Question

The sum of the deviations of a set of values $x_1,x_2$, ...... $x_n$ measured from $50$ is $-10$ and the sum of deviations of the values from $46$ is $70$. The mean is ___________.

• A. $49$
• B. $49.5$
• C. $49.75$
• D. $50$

Answer 1

Answer: (B)

$49.5$

Sum of deviations from $50$ is $-10$

$\Rightarrow \sum (xi-50)=-10$

$\sum x_i-50\sum 1=-10$

$\sum x_i-50n=-10$

$\therefore y-50n=-\mathrm{10.....}\left(1\right)$

Sum of deviations from $46$ is $70$

$\Rightarrow \sum (x_i-46)=70$

$\sum x_i-46\sum 1=70$

$\sum x_i-46n=70$

$\therefore y-46n=\mathrm{70.....}\left(2\right)$

Solving $\left(1\right)$ and $\left(2\right)$, we get

$4n=80$ i.e. $n=20$

Putting value of $n$ in $\left(1\right)$, we get

$y=990$

Mean $=\frac{\sum x_i}{n}=\frac{y}{n}=\frac{990}{20}=49.5$