# 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.
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.

Hawksbill Sea Turtle Carey de Concha (5840602412) Copyright Owner: U.S. Fish and Wildlife Service Southeast Region License: Public Domain

If your teacher gives you the problem card:

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

If your teacher gives you the data 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.

## 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 Lin Noah 25 26 27 27 27 28 28 28 29 30 30 20 20 21 24 26 28 28 29 29 30 32 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.
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?

## 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.

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.

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.