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 “Counseling Theories” class had a pop quiz last week, and their quiz scores just came back. While the Section One students were taking the quiz, you had to leave the room for an urgent university matter. You had your suspicions that the class may have cheated.

Question

Now that the quiz results are back, you are even more suspicious because the standard deviation of the Section One scores is very small, showing that there is not much variability (dispersion of the scores from the mean). Please label which of the four ways in which this distribution differs. Then, give the specific name to this shape of distribution.

What will be an ideal response?

Answer 1

ANS:
These exam scores differ in kurtosis. The tight standard deviation, or very little spread, would be illustrated by kurtosis—specifically as a leptokurtic distribution.