Question

if a set of test scores has a large range but a small standard deviation, describe what this means about students performance on the test.
choose the correct answer below.
a. most of students test scores are around the mean.
b. most of students test scores are around the mean, except that few students got scores much greater than the mean.
c. most of students test scores are around the mean, except that few students got scores much less than the mean.
d. most of students test scores are around the mean, except that few students got scores much greater than the mean and few students got scores much less than the mean.

Explanation:

• Range is the difference between the maximum and minimum values. A large range means there is a big spread between the highest and lowest scores.
• Standard deviation measures the average amount of variation or dispersion of a set of values. A small standard deviation indicates that most of the data points are close to the mean.

So, if there is a large range but a small standard deviation, it means most scores are clustered around the mean (due to small standard deviation), and the large range is caused by a few extreme values (either very high or very low).

Answer:

D. Most of students' test scores are around the mean, except that few students got scores much greater than the mean and few students got scores much less than the mean.