SAT Math Multiple Choice Question 773: Answer and Explanation
8. Class A: 68, 79, 88, 91, 97, 98, 99
Class B: 85, 85, 85, 88, 88, 90, 90
The lists above indicate the tests scores, in increasing order, for two of Mr. Pearlman's classes, each of which has 6 students. Which of the following correctly compares the standard deviation of the scores for each class?
- A. The standard deviation of the scores in Class A is smaller.
- B. The standard deviation of the scores in Class B is smaller.
- C. The standard deviations of the scores in Class A and Class B are equal.
- D. The relationship cannot be determined from the information given.
Correct Answer: B
Problem Solving and Data Analysis (data spread) MEDIUM
As we discussed in Chapter 8, Lesson 3, the standard deviation of a set of numbers tells us how "spread out" the data are from the average-the greater the standard deviation, the greater the spread from the average. It should be clear by inspection that the scores for Class B are more "clustered" than the scores for Class A. For instance, there is only a 5-point difference between the lowest and highest scores in Class B, but a 31-point difference between the lowest and highest scores in Class A. This means that the standard deviation of the scores in Class B is smaller.