Question

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

• A. $25$
• B. $30$
• C. $35$
• D. $40$

Answer 1

The correct option is B $30$

Given $\frac{\sum (x-25)}{n}=25$ and $\frac{\sum (x-35)}{n}=-25$
$\Rightarrow \frac{\sum x-\sum 25}{n}=25$ and $\frac{\sum x-\sum 35}{n}=-25$
$\Rightarrow \frac{\sum x-25n}{n}=25$ and $\frac{\sum x-35n}{n}=-25$
Adding these two equation $2\sum x=60n$. Hence mean $\frac{\sum x}{n}=30$