(13 points)

The double box-and-whisker plot shows the goals scored per game by two soccer teams during a 25 game season.

Express the difference in the measures of center as a multiple of the measure of variation.

13 points The double boxandwhisker plot shows the goals scored per game by two soccer teams during a 25 game season Express the difference in the measures of ce class=

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Answer:

Both distributions are left skewed, so we can use the median and interquartile range.

The median for Team A is [tex]4[/tex]

The median for Team B is [tex]8[/tex]

The interquartile range for Team A [tex]=Q_{3}-Q_{1}=5-2=3[/tex]

The interquartile range for Team B [tex]=Q_{3}-Q_{1}=9-6=3[/tex]

Now we can express the difference in the measures of center as a multiple of the measures of variation as:

[tex]\frac{Median_{A}-Median_{B}}{IQR}=\frac{4-8}{3}=-1.33[/tex]

So, the difference in the medians is about 1.33 times the Interquartile range.

Answer:

The difference in the medians is [tex]\frac{4}{3}[/tex] times the IQR.