PSAT Math Multiple-Choice Question 236: Answer and Explanation

Question: 236

	Bowling Scores
	Ian	Mae	Jin
Game 1	160	110	120
Game 2	135	160	180
Game 3	185	140	105
Game 4	135	130	160
Game 5	185	110	135
Mean Score	160	130	140
Standard Deviation	22	19	27

Ian, Mae, and Jin bowled five games during a bowling tournament. The table above shows their scores. According to the data, which of the following conclusions is correct?

• A. Ian bowled the most consistently because the mean of his scores is the highest.
• B. Mae bowled the least consistently because the standard deviation of her scores is the lowest.
• C. Mae bowled the most consistently because the standard deviation of her scores is the lowest.
• D. Jin bowled the most consistently because the standard deviation of his scores is the highest.

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Problem Solving and Data Analysis/Statistics and Probability

Getting to the Answer: The keyword in the answer choices is "consistently," which relates to how spread out a player's scores are. Standard deviation, not mean, is a measure of spread so you can eliminate choice (A) right away. A lower standard deviation indicates scores that are less spread out and therefore more consistent. Likewise, a higher standard deviation indicates scores that are more spread out and therefore less consistent. Notice the opposite nature of this relationship: lower standard deviation = more consistent; higher standard deviation = less consistent. Choice (C) is correct because the standard deviation of Mae's scores is the lowest, which means she bowled the most consistently.