# Lesson 17

Using Box Plots

### Lesson Narrative

In the previous lesson, students analyzed a dot plot and a box plot in order to study the distribution of a data set. They saw that, while the box plot summarizes the distribution of the data and highlights some key measures, it was not possible to know all the data values of the distribution from the dot plot alone. In this lesson, students use box plots to make sense of the data in context (MP2), compare distributions, and answer statistical questions about them.

Students compare box plots for distributions that have the same median but different IQRs, as well as box plots with the same IQRs but different medians. They recognize and articulate that the centers are the same but the spreads are different in the first case, and the centers are different but the spreads are the same in the second case. They use this understanding to compare typical members of different groups in terms of the context of the problem (MP2).

### Learning Goals

Teacher Facing

• Compare and contrast (orally and in writing) box plots that represent different data sets, including ones with the same median but very different IQRs and vice versa.
• Determine what information is needed to solve problems about comparing box plots. Ask questions to elicit that information.
• Interpret a box plot to answer (orally) statistical questions about a data set.

### Student Facing

Let's use box plots to make comparisons.

### Required Preparation

Print and cut up slips from the Sea Turtles Info Gap blackline master.  Prepare 1 set for every 2 students. Provide access to straightedges for drawing box plots. Consider creating a few paper planes of different sizes or styles to fly for the Paper Planes activity.

### Student Facing

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

### 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.

• 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 $$12-3=9$$.