Apply the information you have already learned about measures of central tendency—such as the mean, median, and mode—and measures of variability—such as the range, standard deviation, and variance—to the four ways distributions can differ (i.e., average value, variability, skewness, and kurtosis). Imagine you are reviewing the midterm exam grades of students in three different sections of a “Counseling Theories” class. Draw yourself pictures of the distributions if that will help you think through the answers. The Section Two students learned about the cheating that occurred in the “Counseling Theories” Section One class because when you—the faculty member—decided to give them an opportunity to cheat as well, the results of the Section Two class were rather different.

Question

The results of Section Two indicated that there was not such a small standard deviation this time, and the median was higher than the mean. After class, you received an e-mail from a student indicating the advanced notice of the cheating opportunity and that not everyone cheated; some of them kept their integrity and did their work themselves, even if their results would be lower test scores than the others. To be more explicit, the mean score of the exam was higher than the previous Section One cheating incident, but there was more of a tail to the left of the distribution. Please label which of the fours ways in which this distribution differs from normal. Then, give the specific name to this shape of distribution.

What will be an ideal response?

Answer 1

ANS:
These exam scores differ in skewness. The evidence that the median was higher than the mean and that the tail to the left was longer combine to indicate that there was negative skewness. There was a clump of very high pop quiz scores, but there were still some scores that were lower.