Question

consider the exam scores for 59 students when 7 students scored between 90 and 100, 12 students scored between 80 and 89, 21 students scored between 70 and 79, and 19 students scored below 70, with their scores spread out to a low of 40. complete parts a through d.

a. how many peaks would you expect for the distribution?

a. there would probably be two peaks, because even though each exam score could be anywhere between 0 and 100, the scores were clustered between 80 to 89 and between 70 to 79

b. there would probably be no peaks. the distribution of grades always tends to be uniform

c. there would probably be many peaks corresponding to the different exam scores that each student had

d. there would probably be one peak because there are no obvious reasons why the exam scores would form different groups

Explanation:

To determine the number of peaks, we analyze the score clusters. The scores have two clusters: 21 students (70 - 79) and 12 students (80 - 89), which are relatively large groups. A peak in a distribution corresponds to a cluster of data. Since there are two distinct clusters (70 - 79 and 80 - 89) with significant counts, we expect two peaks. Option A correctly identifies this by noting the clustering in these two ranges. Option B is wrong as grade distributions aren't always uniform. Option C is wrong because individual scores don't create many peaks; clusters do. Option D is wrong as there are obvious clusters (two groups with high counts).

Answer:

A. There would probably be two peaks, because even though each exam score could be anywhere between 0 and 100, the scores were clustered between 80 to 89 and between 70 to 79