Lesson 17

Using Box Plots

Let's use box plots to make comparisons. 

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.

    A blank grid for “hours of sleep” with the numbers 0 through 14 indicated along the horizontal axis. There are 5 horizontal gridlines.
  2. What questions could be answered by looking at this box plot?

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.

Photograph of a sea turtle.

If your teacher gives you the problem card:

  1. Silently read your card and think about what information you need to be able to answer the question.

  2. Ask your partner for the specific information that you need.

  3. Explain how you are using the information to solve the problem.

    Continue to ask questions until you have enough information to solve the problem.

  4. Share the problem card and solve the problem independently.

  5. Read the data card and discuss your reasoning.

If your teacher gives you the data card:

  1. Silently read your card.

  2. Ask your partner “What specific information do you need?” and wait for them to ask for information.

    If your partner asks for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information.

  3. Before sharing the information, ask “Why do you need that information?” Listen to your partner’s reasoning and ask clarifying questions.

  4. Read the problem card and solve the problem independently.

  5. Share the data card and discuss your reasoning.

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
               
               
               
  2. Draw three box plots, one for each paper airplane. Label the box plots clearly.
    Blank grid. Distance in yards. Horizontal axis from 10 to 35 by 5's.
  3. How are the results for Andre and Lin’s planes the same? How are they different?

  4. How are the results for Lin and Noah’s planes the same? How are they different?



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.

Grid with horizontal axis drawn. 10 to 35 by 5's. Distance in yards.

With the information given, can you estimate the median for Priya’s data? Explain your reasoning.

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.” 
A box plot and dot plot for “grape weights in grams.”

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 of ladybugs and a collection of beetles.

Two sets of box plots for "lengths in millimeters". 

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.

Glossary Entries

  • box plot

    A box plot is a way to represent data on a number line. The data is divided into four sections. The sides of the box represent the first and third quartiles. A line inside the box represents the median. Lines outside the box connect to the minimum and maximum values.

    For example, this box plot shows a data set with a minimum of 2 and a maximum of 15. The median is 6, the first quartile is 5, and the third quartile is 10.

    Box plot from 0 to 16 by 2’s. Number of books. Whisker from 0 to 5. Box from 5 to 10 with vertical line at 6. Whisker from 10 to 15.
  • interquartile range (IQR)

    The interquartile range is one way to measure how spread out a data set is. We sometimes call this the IQR. To find the interquartile range we subtract the first quartile from the third quartile.

    For example, the IQR of this data set is 20 because \(50-30=20\).

    22 29 30 31 32 43 44 45 50 50 59
    Q1 Q2 Q3
  • median

    The median is one way to measure the center of a data set. It is the middle number when the data set is listed in order.

    For the data set 7, 9, 12, 13, 14, the median is 12.

    For the data set 3, 5, 6, 8, 11, 12, there are two numbers in the middle. The median is the average of these two numbers. \(6+8=14\) and \(14 \div 2 = 7\).

  • quartile

    Quartiles are the numbers that divide a data set into four sections that each have the same number of values.

    For example, in this data set the first quartile is 30. The second quartile is the same thing as the median, which is 43. The third quartile is 50.

    22 29 30 31 32 43 44 45 50 50 59
    Q1 Q2 Q3
  • range

    The range is the distance between the smallest and largest values in a data set. For example, for the data set 3, 5, 6, 8, 11, 12, the range is 9, because \(12-3=9\).