PSAT Math Grid-Ins Question 79: Answer and Explanation

Question: 79

The average (arithmetic mean) of the data list {2, 4, 5, 8, 9, x, 3} is 5. What is the value of x ?

Correct Answer: 4

Explanation:

4

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 requires finding the value of x in the given data set using the average of the data set. The values given in the data, besides x, are: 2, 4, 5, 8, 9, and 3. The average is given as 5. To find the missing value x, plug the known values into the average formula and solve for x:

Grid in 4 as the correct answer.

Alternatively, to use the balance approach, write down how much each value is above or below the average of 5. For example, the first value of 2 is 3 below the average: 2 - 5 = -3.

Now, observe that, excluding the variable, the values are -3 + (-1) + 0 + 3 + 4 + (- 2) = 1. Without the variable, the total is 1 more than what you'd expect based on the average. So for the values to balance out to the average, the variable value must be one less than the average of 5, or 5 - 1 = 4. Grid in 4.