Open Up Resources Logo

Lesson 17Using Box Plots

Let's use box plots to make comparisons. 

Learning Targets:

  • I can use a box plot to answer questions about a data set.
  • I can use medians and IQRs to compare groups.

17.1 Hours of Slumber

Ten sixth-grade students were asked how much sleep, in hours, they usually get on a school night. Here is the five-number summary of their responses.

  • Minimum: 5 hours
  • First quartile: 7 hours
  • Median: 7.5 hours
  • Third quartile: 8 hours
  • Maximum: 9 hours
  1. On the grid, draw a box plot for this five-number summary.

  2. What questions could be answered by looking at this box plot?

 
A blank grid for “hours of sleep” with the numbers 0 through 14 indicated along the horizontal axis. There are 5 horizontal gridlines.

17.2 Info Gap: Sea Turtles

Your teacher will give you either a Problem Card or a Data Card about sea turtles that nest on the Outer Banks of North Carolina. Do not show or read your card to your partner.

An image of a sea turtle
“Hawksbill Sea Turtle Carey de Concha (5840602412)” by U.S. Fish and Wildlife Service Southeast Region via Wikimedia Commons. Public Domain.

If your teacher gives you the problem card:

  1. Silently read your card, and think about what information you need to answer the question.
  2. Ask your partner for the specific information that you need.
  3. Explain to your partner how you are using the information to solve the problem.
  4. Solve the problem, and explain your reasoning to your partner.

If your teacher gives you the data card:

  1. Silently read the information on your card.
  2. Ask your partner, “What specific information do you need?” Wait for your partner to ask for information. Only give information that is on your card. (Do not figure out anything for your partner!)
  3. Before telling your partner the information, ask, “Why do you need that information?”
  4. After your partner solves the problem, ask them to explain their reasoning. Listen to their explanation.

Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.

17.3 Paper Planes

Andre, Lin, and Noah each designed and built a paper airplane. They launched each plane several times and recorded the distance of each flight in yards.

Andre 25 26 27 27 27 28 28 28 29 30 30
Lin 20 20 21 24 26 28 28 29 29 30 32
Noah 13 14 15 18 19 20 21 23 23 24 25

Work with your group to summarize the data sets with numbers and box plots. 

  1. Write the five-number summary for the data for each airplane. Then, calculate the interquartile range for each data set.
    min Q1 median Q3 max IQR
    Andre
    Lin
    Noah
  2. Draw three box plots, one for each paper airplane. Label the box plots clearly.
    A blank grid with the horizontal axis labeled "distance in yards". The numbers 10 through 35, in increments of 5, are indicated. There are 4 evenly spaced vertical gridlines between each number indicated.
  3. How are the results for Andre's and Lin’s planes the same? How are they different?
  4. How are the results for Lin's and Noah’s planes the same? How are they different?

Are you ready for more?

Priya joined in the paper-plane experiments. She launched her plane eleven times and recorded the lengths of each flight. She found that her maximum and minimum were equal to Lin’s. Her IQR was equal to Andre’s.

Draw a box plot that could represent Priya’s data.

a blank dot plot showind distance in yards
With the information given, can you estimate the median for Priya’s data? Explain your reasoning.

Lesson 17 Summary

Box plots are useful for comparing different groups. Here are two sets of plots that show the weights of some berries and some grapes.

A box plot and dot plot for “berry weights in grams.” The numbers 1 through 8 are indicated. The box plot is above the dot plot. The five-number summary for the box plot are as follows: Minimum value, 2. Maximum value, 6.5. Q1, 2.5. Q2, 3.5. Q3, 4. The data for the dot plot are as follows: 2 grams, 2 dots. 2.5 grams, 3 dots. 3 grams, 4 dots. 3.5 grams, 4 dots. 4 grams, 2 dots. 4.5 grams, 2 dots. 5.5 grams, 1 dot. 6.5 grams, 1 dot.
A box plot and dot plot for “grape weights in grams.” The numbers 1 through 8 are indicated. The box plot is above the dot plot. The five-number summary for the box plot is as follows: Minimum value, 3. Maximum value, 9. Q1, 4.5. Q2, 5. Q3, 6. The data for the dot plot are as follows: 3 grams, 1 dot. 3.5 grams, 2 dots. 4 grams, 2 dots. 4.5 grams, 4 dots. 5 grams, 4 dots. 5.5 grams, 4 dots. 6 grams, 3 dots. 6.5 grams, 3 dots. 7 grams, 1 dot.

Notice that the median berry weight is 3.5 grams and the median grape weight is 5 grams. In both cases, the IQR is 1.5 grams. Because the grapes in this group have a higher median weight than the berries, we can say a grape in the group is typically heavier than a berry. Because both groups have the same IQR, we can say that they have a similar variability in their weights.

These box plots represent the length data for a collection ladybugs and a collection of beetles.

Two sets of box plots for "lengths in millimeters". The numbers 4 through 16 are indicated in increments of 2. There are tick marks midway between the indicated numbers. The top box plot is for "ladybugs". The five-number summary is as follows: Minimum value, 6. Maximum value, 10.5. Q1, 8.5. Q2, 9. Q3, 10. The bottom box plot is for "beetles". The five-number summary is as follows: Minimum value, 5. Maximum value, 15.5. Q1, 7.5. Q2, 9. Q3, 13.5.

The medians of the two collections are the same, but the IQR of the ladybugs is much smaller. This tells us that a typical ladybug length is similar to a typical beetle length, but the ladybugs are more alike in their length than the beetles are in their length.

Lesson 17 Practice Problems

  1. Here are box plots that summarize the heights of 20 professional male athletes in basketball, football, hockey, and baseball.

    Four box plots for "height in inches" labeled "basketball", "football", "hockey", and "baseball". The numbers 65 through 90, in increments of 5, are indicated. From top to bottom the data for the box plots are as follows: For "basketball": Minimum value, 67.3. Maximum value, 91.1. Q1, 76.1. Q2, 78.5. Q3, 80.3. For "football": Minimum value, 66.1. Maximum value, 77.9. Q1, 70.1. Q2, 73.8. Q3, 75.1. For "hockey": Minimum value, 68.8. Maximum value, 76.8. Q1, 72. Q2, 73.1. Q3, 75. For "baseball": Minimum value, 70. Maximum value, 76.2. Q1, 72. Q2, 72.8. Q3, 74.5.
    1. In which two sports are the players’ height distributions most alike? Explain your reasoning.
    2. Which sport shows the greatest variability in players’ heights? Which sport shows the least variability?

  2. Here is a box plot that summarizes data for the time, in minutes, that a fire department took to respond to 100 emergency calls. 

    Select all the statements that are true, according to the box plot.

    1. Most of the response times were under 13 minutes.
    2. Fewer than 30 of the response times were over 13 minutes.
    3. More than half of the response times were 11 minutes or greater.
    4. There were more response times that were greater than 13 minutes than those that were less than 9 minutes.
    5. About 75% of the response times were 13 minutes or less.
    A box plot for "time in minutes.” The numbers 2 through 20, in increments of two, are indicated. The five-number summary for the box plot is as follows: Minimum value, 4. Maximum value, 18. Q1, 8. Q2, 9. Q3, 13.

  3. Pineapples were packed in three large crates. For each crate, the weight of every pineapple in the crate was recorded. Here are three box plots that summarize the weights in each crate.

    Select all of the statements that are true, according to the box plots.

    1. The weights of the pineapples in Crate 1 were the most variable.
    2. The heaviest pineapple was in Crate 1.
    3. The lightest pineapple was in Crate 1.
    4. Crate 3 had the greatest median weight and the greatest IQR.
    5. More than half the pineapples in Crate 1 and Crate 3 were heavier than the heaviest pineapple in Crate 2.
    Three box plots for “weight in pounds” are labeled “crate 1,” “crate 2,” and “crate 3.” The numbers 0 through 7 are indicated. The five-number summary for the box plots are as follows: crate 1: Minimum value, 1.5. Maximum value, 6.25. Q1, 3.25. Q2, 4. Q3, 4.75. crate 2: Minimum value, 0.75. Maximum value, 3.4. Q1, 1.75. Q2, 2. Q3, 2.25. crate 3: Minimum value, 2.7. Maximum value, 5.1. Q1, 3.6. Q2, 4.1. Q3, 4.4.

  4. Two TV shows each asked 100 viewers for their ages. For one show, the mean age of the viewers was 35 years and the MAD was 20 years. For the other show, the mean age of the viewers was 30 years and the MAD was 5 years.

    A sixth-grade student says he watches one of the shows. Which show do you think he watches? Explain your reasoning.