The sum of the deviations of a set of n values x₁, x₂,...., x_n, measured from 15 and −3 are −90 and 54 respectively. Find the value of n and mean.

Ifbe the mean of the n observations, then we have

Given that the sums of the deviations of a set of n valuesmeasured from 15 and -3 are -90 and 54 respectively. So that we get two equations

These equations can be rewritten as

We have to solve the above equations forandunknowns.

Subtracting the first equation from the second equation, we have

Substitute the value of n in the first equation, we have