Question

If the sum of the deviations of $50$ observations from $30$ is $50$, then the mean of these observations is:

• A. $50$
• B. $51$
• C. $30$
• D. $31$

Answer 1

The correct option is D $31$

Sum of deviations of $50$ elements from $30=50$
$\Rightarrow \sum _{i=1}^{50}(x_i-30)=50\Rightarrow \sum _{i=1}^{50}{x}_i-1500=50\Rightarrow \sum _{i=1}^{50}{x}_i=1550\therefore \text{Mean}=\frac{\sum x_i}{n}=\frac{1550}{50}=31$