4.2.2—A pooled estimate of a population

When samples estimate a common population mean, a pooled estimate weights each sample mean by its sample size: x̄=(n₁x̄₁+n₂x̄₂)/(n₁+n₂). Variance pooling requires its own assumptions.

Pool only when the samples target the same parameter and independence and comparable modelling assumptions are reasonable. Do not average sample means equally unless sample sizes match.

Means 12 from n=20 and 15 from n=10 give pooled mean (20·12+10·15)/30=13, not 13.5.

Pooling cannot repair biased sampling, and a pooled mean does not imply the two populations have identical distributions.