Question

The box-and-whisker plot represents the number of points scored by teams in a soccer league last year.

A) What are the range, interquartile range, and median of the box-and-whisker plot?

B) The league commissioner believes about half of the teams in the league scored 48 points of more last year. Use the Graph to explain whether this is reasonable.

C) If the box-and-whisker plot represented data from 20 teams, about how many of the teams scored between 38 and 48 points? Explain.

Answer 1

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Explanation:

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Answer 2

a.) The Range, interquartile range and median are 24, 16 and 48 respectively.

b.) The league commissioner's statement is reasonable.

c.) About 25% scored between 38 and 48 points.

From the graph:

• Minimum = 32
• Maximum = 56

Range = Maximum - Minimum

Range = 56 - 32 = 24

The median = 48 (vertical line inside the box).

The interquartile range = Q3 - Q1

• Q3 = 54
• Q1 = 38

Interquartile Range = 54 - 38 = 16

B.)

The median represents 50th quartile, which is half the total percentile. Hence, the commission's claim is reasonable. 50% scored below 48 and also about 50% scored above 48.

C.)

From the graph:

• 25th percentile = 38
• 50th percentile = 48

50% - 25% = 25% . Hence, about 25% scored between 38 and 48 points.