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

Question

Emery Adams · Accepted Answer

Since standard deviation #(SD)# is defined as the square root of the variance #(Var)#, the variance is the square of #SD#.
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 #SD#, which will then be in the same unit as the mean. Summary #SD=root 2 (Var)  hArr Var=SD^2#

Quinn Allen · Answer

undefined The variance of a distribution is equal to the square of its standard deviation. Therefore, to find the variance ($ \sigma^2 $) of a distribution when the standard deviation ($ s $) is known, you square the value of the standard deviation. In this case, since $ s = 7 $, the variance is $ \sigma^2 = 7^2 = 49 $. Thus, the variance of the distribution is $ 49 $.