PSAT Math Multiple-Choice Question 507: Answer and Explanation

Question: 507

Strawberry	Chocolate Coating (g)
1	17.8
2	22.5
3	19.1
4	20.6
5	16.3
6	18.9
7	?

Chris is coating strawberries in chocolate for dessert. The table above displays 6 strawberries and their corresponding amounts of chocolate coating in grams (g). If Chris adds a 7th strawberry coated in chocolate, what is one possible value for the amount of chocolate coating that would decrease the mean of the data but increase the range?

• A. 15.8 g
• B. 17.1 g
• C. 19.2 g
• D. 23.1 g

Correct Answer: A

Explanation:

A

The question asks for a value that decreases the mean but increases the range. Since the question asks for a specific value and the answers contain numbers in increasing order, plug in the answers. Begin by labeling the answers as "chocolate coating in grams." Before plugging in the answers, calculate the original mean and range. Since the range is easier to calculate than the mean, start with range. The range of a list of values is the greatest value minus the least value. According to the table, the greatest value is 22.5 and the least value is 16.3. The greatest minus the least is 22.5 – 16.3, or 6.2. To find the value that increases the range, the value must not be between the greatest and least values in the table. Eliminate (B) and (C) for this reason. For averages, use the formula T = AN, in which T is the total, A is the average, and N is the number of things. The Total is 17.8 + 22.5 + 19.1 + 20.6 + 16.3 + 18.9 = 115.2 and the Number of things is 6, so the formula becomes 115.2 = A(6). Divide both sides by 6 to find that A = 19.2. Since (A) and (D) satisfied the requirement for an increased range, use them to find the new mean. To find the new mean using 15.8, use the formula T = AN. The new Total is 115.2 + 15.8 = 131, and the new Number of things is 7. The formula becomes 131 = A(7), then divide both sides by 7 to find the new A = 18.7, which is lower than the original average. Since the value in (A) also satisfies both requirements, stop here. The correct answer is (A).