(1) Raw data: { 5 5 5 6 7 }

a. Compute the mean and the median of the raw data in (1) above. Based solely on the relationship between the mean and the median, would you say that the distribution of scores is symmetrical, negatively skewed, or positively skewed?

b. Transform the data in (1) above by subtracting the mean that you computed in (2) from each score. Report the resulting set of transformed scores. Compute the mean of this set of transformed scores.

(Hint: If you start with N=5 scores in (1), you should get 5 transformed scores for (3) -- one for each of the original 5 scores in (1).)

c. Square each of the transformed scores that you obtained in (3). Compute the mean of these squared scores.

d. List all possible samples of size n=3 that you can obtain from the raw data you reported in (1) above. For each sample of size n=3 that you listed, compute the mean of the sample. What is the mean of these sample means.

(Hint: there is a total of 10 ways to choose samples of size n=3 from the N=5 scores you report in (1). So you should get 10 sample means -- one for each of the samples of size n=3 that you list.)