Question

Which of the following measures of dispersion are based on deviations from the mean?

Answer 1

Answer:

D.

Step-by-step explanation:

The mean deviation is the measure of dispersion used to evaluate the spread of the data calculated by taking deviation from mean. The mean deviation formula is

$M.D=\frac{sum|x-xbar|}{n}$

|x-xbar| are known as absolution deviations.

So, the mean deviation is the measures of dispersion that is based on deviations from the mean.

Standard deviation is also computed by computing mean deviation first i.e.

$s=\sqrt\frac{sum(x-xbar)^2}{n-1}$

Variance is also computed by mean deviation first

$variance=s^2=\frac{sum(x-xbar)^2}{n-1}$

Note: All formula for sample are considered and formulas for population also results in the same conclusion.

Hence, variance, standard deviation and mean deviation all are based on deviation from mean.