Protocol
Weight a combined average by what it represents
A tiny group does not acquire equal weight because its result occupies one spreadsheet cell.
When it fits
- You need one average from groups of different sizes.
When to avoid it
- Rounded group means produce an approximate combined mean; incompatible groups may not deserve pooling at all.
Why it matters
Recover each group's total from its mean and count, add the totals, then divide by the combined count. An average of group averages answers a different question unless equal group weighting is intentional.
Steps
- Check that the groups measure compatible observations.
- Multiply each mean by its corresponding count.
- Divide the sum of those products by the total count.
An example
Ten cases averaging 10 minutes and ninety averaging 20 minutes give a combined mean of 19 minutes, not 15.
Check your result
The weighting matches whether you mean the average case, person, group or period.
Keep this limit in mind
- Rounded group means produce an approximate combined mean; incompatible groups may not deserve pooling at all.
Connected ideas
Useful withChoose the average that fits the questionCompare with
Build an overall rate from totals
Evidence and sources
Supports
The mean of combined groups is the sum of each group mean multiplied by its count, divided by the total count.
Groups must concern compatible observations and the counts must represent the intended weighting.
Introductory Statistics 2e, 2.5: Measures of the Center of the Data · Mean equals total divided by count; weighted-frequency expression