Question

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

Their ages are shown on the box-and-whisker plot below.

Which set of data could have been used to construct the box-and-whisker plot?
A. 15, 16, 17, 20, 20, 21, 21

B. 15, 16, 17, 19, 20, 20, 20

C. 15, 15, 16, 20, 20, 21, 21

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

Answer 1

Option: D is the correct answer.

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

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.