Question

Express the difference between the measures of center as a multiple of the measure of variation.
Given is a box plot for the number of questions attempted in subject 1 by different students.


The following table shows the number of questions attempted by students in subject 2.

Number of questions attempted	2	4	5	7	10	12	15
Number of students	5	7	3	9	3	8	2

• A. The difference between the measures of center is double the measure of variation.
• B. The difference between the measures of center is equal to the measure of variation.
• C. The difference between the measures of center is half the measure of variation.
• D. The difference between the measures of center is three times the measure of variation.

Answer 1

The correct option is B The difference between the measures of center is equal to the measure of variation.

Solution:
The IQR of the given box plot:
$Q_1=10$
$Q_3=18$
$IQR=Q_3-Q_1=18-10=8$
Median = 15
On arranging the data for subject 2, we get the median of the data as 7.


$Q_1=4$
$Q_3=12$
$IQR=Q_3-Q_1=12-4=8$

The difference between the measures of center as a multiple of the measure of variation:
$\frac{\text{Median of first data set - median of second data set}}{IQR}=\frac{15-7}{8}=1$

Therefore, the difference between the measures of center is equal to the measure of variation.