Question

Find the arithmetic mean of the five observations 14, 56, 23, 44, 23 where the estimated mean is given as 30.

• A. 30
• B. 32
• C. 33
• D. 31

Answer 1

The correct option is B 32

Data given: 14, 56, 23, 44, 23

Estimated mean = 30

$Arithmeticmean=Estimatedmean+\frac{\text{Sum of deviations}}{\text{Number of Observations}}$
=A + $\frac{\Sigma (xi-A)}{N}$

=30 + $\frac{(14-30)+(56-30)+(23-30)+(44-30)+(23-30)}{5}$

= 30 + $\frac{(-16)+\left(26\right)+(-7)+\left(14\right)+(-7)}{5}$
= 30 + $\frac{10}{5}$ = 32