Question bank / One-variable data: distributions and measures of center and spread

Math · Problem-Solving and Data AnalysisMedium
Goals scored Number of games
0 2
1 4
2 3
3 2
5 1

The table summarizes the number of goals a soccer team scored in each of its 1212 games last season. What is the median number of goals the team scored per game?

A

11

B

1.51.5

C

1.751.75

D

22

Show answer and explanation

Answer: B

With 1212 games, the median is the average of the 66th and 77th values in order. The first 22 values are 00 and the next 44 are 11, so the 66th value is 11. The next 33 values are 22, so the 77th value is 22. The median is 1+22=1.5\frac{1 + 2}{2} = 1.5.

Choice D is the middle of the five listed goal values, 0,1,2,3,50, 1, 2, 3, 5, which ignores how many games had each value.

Why the other choices are wrong

  • A. 1 is the mode, the most common number of goals, not the median.
  • C. 1.75 is the mean, 21 total goals divided by 12 games.
  • D. 2 is the middle of the distinct values 0, 1, 2, 3, 5, which ignores how many games had each value.
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