# Lesson 16

Box Plots

### Lesson Narrative

In this lesson, students use the five-number summary to construct a new type of data display: a box plot. Similar to their first encounter with the median, students are introduced to the structure of a box plot through a kinesthetic activity. Using the class data set that contains the numbers of letters in their names (from an earlier lesson), they first identify the numbers that make up the five-number summary. Then, they use their numbers to position themselves on a number line on the ground, and are guided through how a box plot would be constructed with them as the data points.

Later, students draw and make sense of the structure of a box plot on paper (MP7). They notice that, unlike the dot plot, it is not possible to know all the data points from a box plot. They understand that the box plot summarizes a data set by showing the range of the data, where the middle half of the data set is located, and how the values are divided into quarters by the quartiles.

### Learning Goals

Teacher Facing

• Compare and contrast (orally) a dot plot and a box plot that represent the same data set.
• Create a box plot to represent a data set.
• Describe (orally) the parts of a box plot that correspond with each number in the five-number summary, the range, and the IQR of a data set.

### Student Facing

Let's explore how box plots can help us summarize distributions.

### Required Preparation

For the Human Box Plot activity:

• Each student will need the index card that shows their name and the number of letters in their name (used for the Finding the Middle activity), as well as a class data set.
• Compile the numbers on the cards into a single list or table. Prepare one copy of the data set for each student.
• Have some extra index cards available for students who might have been absent in that earlier lesson.
• Prepare five index cards that are labeled with "minimum," "maximum," "Q1," "Q2," and "Q3."
• Make a number line on the ground using thin masking tape (0.5 inch). It should show whole number intervals and span at least from the lowest data value to the highest. The intervals should be at least a student's shoulder's width.
• Prepare a roll of wide masking tape (2- or 3-inch wide) to create a box and two whiskers on the ground.

### Student Facing

• I can use the five-number summary to draw a box plot.
• I know what information a box plot shows and how it is constructed.

### 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 $$12-3=9$$.

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