JAMB 2013 · UTME · Q45

If the variance of $3 + x$ , $6$ , $4$ , $x$ and $7 - x$ is 4 and the mean is 5, find the standard deviation.

Worked solution (try it first)

The standard deviation is the square root of the variance, so it is $\sqrt4 = 2$ , option D.
As a check: the mean is $\frac{20 + x}{5} = 5$ , so $x = 5$ .
The numbers are 8, 6, 4, 5, 2, whose squared deviations 9, 1, 1, 0, 9 add up to 20, and $\frac{20}{5} = 4$ .