PSAT Math Grid-Ins Question 86: Answer and Explanation

Question: 86

	Jerseys	Shorts	T-Shirts	Tank Tops	Sweatshirts	Sweatpants
Red	6	3	4	7	8	8
Green	2	7	5	3	5	4
Blue	8	9	7	5		4

The table above shows the types and colors of sportswear in stock at a sporting goods store. If the mean number of blue articles of clothing in stock is 7, then what is the number of blue sweatshirts the store has in stock?

Correct Answer: 9

Explanation:

9

Difficulty: Medium

Category: Statistics

Strategic Advice: When the goal is to find a missing value in a set of data and the average is given, consider using the balance approach. We'll demonstrate both approaches starting with the average formula.

Getting to the Answer: The question is about blue sportswear, so ignore the data for the other colors. The given numbers for blue sportswear are 8, 9, 7, 5, and 4. The average is given as 7. If you call the missing value x, plugging the known values into the average formula results in the following:

Grid in 9 as the correct answer.

Alternatively, to use the balance approach, write down how much each value is above or below the average of 7. For example, the value for jerseys is 1 above the average: 8 - 7 = 1.

Jerseys	Shorts	T-Shirts	Tank Tops	Sweatshirts	Sweatpants
8: +1	9: +2	7: 0	5: -2		4: -3

Now, observe that, excluding sweatshirts, the values are +1 + 2 + 0 - 2 - 3 = -2. Without the value for sweatshirts, the total is 2 less than what you'd expect based on the average. So for the values to balance out to the average, the sweatshirts' value must be 2 more than the average of 7, or 7 + 2 = 9. Grid in 9.