Question

the sum of deviation of n observations from 25 is 25 and sum of deviation of the same n observation from 35 is -25 find the mean of the observations

Answer 1

please find the attachment

Answer 2

Answer-

Mean of the sample is 30

Solution-

Given, the sum of deviation of n observations from 25 is 25 and sum of deviation of the same n observation from 35 is -25, so

$\sum_{i=1}^{n}(x_i-25)=25,\ \sum_{i=1}^{n}(x_i-35)=-25$

$\Rightarrow n\overline{x}-25n=25,\ n\overline{x}-35n=-25$

Solving these equation will yield the result,

Subtracting both equation,

$\Rightarrow (n\overline{x}-25n)-(n\overline{x}-35n)=25-(-25)$

$\Rightarrow -25n+35n=50$

$\Rightarrow 10n=50$

$\Rightarrow n=5$

Putting this value in the first equation,

$\Rightarrow 5\overline{x}-25\times 5=25$

$\Rightarrow 5\overline{x}-125=25$

$\Rightarrow 5\overline{x}=150$

$\Rightarrow \overline{x}=30$

Therefore, the mean of the sample is 30