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The number of home runs a baseball player earned each season in his career are listed.

9, 16, 22, 25, 25, 29, 30, 31, 34, 35, 37, 39, 39

Which of the following box plots best represents the data given?

A box plot uses a number line from 6 to 45 with tick marks every one unit. The box extends from 20.5 to 38 on the number line. A line in the box is at 32. The lines outside the box end at 11 and 43. The graph is titled Career Home Runs and the line is labeled Number of Home Runs.
A box plot uses a number line from 10 to 49 with tick marks every one unit. The box extends from 20.5 to 32 on the number line. A line in the box is at 30. The lines outside the box end at 12 and 46. The graph is titled Career Home Runs and the line is labeled Number of Home Runs.
A box plot uses a number line from 7 to 46 with tick marks every one unit. The box extends from 22.5 to 33.5 on the number line. A line in the box is at 30. The lines outside the box end at 10 and 40. The graph is titled Career Home Runs and the line is labeled Number of Home Runs.
A box plot uses a number line from 6 to 45 with tick marks every one unit. The box extends from 23.5 to 36 on the number line. A line in the box is at 30. The lines outside the box end at 9 and 39. The graph is titled Career Home Runs and the line is labeled Number of Home Runs.

1 answer

To determine which box plot best represents the given data, we need to calculate the five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

The data provided is: 9, 16, 22, 25, 25, 29, 30, 31, 34, 35, 37, 39, 39

  1. Minimum: The smallest number in the dataset is 9.
  2. Maximum: The largest number in the dataset is 39.
  3. Median: With 13 data points, the median is the 7th value:
    • Ordered list: 9, 16, 22, 25, 25, 29, 30, 31, 34, 35, 37, 39, 39 → Median = 30
  4. First Quartile (Q1): The median of the first half of the data (9, 16, 22, 25, 25, 29) is the average of the 3rd and 4th values:
    • Q1 = (22 + 25) / 2 = 23.5
  5. Third Quartile (Q3): The median of the second half of the data (30, 31, 34, 35, 37, 39, 39) is the average of the 3rd and 4th values:
    • Q3 = (34 + 35) / 2 = 34.5

Now we summarize the findings:

  • Minimum = 9
  • Q1 = 23.5
  • Median = 30
  • Q3 = 34.5
  • Maximum = 39

Based on this five-number summary, we can now check which box plot matches:

  • The box should extend from Q1 (23.5) to Q3 (34.5) which is approximate.
  • The line inside the box (the median) should be at 30.
  • The whiskers should extend from the minimum (9) to the maximum (39).

Checking the provided box plots:

  1. The first plot has a box from 20.5 to 38 (incorrect Q1 and Q3).
  2. The second plot has a box from 20.5 to 32 (incorrect Q1 and Q3).
  3. The third plot has a box from 22.5 to 33.5 (incorrect Q1 and Q3).
  4. The fourth plot has a box from 23.5 to 36 (correct Q1 but incorrect Q3).

None of the box plots represent the data accurately. The closest representation would be the fourth option, as it correctly represents Q1, the median, and includes the correct minimum and maximum values; however, it has an incorrect Q3.

Please double-check the options if any corrections need to be made or if a further explanation is required.