What is the Average of Averages?
In statistics and data analysis, the "average of averages" (also known as the mean of means) is the result of taking multiple distinct groups of data, calculating the arithmetic mean for each group, and then calculating the mean of those individual results. While this is a common operation in Excel, it requires caution because it can lead to misleading results if the sample sizes of the original groups are not identical.
How to Calculate it in Excel
To perform this calculation in Excel manually, you follow a two-step process:
- Step 1: Calculate the average for each range using the
=AVERAGE(range)formula. For example, if your data is in columns A and B, you might use=AVERAGE(A1:A10)in cell C1 and=AVERAGE(B1:B10)in cell C2. - Step 2: Calculate the average of those results. Use the formula
=AVERAGE(C1, C2).
The Mathematical Danger: Weighted vs. Simple Averages
When you calculate the average of averages in Excel, you are treating every group as having equal weight. However, if Group A has 100 entries and Group B has only 5 entries, the simple average of their means does not represent the true mean of the entire population. In such cases, you should use a Weighted Average or simply calculate the average of the entire raw dataset at once using =AVERAGE(A1:B10).
Frequently Asked Questions
Is the average of averages the same as the grand average?
Only if all the groups have the same number of data points. If the counts differ, the grand average (total sum divided by total count) will differ from the average of averages.
When should I use this calculator?
This tool is perfect for quick comparisons when you already have pre-calculated summary statistics from different reports and need to find the midpoint between those summary figures.