# If I know the mean, standard deviation, and size of sample A and sample B, how do I compute the standard deviation of the union of samples A and B? What if samples A and B are of different sizes?

##### 1 Answer

Sep 12, 2016

Please see below.

#### Explanation:

Let us start with samples with unequal sizes.

Let the mean, standard deviation and size of sample

and mean, standard deviation and size of sample

Then mean of comibined sample

and Standard Deviation of combined sample

**Note** that it is important to work out mean of combined sample first, as to is used to calculate Standard Deviation of combined sample.

**If the sample sizes are equal then the above reduces to**