Data Matters with Fathom! Dynamic Statistics™ software

Activity 5.2

There are two tasks in this project.

1. Take many random samples from the representative U.S. sample and save the samples’ means, then get a histogram of the samples’ means.
2. Collect a distribution of proportions that is normally distributed and check the symmetry.

Here’s how to do them.

1. Take many random samples from the representative U.S. sample and save the samples’ means. Get a histogram of the samples’ means.

Open RepUSSampleMarch2001.ftm.

Click on the collection, select Analyze, Sample Cases. Press “Ctrl-I” and pick whatever sample size you want to work with. Decide whether you want Animation on or off, then set it.

Click on the Measures tab. Add a measure, Mean, with the formula mean([your attribute]), replacing [your attribute] with whatever attribute you want to work with.

Select Analyze, Collect Measures.

You might as well add the histogram now. Drag a case table onto the workspace so you can see the data. Drag a new graph onto the workspace and drag the measure, Mean, onto Drop an attribute here.

Select the Measures Collection again and press “Ctrl-I” to get the Collection Inspector. Set Animation how you want it and set the number of measures to however many you would like above 400. (Otherwise, you won’t be able to see the distribution very well.)

How would you describe the distribution? What is the mean? What is the median?

Use the Collection Inspector on the Sample Collection to change the sample size. Does the sample size make a difference?

2. Collect a distribution of proportions that is normally distributed and check the symmetry.

Open the workspace of one of the projects where we took samples and recorded their proportions. For example, the project in Section 3.3 has proportions from random samples. If your probability was near 0 or near 100% and your sample size is small, the distribution won’t be normal. Inspect and edit the original collection to set the probability near 50%.

If you don’t have copies of your workspaces, go back and follow the steps to collect proportions from random samples.

Get the mean and median of one of the proportions: Select Analyze Parameters, Estimate Parameters, then Empty Estimate, Estimate Mean. To get the mean, drag a proportion onto Attribute (continuous): <unassigned>. Sort the proportions (right-click on the proportion and select Sort Ascending) and scroll down to get the median.

Does it appear that the distribution is symmetrical? Try other sample sizes. Does sample size matter? Try other probabilities. How do sample size and probability affect the symmetry?