# Histograms Manage a Flood of Data

**OBJECTIVE**

Students will understand:

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

Alignment with NCTM Standards (PDF)

**MATERIALS**

Activity 2 (PDF); Calculator

**REPRODUCIBLES**

**DIRECTIONS**

- 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.
- Give students this example: If a histogram showed the number of books students read during several months (in intervals) on the x-axis, the y-axis would show the number of students.
- Explain that actuaries can use histograms to compare ranges of data—e.g., about populations—and graph the mean.
- Review the definition of
*mean*. The mean in this activity represents the single amount of money each person filing a claim would have to pay so that the total amount would cover the costs of all claims, regardless of individual claim amounts. For example, if 5 different people have the following claim amounts—$10, $15, $25, $30, $100—then the mean would be $36. Note: This is not how premiums are determined. This example is used to illustrate the concept and definition of*mean*. - Distribute copies of Histograms Manage a Flood of Data (PDF).
- Tell students to examine information in the table and draw bars to graph the data. Remind students that there should be no gaps between the bars. The average paid claim amounts are between the ranges labeled below the horizontal axis.

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.

Background:

For more about floods, visit www.floodsmart.gov and www.fema.gov/hazard/flood/index.shtm.

**HOME CONNECTION**

Welcome Families (PDF)

Family Activity 1: Insuring for the Uncertain (PDF)

Family Activity 2: Banking on Inflation (PDF)

Family Activity 3: Planning for the Future (PDF)