Pooled Variance Calculator

Formula

The formula to calculate the Pooled Variance (PV) is:

\[ PV = \frac{(n-1) \cdot S1 + (m-1) \cdot S2}{n + m - 2} \]

Where:

\( PV \) is the Pooled Variance
\( n \) is the sample size of the first sample
\( m \) is the sample size of the second sample
\( S1 \) is the sample variance for sample 1
\( S2 \) is the sample variance for sample 2

What is Pooled Variance?

Pooled Variance is a method used in statistics to estimate the variance of two or more different populations when the population means are unknown and the sample sizes are different. It is a weighted average of the variances of the samples, adjusted for the sample sizes.

Example Calculation

Let's assume the following values:

Sample Size of First Sample (n) = 10
Sample Size of Second Sample (m) = 12
Sample Variance of First Sample (S1) = 4.5
Sample Variance of Second Sample (S2) = 5.2

Using the formula to calculate the Pooled Variance:

\[ PV = \frac{(10-1) \cdot 4.5 + (12-1) \cdot 5.2}{10 + 12 - 2} = \frac{40.5 + 57.2}{20} = \frac{97.7}{20} = 4.885 \]

The Pooled Variance is 4.885.