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:

The range is calculated as the difference between the maximum and minimum values in a data set. A large range implies that there is a significant spread between the highest and lowest scores. The standard deviation measures the average amount of variation or dispersion of a set of values from the mean. 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 that most of the scores are clustered around the mean (due to the small standard deviation), but there are a few extreme values (high and low) that cause the large range.

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.