A hockey coach recorded the number of shots taken by the home team and the number taken by the visiting team in 20 games. He displayed the results in the box plots below.

A box plot titled Number of Shots Taken by home team players. The number line goes from 10 to 32. The whiskers range from 16 to 32, and the box ranges from 20 to 23. A line divides the box at 22.
Number of Shots Taken by Home Team Players

A box plot titled Number of Shots Taken by visiting team players. The number line goes from 10 to 32. The whiskers range from 14 to 32, and the box ranges from 16 to 24. A line divides the box at 18.
Number of Shots Taken by Visiting Team Players

Which describes an inference that the coach might make after comparing the medians of the two data sets?
The home team took more shots than the visiting team.
The visiting team took more shots than the home team.
The home team had more variability in the number of shots taken.
The visiting team had more variability in the number of shots taken.

The most accurate inference from this boxplot is that: The visiting team had more variability in the number of shots taken.

Step-by-step explanation:

The box and whiskers plot is a way of presenting data that gives 5 major information about the distribution

From the whiskers of the plot, one can read

- The minimum value

- The maximum value

Then, from the boxplot, one can read

- The Median, represented by the middle line of the boxplot.

- The first Quartile or 25th percentile, represented by the lower end of the boxplot.

- The third quartile or 75th percentile, represented by the upper end of the boxplot.

Other variables that can be obtained from these five data points include

- The range of the distribution (maximum value minus minimum value)

- The interquartile range (a measure of variation, which is the difference between the third and first quartile of the distribution)

For the two boxplots that the coach made

Home team

Whiskers range from 16 to 32

Minimum value = 16

maximum value = 32

the box ranges from 20 to 23. A line divides the box at 22.

First quartile = 20

Third quartile = 23

Median = 22

IQR = 23 - 20 = 3

For the visiting team

Whiskers range from 14 to 32

Minimum value = 14

maximum value = 32

the box ranges from 16 to 24. A line divides the box at 18.

First quartile = 16

Third quartile = 24

Median = 18

IQR = 24 - 16 = 8

Since the median only represents the midpoint of the distribution, one cannot conclude with certainty that home team took more shots than the visiting team, information on the mean would confirm that.

A less controversial and evident inference is that the visiting team had more variability in their shots as their distribution has a higher Interquartile Range (IQR of 8 > 3) which is a direct measure of variation for distributions.

Hope this Helps!!!

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