Graduate Management Admission Test (GMAT) Practice Test

What is the sum of differences between each term and the average?

1. 0

2. 1

3. It cannot be determined

4. Varies based on sample size

The correct answer is: 0

The sum of differences between each term in a set of data and the average of that set is always equal to zero. This is because the average (or mean) is defined as the sum of all the terms divided by the number of terms. When you calculate the difference between each term and the average, you are essentially measuring how far each term is from the mean. If you sum these differences, you are adding positive differences (from terms above the mean) and negative differences (from terms below the mean). Since each positive difference has a corresponding negative difference that balances it out, the total sum will always equal zero. For example, consider a simple set of numbers such as 2, 4, and 6. The average of these numbers is 4. The differences from the average are -2 (for 2), 0 (for 4), and +2 (for 6). When you sum these differences, you get -2 + 0 + 2 = 0. This concept applies regardless of the size of the sample; thus, the total will always remain zero, not varying based on the number of terms in the set.