# If the standard deviation of a distribution is s = 7, what is its variance?

##### 1 Answer
Jan 31, 2015

Since standard deviation $\left(S D\right)$ is defined as the square root of the variance $\left(V a r\right)$, the variance is the square of $S D$.
In your case this would be 49.

The variance is the sum of all the squared differences from the mean, divided by the number of cases. One reason it's squared (but not the only one), is to avoid $+$ and $-$ issues.

Since variance is a squared unit, it would give funny results, for instance if you measure height in meters. The variance would then be in square meters (and it is).

That's why we take the square root of the variance to get $S D$, which will then be in the same unit as the mean.

Summary

$S D = \sqrt[2]{V a r} \Leftrightarrow V a r = S {D}^{2}$