# Why is variance invariant with regards to translation?

##### 1 Answer

Jul 16, 2016

Because the variance is calculated in terms of the deviations from the mean, which stays the same under a translation .

#### Explanation:

The variance is defined as the expectation value

When the data set is translated, then all the data-points are shifted by the same amount

The mean also shifts by the same amount

so that the deviations from the mean stay the same :