# Shake It Up with Scatterplots

**OBJECTIVE**

Students will understand:

- How to use a scatterplot to compare two sets of data to determine if they are related.
- The definition of regression line (the "line of best fit").
- How scientists and actuaries use math and data to study earthquake probability.

Alignment with NCTM Standards (PDF)

**MATERIALS**

Activity 1: Shake It Up with Scatterplots (PDF); Rulers

**REPRODUCIBLES**

**DIRECTIONS**

- Introduce the actuarial profession briefly and define premium. Explain that students will use tools throughout the lessons, similar to those used by actuaries, to strengthen their math, data analysis, and probability skills.
- Tell students they will make a scatterplot and use it to analyze the effects of an earthquake. Explain that a scatterplot compares two different sets of data. Students will use the scatterplot to determine if there is a strong relationship between the variables presented. They will analyze the relationship and discuss effects.
- Ask students what they would like to know about earthquakes if they were to compare two variables to find out if the data are closely related. These variables would become labels on the horizontal and vertical axes of a scatterplot (e.g., intensity and distance from the epicenter).
- Distribute copies of Shake It Up with Scatterplots (PDF) to students. Explain that they will be looking at information about an earthquake event near the real town of Parkfield, California, which is famous for its seismic activity. Explain that the data used here are distance from the epicenter of the earthquake (in kilometers) and intensity at that location. Magnitude is measured at the source of an earthquake, while intensity is measured wherever the earthquake is felt. Often, but not always, the closer to the epicenter, the greater the intensity.
- Instruct students to study the data and plot it in the scatterplot. Students should draw a regression line, or"line of best fit": a straight line that lies close to most, but does not necessarily touch all, points. When students plot the points, they should see that points fall roughly in a straight line indicating that there is a strong relationship between the two sets of data. Discuss effects of the relationship between distance from the epicenter and intensity. How might living closer to the epicenter affect homeowners' decisions about insurance (e.g., they might consider earthquake policies, their homes' building materials, etc.)?

Real-World Connections:

An *actuary* is a statistical expert who determines the financial impact of randomly occurring events like earthquakes, injuries from an accident, even death. Actuaries work primarily in the insurance industry and for state and federal government agencies. Actuaries use math and statistics to determine the probability of major events in a geographic area (like an earthquake in central California). They also use additional information, like the expected magnitude of an earthquake, to help an insurance company set premium rates. A *premium* is the amount paid by a customer, usually annually, for a given amount of insurance coverage.

Background:

For additional information and statistics about earthquakes and their intensity, visit www.ngdc.noaa.gov/seg/hazard/intsrch.shtml. For additional information about the Modified Mercalli Intensity Scale and the Richter Scale, visit http://pubs.usgs.gov/gip/earthq4/severitygip.html.

**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)