Combined Mean
A combined mean is the average of two or more groups taken together. The key idea is that you must combine the totals first, then divide by the combined number of data values.
Method
- Find each group total
- If a group mean and group size are given, multiply them to get that group’s total.
- If totals are already given, use them directly.
- Add the totals
- This gives the sum of all values in every group.
- Add the group sizes
- This gives the total number of values.
- Divide
- Combined mean = total of all values ÷ total number of values.
- Simplify your answer
- Write the result in lowest terms if it is a fraction, or as a simplified decimal when appropriate.
Check your work
- The combined mean should usually lie between the smallest and largest group means.
- If one group is much larger, the combined mean should be closer to that group’s mean.
Common mistake to avoid
Do not average the means directly unless the groups have the same size. Weighted information matters, so the group sizes must be included.
Use this method every time: totals first, then divide by the total number of data values.