Question

If the sum of the deviations of a set of values $x_1,x_2,x_3,\dots ,x_n$ measured from 50 is -10 and the sum of deviations of the values from 46 is 70, then the mean is:

• A. 49
• B. 49.5
• C. 49.75
• D. 50

Answer 1

The correct option is B 49.5

Given:
$x_1-50+x_2-50+\dots +x_n-50=-10$
$\Rightarrow (x_1+x_2+\dots +x_n)-50n=-10$
$\Rightarrow (x_1+x_2+\dots +x_n)=-10+50n$ ....(i)
Also given that,
$x_1-46+x_2-46+\dots +x_n-46=70$
$\Rightarrow x_1+x_2+\dots +x_n-46n=70$
$\Rightarrow x_1+x_2+\dots +x_n=70+46n$ ....(ii)
From Eqs. (i) and (ii)
$-10+50n=70+46n$
$\Rightarrow 4n=80$
$\Rightarrow n=20$
From Eq. (i).
$x_1+x_2+\dots +x_n=-10+50\times 20=990$
$\Rightarrow$ Mean$=\frac{x_1+x_2+\dots +x_n}{n}=\frac{990}{20}=49.5$