Histograms Manage a Flood of Data
STANDARDS (CCSS AND NCTM)
- 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
- Standards Chart: Common Core State and NCTM Standards (PDF)
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.
Activity 2 (PDF); Calculator
Introductions to Histograms
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.
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.
3. Explain that actuaries can use histograms to compare ranges of data—e.g., about populations—and graph the mean.
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.
5. Guided Practice: 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.
6. Independent Practice: Distribute copies of Histograms Manage a Flood of Data (PDF).
Check for Understanding: Review worksheet answers with the class.
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.