On this page
Record the fictional group sizes
| Stratum | Population units | Sample units | Sample mean |
|---|---|---|---|
| A | 750 | 20 | 4 |
| B | 250 | 20 | 12 |
Calculate the unweighted pooled mean
The sample has equal counts in A and B, so the pooled mean is (20 × 4 + 20 × 12)/40 = 8. It weights the groups at 50% each. That is the composition of the collected sample, not of the 1,000-unit population.
Calculate the population mean estimator
Population shares are 750/1,000 = 0.75 and 250/1,000 = 0.25. The stratified estimate is 0.75 × 4 + 0.25 × 12 = 6. Within-group random selection and usable observations are assumptions of this exercise.
Preserve what the sample can estimate
Oversampling B may help study B separately, but it does not make B half the population. The two-unit difference between 8 and 6 here comes entirely from weights. These sample means do not reveal the exact population means or a variance estimate without further within-group information.