24. Cut up 90 small slips of paper, and write each number from 1 to 9 on 10 slips each. Put the slips in a large bowl and mix them up.

(a) Take out a slip, write down the number on it, and put it back. Do this 20 times. Make a histogram, and figure the mean and the variance of the result. You should get an approximately rectangular distribution.

(b) Take two slips out, figure out their mean, write it down, and put the slips back.7 Repeat this process 20 times. Make a histogram;

then figure the mean and the variance of this distribution of means. The variance should be about half of the variance of the distribution of individual scores.

(c) Repeat the process again, this time taking three slips at a time. Again, make a histogram and figure the mean and the variance of the distribution of means.

The distribution of means of three slips each should have a variance of about a third of the distribution of individual scores. Also note that as the sample size increases, your distributions get closer to normal. (Had you begun with a normally distributed distribution of slips, your distributions of means would have been fairly close to normal regardless of the number of slips in each sample.)