1. Use the data from the population in and find the population variance.

2. Consider the following three samples:

I 122333 445

II 7 8 8 9 9 9 10 10 11

III 1 1 1 2 2 3 4 4 5 5 5

a. Graph the frequency distribution for each of the three samples.

b. Compute the average of each sample.

c. Compute the variance of each sample.

d. Compare the average of samples I and II. What characteristic of the two data sets explains the difference in the averages?

e. Notice that the variances of sets I and II are equal. What geometric property of these two distributions accounts for this equality?

f. Note that sets I and III have the same average. Why is this possible for two data sets that seem so different?

g. Compare the shape of distributions I and III. Why would you expect the variance of I to be smaller than the variance of III?