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?