Graduate Management Admission Test (GMAT) Practice Test

Can an overall average be derived from weighted averages?

1. Yes

2. No

3. Only under certain conditions

4. It depends on the data set

The correct answer is: Yes

An overall average can indeed be derived from weighted averages. When calculating a weighted average, each group in the dataset contributes to the overall average based on its size (weight) and its average value. This means that if you have multiple groups with their own weighted averages, you can combine these to determine an overall average. To derive the overall average, you multiply each group’s weighted average by its weight (the number of data points in that group), sum these products, and then divide by the total number of data points across all groups. This process ensures that each group's contribution to the total average reflects both its size and performance, ultimately leading to a meaningful overall average. In this context, the derivation of an overall average is not conditional on the specific nature of the data set beyond the requirement that there must be groups and their respective weights to consider. Therefore, the answer affirming that an overall average can be calculated from weighted averages is a straightforward and accurate principle in statistics.