Question

The sum of deviations of $n$ observations from $25$ is $25$ and sum of deviations of the same $n$ observations from $35$ is $-25$. Find the mean of the observations

Answer 1

$\sum x_i-25n=25$

$\sum x_i-35n=-25$

$10n=50n=5$

$\sum x_i-25n=25$

$\sum x_i-12n=25$

$\sum x_i=150$

$\therefore$ $\overline{x}=\frac{\sum x_i}{n}\overline{x}=\frac{150}{5}\overline{x}=30.$