Unit 8, Lesson 17
Using Box Plots
Grade 6
17.1
Warm-up
Ten sixth-grade students are 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
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On the grid, draw a box plot for this five-number summary.
- What questions could be answered by looking at this box plot?
17.2
Activity
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
If your teacher gives you the problem card:
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Silently read your card, and think about what information you need to answer the question.
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Ask your partner for the specific information that you need. “Can you tell me ?”
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Explain to your partner how you are using the information to solve the problem. “I need to know because . . . .”
Continue to ask questions until you have enough information to solve the problem.
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When you have enough information, share the problem card with your partner, and solve the problem independently.
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Read the data card, and discuss your reasoning.
If your teacher gives you the data card:
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Silently read your card. Wait for your partner to ask for information.
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Before telling your partner any information, ask, “Why do you need to know ?”
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Listen to your partner’s reasoning and ask clarifying questions. Only give information that is on your card. Do not figure out anything for your partner!
These steps may be repeated.
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When your partner says they have enough information to solve the problem, read the problem card, and solve the problem independently.
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Share the data card, and discuss your reasoning.
17.3
Activity
Andre, Lin, and Noah each design and build a paper airplane. They launch each plane several times and record 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.
- 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 -
Draw three box plots, one for each paper airplane. Label the box plots clearly.
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How are the results for Andre's and Lin’s planes the same? How are they different?
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How are the results for Lin's and Noah’s planes the same? How are they different?
Student Lesson 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.
<p>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.</p>
<p>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.</p>
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.
<p>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.</p>
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.
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