Question

The sum of deviations of 'n' observations from 20 is 20 and sum of deviations same 'n' observations from 30 is - 20 . Find the mean of the observations.

• A. 50
• B. 25
• C. 20
• D. 35

Answer 1

The correct option is B 25

As we know ,

$Arithmeticmean=Estimatedmean+Averageofdeviations=Estimatedmean+\frac{\text{Sum of deviations}}{\text{Number of Observations}}$

Let mean of observations is A
So,
A = 20 + $\frac{20}{n}$ ..................................1

A = 30 + $\frac{-20}{n}$ ...................................2

Adding equation (1) and (2)

2A = 20 +30 + $\frac{20}{n}$ + $\frac{-20}{n}$ = 50

Hence , A = 25