Chapter 10.4, Problem 5IP

To determine

To calculate: The centers and variations and to find which season the team was more consistent.

Answer to Problem 5IP

The points scored this season has a median of 20 points with an inter quartile range of 10 points.

The points scored last season has a median of 20 points with an inter quartile range of 15 points.

The football team was more consistent this season.

Explanation of Solution

Given information: The double box plot shows the points scored by football team for two seasons.

Calculation:

The distribution for points scored this season is symmetric, while that of points scored last season is not symmetric. Use the median to compare the centers and the inter quartile range to compare the variations.

In box plot, a box is drawn from the first quartile to the third quartile and median is where the vertical line goes through.

For This Season:

  $median=20$

  $\text{Left quartile}=15$

  $\text{Right quartile=25}$

Therefore, $$

  $\text{inter quartile}=\text{ right quartile}-\text{ left quartile}$

  $\text{inter quartile}=\text{ 25-15}$

  $\text{inter quartile}=\text{ 10}$

The points scored this season has a median of 20 points with an inter quartile range of 10 points.

For last:

  $median=20$

  $\text{Left quartile}=10$

  $\text{Right quartile=25}$

Therefore, $$

  $\text{inter quartile}=\text{ right quartile}-\text{ left quartile}$

  $\text{inter quartile}=\text{ 25-10}$

  $\text{inter quartile}=\text{ 15}$

The points scored last season has a median of 20 points with an inter quartile range of 15 points.

	This season	Last Season
median	20	20
inter quartile range	10	15

Median of both seasons is 20 points. But last season’s inter quartile range is greater than this season’s. So, the football team was more consistent this season.