# Combined Variance

Like combined mean, the combined variance or standard deviation can be calculated for different sets of data. Suppose we have two sets of data containing and observations with means and and variances and . If is the combined mean and is the combined variance of observations, then combined variance is given by:

It can be written as:

Here

The combined standard deviation can be calculated by taking the square root of .

__Example__:

For a group of 50 male workers the mean and standard deviation of their daily wages are 63 dollars and 9 dollars respectively. For a group of 40 female workers these values are 54 dollars and 6 dollars respectively. Find the mean and variance of the combined group of 90 workers.

__Solution__:

Here , ,

, ,

Combined Arithmetic Mean

Combined Variance