PSAT Math Multiple-Choice Question 391: Answer and Explanation

Question: 391

	Huiping	Deanna	Katya
Dive 1	8.2	9.0	7.7
Dive 2	7.3	7.1	8.4
Dive 3	8.6	6.5	7.5
Dive 4	8.0	8.6	8.1
Dive 5	9.1	6.1	8.1
Dive 6	8.4	8.9	7.2
Mean Score	8.27	7.70	7.83
Standard Deviation	0.61	1.29	0.45

Huiping, Deanna, and Katya are three varsity divers who recently competed in an exhibition diving meet. Their diving scores for each of their six dives are shown in the above table. According to the data, which of the following is a valid conclusion?

• A. Huiping dived the most consistently because her mean score is the highest.
• B. Katya dived the most consistently because her standard deviation is the lowest.
• C. Katya dived the least consistently because her mean score is the lowest.
• D. Deanna dived the most consistently because her standard deviation is the highest.

Correct Answer: B

Explanation:

B

Difficulty: Easy

Getting to the Answer: Consider the difference between mean and standard deviation: mean is a measure of center, while standard deviation is a measure of spread. The four answers all involve diving consistency, which means the explanation should involve standard deviation. Eliminate (A) and (C). Higher diving consistency means lower standard deviation (and vice versa); the only choice that reflects this—and correctly represents the data in the table—is (B).