Question

Which measure of variation is preferred when

(a) the mean is used as a measure of center?

(b) the median is used as a measure of center?

Short answer

(a) The standard deviation is used as a measure of variation.

(b) The interquartile range is used as a measure of variation.

Step-by-step solution

Part (a) Step 1: Given Information

We have to find out the measure of variation when mean is used as a measure of center.

Part (a) Step 2: Explanation 

When the mean is taken as a measure of center then we use standard deviation as a measure of variation because it is defined as to move one standard unit away from the mean in either directions.

Part (b) Step 1: Given Information

We have to find out the measure of variation when median is used as a measure of center.

Part (b) Step 2: Explanation

When median is taken as the measure of center then we use interquartile range as the measure of variation because it is defined using median only and it is the difference between the first quartile and third quartile and it also tells the position of median in the boxplot.