Stat 100

A workbook/notes for an online course in beginning statistics can be found at The main text for the course is Statistics by Freedman, Pisani, and Purves.

We use the Data Program for analyzing data, and the Box Model Program for simulations.

Here are a couple of illustrations from the Box Model program.

The central limit theorem (histogram of sums)

To see the histogram of a sum of independent draws of tickets from a box (i.e., with replacement), enter into the "Box" area some numbers for the tickets. For example, if you type '0,0,0,0,0,0,1,2,3,4,5,6,10,10,10,' you create a box with six 0's, three 10's, and one each of 1, 2, 3, 4, 5, and 6. Press 'OK' to see the histogram of the tickets (one draw), as well as the histograms of the sum of two, three, four, and five draws. Press "More draws" to see the histograms for higher sums. Are they getting more normal-curve looking?

Confidence intervals

The example here uses the box with '1,2,3,4,5,6,' as if rolling a fair six-sided die. You can choose the number of rolls ("# Draws per sample," whose default is 10), then press one of the "More sample" buttons to see that number of confidence intervals. These are z-intervals. About 95% should have the box average, 3.5, in them.