### Lesson Plan

# Managing Data With Histograms

Students will learn how a histogram can reveal frequency distribution information. Students will also study a real-world application of how actuaries use histograms to determine the frequency of events and determine risk.

Grades

6–8

### Objectives

**Students will:**

- Understand that a histogram is a type of bar graph that represents frequency distribution
- Understand the definition of
*mean*and how it applies to histograms - Understand how an actuary may use histograms to analyze the frequency of events to determine risk

### Materials

- Shake, Rattle, and Roll Worksheet: Histograms Manage a Flood of Data printable
- Answer Key: Shake, Rattle, and Roll Worksheets printable
- Standards Chart: Shake, Rattle, and Roll printable
- Calculators
- Introducing Shake, Rattle, and Roll: A Letter to Parents printable

- Shake, Rattle, and Roll Family Activity: Insuring for the Uncertain printable
- Shake, Rattle, and Roll Family Activity: Banking on Inflation printable
- Shake, Rattle, and Roll Family Activity: Planning for the Future printable

### Set Up

- Make a class set of the Shake, Rattle, and Roll Worksheet: Histograms Manage a Flood of Data printable.
- Print a copy of the Answer Key: Shake, Rattle, and Roll Worksheets printable for your use.
- Make class sets of the following printables, then staple together in packets to send home with students:
- Introducing Shake, Rattle, and Roll: A Letter to Parents printable

- Shake, Rattle, and Roll Family Activity: Insuring for the Uncertain printable
- Shake, Rattle, and Roll Family Activity: Banking on Inflation printable
- Shake, Rattle, and Roll Family Activity: Planning for the Future printable

- Introducing Shake, Rattle, and Roll: A Letter to Parents printable

### Lesson Directions

### Introduction to Histograms

**Step 1: **Group students into pairs. Ask each student to measure the distance of his or her partner's forearm, i.e., the distance between elbow and fingertip in centimeters. Have each student write his or her measurement on the board.

**Step 2:** Ask students, if they wanted to graph this data, what type of graph would they use? After some discussion, introduce the idea of a histogram. Explain that a histogram is a kind of bar graph showing the frequency with which something happens within given intervals. While bar graphs compare fixed amounts, histograms compare a range of data.

**Step 3:** Explain that actuaries can use histograms to compare ranges of data — e.g., about populations — and graph the mean.

**Step 4:** Review the definition of mean. Ask how we could determine the mean for our set of forearm data. If necessary, point out that the method would be to add up the amount of each measurement and divide by the number of measurements.

**Step 5:** Ask students to produce a histogram of the forearm data on the board and calculate the mean. Ask students to be prepared to explain how they developed the intervals they placed on the horizontal axis.

### Independent Practice

**Step 6:** Distribute copies of the Shake, Rattle, and Roll Worksheet: Histograms Manage a Flood of Data printable. Ask students to complete the worksheet independently.

**Step 7: Check for Understanding:** Review the worksheet answers, included in the Answer Key: Shake, Rattle, and Roll Worksheets printable, with the class.

### Lesson Extensions

### Real-World Connections

Actuaries are often called upon to estimate, based on available data, the likelihood (probability) an area will flood, and to estimate the cost of the resulting damage if flooding does occur. Histograms can be used to provide a good picture of average claim costs to better estimate total costs of insuring a particular geographic area against floods. Actuaries use this information to determine what premium to charge to cover flood damage.

For more about floods, visit the FEMA website.

### Home Connections

Send home the Shake, Rattle, and Roll Family Activity packets, which should include:

- Introducing Shake, Rattle, and Roll: A Letter to Parents printable

- Shake, Rattle, and Roll Family Activity: Insuring for the Uncertain printable
- Shake, Rattle, and Roll Family Activity: Banking on Inflation printable
- Shake, Rattle, and Roll Family Activity: Planning for the Future printable

### Standards

**Grade 6:**Statistics and Probability (**CCSS**6.SP.B.4 and 5)**Grades 6–8:**Make Sense of Problems, Construct Viable Arguments, Model With Mathematics, and Look for and Make Use of Structure (**CCSS**MP1, 3, 4, and 7);**NCTM**Data Analysis and Probability

For more information, download the comprehensive Standards Chart: Shake, Rattle, & Roll printable.