the use of this method is also called the pooled variance.