Statistics Unit

2.9 Interpreting Box and Whisker Plots

  1. Below are the prices of snowboards at two competing snowboard stores:

    Middletown Snowboards Snowboard Central
    345, 350, 356, 360, 375, 405 343, 370, 386, 392, 395, 402

    1. Identify the 5 number summary statistics of each set of data.

      2. Middletown Snowboards Snowboard Central

      Low = 345
      Lower Quartile = 350
      Median = 358
      Upper Quartile = 375
      High = 405

      Low = 343
      Lower Quartile = 370
      Median = 389
      Upper Quartile = 395
      High = 402

    2. Draw a double box-and-whisker plot of the above data on the scale below:
      3. The scale is a number line that goes from 340 to 410 counting by 10.

      The box and whisker plot is for Middletown Snowboards. The far left whisker is at 345. The far right whisker is at 405. The box is drawn with 350 on the left side, 358 is the median and 375 is the right side of the box.

      The box and whisker plot is for Snowboard Central. The far left whisker is at 343 and the far right whisker is at 402. The box is drawn with the left side being at 370, the median is at 389 and the right side of the box is at 395.

    3. What is the median price for a snowboard at Middletown Snowboards?

      4. $358

    4. What is the lowest price you could pay for a snowboard at Snowboard Central?

      5. $343

    5. What is the most expensive board at Middletown Snowboards?

      6. $405

    6. What is the range of prices for snowboards at Snowboard Central?

      7. $59

    7. Which price represents the 75th percentile for Middletown Snowboards?

      8. $375

    8. Which store would you rather buy a snowboard from? Why?

      9. Middletown Snowboards, because the majority of the prices are below the majority of the prices at Snowboard Central.

  2. The accompanying box-and-whisker plot represents the cost, in dollars, of twelve CD’s.

    The scale for the Box and Whisker plot is from 0 to 30 counting by 1. The low number is 7, the quartile 1 number is 14.5, the median is 20.5, the quartile 3 number is 26 and the high number is 29.The far left whisker is at 7. The far right whisker is at 29. The box is drawn with the left side at 14.5, the median at 20.5 and the right side at 26.

    1. Which cost is the upper quartile?

      2. $26

    2. What is the range of the costs of the CD’s?

      3. $22

    3. What is the median?

      4. $20.50

    4. Which cost represents the 100th percentile?

      5. $29

    5. How many CD’s cost between $14.50 and $26.00?

      6. 6

    6. How many CD’s cost less than $14.50?

      7. 3

  3. The accompanying box-and-whisker plot represents the scores earned on a math test.

    The scale for the Box and Whisker plot is 55 to 100 counting by 5. the low number is 55, the quartile 1 number is 70, the median is 75, the quartile 3 number is 85 and the high number is 100. The far left whisker is at 55, the left side of the box is at 70, the median is at 75, the right side of the box is at 85 and the far right whisker is at 100.

    1. What is the median score?
      1. 75
      2. 70
      3. 85
      4. 77

      i. 75

    2. What score represents the first quartile?
      1. 55
      2. 70
      3. 100
      4. 75

      ii. 70

    3. What statement is not true about the box and whisker plot shown?
      1. 75 represents the mean score
      2. 100 represents the maximum score
      3. 85 represents the 3rd quartile
      4. 55 represents the minimum score

      i. 75 represents the mean score

    4. A score of an 85 on the box-and-whisker plot shown refers to:
      1. the third quartile
      2. the median
      3. the maximum score
      4. the mean

      i. the third quartile

  4. What is the median price for a snowboard at Middletown Snowboards?

    The scale on the Box and Whisker plot is from 55 to 100 counting by 5. The low number is 55, the quartile 1 number is 70, the median is 75, the quartile 3 number is 85 and the high number is 100.

    1. 70
    2. 75
    3. 77
    4. 85

    b. 75

  5. What percentage of values in the data set shown are greater than 6?

    The scale on the Box and Whisker plot is from 0 to 12 counting by 1. The low number on the plot is 2, the quartile 1 number is 6, the median is 8.5, the quartile 3 number is 10 and the high number is 12.

    1. 25%
    2. 50%
    3. 75%
    4. 100%

    c. 75%

  6. A movie theater recorded the number of tickets sold daily for a popular movie during the month of June. The box-and-whisker plot shown below represents the data for the number of tickets sold, in hundreds.

    The scale on the Box and Whisker plot is from 0 to 10 counting by 1. The low number on the plot is 1, the quartile 1 number is 3, the median is 4, the quartile 3 number is 6 and the high number is 9.

    Which conclusion can be made using this plot?

    1. The second quartile is 600.
    2. The mean of the attendance is 400.
    3. The range of the attendance is 300 to 600.
    4. Twenty-five percent of the attendance is between 300 and 400.

    d. Twenty-five percent of the attendance is between 300 and 400.

  7. The accompanying box-and-whisker plots can be used to compare the annual incomes of three professions.

    The scale on the Box and Whisker plot is from 0 to 140 counting by 10. Each number represents the annual income in thousands of dollars. There are three plots. The first one is for the income for Nuclear Engineers. The low number is 50, the quartile 1 number is 60, the median is 70, the quartile 3 number is 100 and the high number is 120. The second plot is for the income for Police Officers. The low number is 12, the quartile 1 number is 22, the median is 30, the quartile 3 number is 43 and the high number is 60. The third plot is for the income for Musicians. The low number is 8, the quartile 1 number is 20, the median is 30, the quartile 3 number is 80 and the high number is 122.

    Based on the box-and-whisker plots, which statement is true?

    1. The median income for nuclear engineers is greater than the income of all musicians.
    2. The median income for police officers and musicians is the same.
    3. All nuclear engineers earn more than all police officers.
    4. A musician will eventually earn more than a police officer.

    b. The median income for police officers and musicians is the same.

  8. The data set 5, 6, 7, 8, 9, 9, 9, 10, 12, 14, 17, 17, 18, 19, 19 represents the number of hours spent on the Internet in a week by students in a mathematics class. Which box-and-whisker plot represents the data?
    1. The scale on the Box and Whisker Plot goes from 2 to 20 counting by 2. The low number is 2, the quartile 1 number is 8, the median is 12, the quartile 3 number is 17 and the high number is 19.
    2. The scale on the Box and Whisker plot is from 2 to 20 counting by 2. The low number is 5, the quartile 1 number is 8, the median is 10, the quartile 3 number is 17 and the high number is 19.
    3. The scale on the Box and Whisker plot is from 2 to 20 counting by 2. The low number is 5, the quartile 1 number is 8, the median is 14, the quartile 3 number is 16 and the high number is 19.
    4. The scale on the Box and Whisker plot is from 2 to 20 counting by 2. The low number is 5, the quartile 1 number is 8, the median is 12, the quartile 3 number is 17 and the high number is 19.

    b