PSAT/NMSQT Prep 2022 - Eggert M.D., Strelka A. 2022

On test day
Tables, statistics, and probability
Data analysis

The PSAT tests the concept of average (arithmetic mean) fairly heavily. The average formula will serve you well on questions that ask about a sum of values or the average of a set of values, but for questions that give you the average and ask for a missing value in the data set, there is an alternative that can be faster: the balance approach.

The balance approach is based on the idea that if you know what the average is, you can find the totals on both sides of the average and then add the missing value that makes both sides balance out. This approach is especially helpful if the values are large and closely spaced. Imagine that a question gives you the set {976, 980, 964, 987, x} and tells you that the average is 970. You would reason as follows: 976 is 6 over the average, 980 is 10 over, 964 is 6 under, and 987 is 17 over. That’s a total of 6 + 10 − 6 + 17 = 27 over, so x needs to be 27 under the average, or 970 − 27 = 943.

Try solving the question below both ways, using first the average formula and then the balance approach. If you find the latter to be fast and intuitive, add it to your test day arsenal.

23. 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?

The correct answer and both ways of solving can be found at the end of the chapter.