Question

The U.S. Women's Olympic Gymnastics Team consisted of seven members

Answer 1

The answer would be letter D

Answer 2

Answer:

Option: D is the correct answer.

            D.  15, 16, 16, 19, 19, 20, 21

Step-by-step explanation:

Clearly from the box and whisker plot we observe that:

Minimum value-- 15

Maximum value-- 21

First quartile or Lower quartile ($Q_1$)-- 16

Middle quartile or Median ($Q_2$)-- 19

Third quartile or upper quartile ($Q_3$)-- 20

Interquartile Range-- $Q_3-Q_1$

i.e.   IQR= 20-16

             =4

A)

    15, 16, 17, 20, 20, 21, 21

From this set of data we have:

Minimum value-- 15

Maximum value-- 21

First quartile or Lower quartile ($Q_1$)-- 16

Middle quartile or Median ($Q_2$)-- 20

Third quartile or upper quartile ($Q_3$)-- 21

As median does not match and also the upper quartile.

Hence, this data set could not be used.

B)

                15, 16, 17, 19, 20, 20, 20

Here we do no have a maximum value as 21.

Hence, this data set can't be used.

C)

           15, 15, 16, 20, 20, 21, 21

Minimum value-- 15

Maximum value-- 21

First quartile or Lower quartile ($Q_1$)-- 15

Middle quartile or Median ($Q_2$)-- 20

Third quartile or upper quartile ($Q_3$)-- 21

As the lower quartile and upper quartile both does not match.

Hence, this data set can't be used.

D)

             15, 16, 16, 19, 19, 20, 21

Minimum value-- 15

Maximum value-- 21

First quartile or Lower quartile ($Q_1$)-- 16

Middle quartile or Median ($Q_2$)-- 19

Third quartile or upper quartile ($Q_3$)-- 20

Interquartile Range-- $Q_3-Q_1$

i.e.   IQR= 20-16

             =4

Hence, this data set satisfies all the properties of the box and whisker plot.

                     Hence, option: D is the correct answer.