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

Question

raven1wish raven1wish

10-04-2018
Mathematics

contestada

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

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lb3790 lb3790 · Answer 1 · 2018-04-10T22:30:35+02:00

lb3790 lb3790

10-04-2018

The answer would be letter D

Answer Link

virtuematane virtuematane · Answer 2 · 2019-05-16T07:20:49+02:00

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 ([tex]Q_1[/tex])-- 16

Middle quartile or Median ([tex]Q_2[/tex])-- 19

Third quartile or upper quartile ([tex]Q_3[/tex])-- 20

Interquartile Range-- [tex]Q_3-Q_1[/tex]

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 ([tex]Q_1[/tex])-- 16

Middle quartile or Median ([tex]Q_2[/tex])-- 20

Third quartile or upper quartile ([tex]Q_3[/tex])-- 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 ([tex]Q_1[/tex])-- 15

Middle quartile or Median ([tex]Q_2[/tex])-- 20

Third quartile or upper quartile ([tex]Q_3[/tex])-- 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 ([tex]Q_1[/tex])-- 16

Middle quartile or Median ([tex]Q_2[/tex])-- 19

Third quartile or upper quartile ([tex]Q_3[/tex])-- 20

Interquartile Range-- [tex]Q_3-Q_1[/tex]

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.