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, except that few students got scores much less than the mean. B. Most of students' test scores are around the mean. C. 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. D. Most of students' test scores are around the mean, except that few students got scores much greater than the mean. Clear all Check answer
Solution
Step 1 ：The range of a set of data is the difference between the highest and lowest values in the set. On the other hand, the standard deviation is a measure of how spread out numbers are from the mean.
Step 2 ：If a set of test scores has a large range but a small standard deviation, it means that most of the scores are close to the mean (small standard deviation), but there are a few scores that are much higher or much lower than the rest (large range).
Step 3 ：Therefore, the correct answer should be C. 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.
Step 4 ：\(\boxed{\text{C. Most of students' test scores are around the mean, except that few students got scores much greater than the mean and few students got scores much less than the mean.}}\)
