# If you add two independent random variables, what is the standard deviation of the combined distribution, if the standard deviations of the two original distributions were, for example, 7 and 5?

##### 1 Answer

Jan 24, 2015

You cannot just add the standard deviations.

Instead, you add the **variances**. Those are built up from the *squared* differences between every individual value from the mean (the squaring is done to get positive values only, and for other reasons, that I won't delve into).

*Standard deviation* is defined as the *square root* of the *variance* .

The other way around, variance is the square of SD.

**So:**

- You square the individual SD's to get the variances

- Then you add these together to get the total variance

- Then you take the square root to get the total SD

**Your case:**

Total variance =

Total SD =

This works for any number of **independent** variables (mark the bold type for independent!)