Data Matters with Fathom! Dynamic Statistics™ software

Activity 8.3

A scatter plot is like a statistic. When a researcher gathers data and summarizes them in a scatter plot, there are similarities with what happens when that researcher summarizes the data with proportions and with averages.

To see this, in this project you will take samples from the representative U.S. sample and get scatter plots from those samples. As you replace the samples, you will somewhat see how random sampling affects scatter plots.

Open RepUSSampleMarch2001.ftm. Select Analyze, Sample Cases. Drag a case table onto the workspace. Drag a graph onto the workspace and drag a number-line attribute to the bottom of the graph. Drag another numeric attribute to the left edge of the graph. If you let go of the attribute on the correct spot, the graph will transform into a scatter plot.

Right-click on the scatter plot and select Least-Squares Line. That shows you a line that does a fairly good job of summarizing whatever linear pattern there is in the scatter plot.

Double-click on the Sample Collection and set the sample size to 20, then click on Sample More Cases.

Click on Sample More Cases a bunch of times. See what happens to the scatter plot. Try other pairs of attributes. Try increasing the sample size to 200. How does the increased sample size influence how random sampling affects the scatter plot?

What is the relationship between the image seen in a scatter plot of a sample’s data and the image seen in a scatter plot of the entire population’s data?