# Lesson 7

Using Histograms to Answer Statistical Questions

### Lesson Narrative

In this lesson, students create, read, and interpret histograms (MP2). They characterize the distribution displayed in a histogram in terms of its shape and spread, and identify a measurement that is typical for the data set by looking for the center in a histogram (MP7). Students also use histograms to make comparisons and to better understand what different spreads and values of center mean in a given context.

### Learning Goals

Teacher Facing

• Compare and contrast (in writing) histograms that represent two different data sets measuring the same quantity.
• Critique (orally) a description of a distribution, recognizing that there are multiple valid ways to describe its center and spread.
• Describe (orally and in writing) the distribution shown on a histogram, including making claims about the center and spread.

### Student Facing

Let's draw histograms and use them to answer questions.

### Student Facing

• I can draw a histogram from a table of data.
• I can use a histogram to describe the distribution of data and determine a typical value for the data.

### Glossary Entries

• center

The center of a set of numerical data is a value in the middle of the distribution. It represents a typical value for the data set.

For example, the center of this distribution of cat weights is between 4.5 and 5 kilograms.

• distribution

The distribution tells how many times each value occurs in a data set. For example, in the data set blue, blue, green, blue, orange, the distribution is 3 blues, 1 green, and 1 orange.

Here is a dot plot that shows the distribution for the data set 6, 10, 7, 35, 7, 36, 32, 10, 7, 35.

• frequency

The frequency of a data value is how many times it occurs in the data set.

For example, there were 20 dogs in a park. The table shows the frequency of each color.

color frequency
white 4
brown 7
black 3
multi-color 6

• histogram

A histogram is a way to represent data on a number line. Data values are grouped by ranges. The height of the bar shows how many data values are in that group.

This histogram shows there were 10 people who earned 2 or 3 tickets. We can't tell how many of them earned 2 tickets or how many earned 3. Each bar includes the left-end value but not the right-end value. (There were 5 people who earned 0 or 1 tickets and 13 people who earned 6 or 7 tickets.)

The spread of a set of numerical data tells how far apart the values are.

For example, the dot plots show that the travel times for students in South Africa are more spread out than for New Zealand.