AI averaged two percentages. Does that give the rate for everyone?

Keep each numerator and denominator. To pool the same outcome across non-overlapping groups, divide total successes by total eligible cases.

First say whether you want the average group rate or the rate across all cases. They answer different questions when the groups have different sizes. NIST’s weighted-mean formula makes the role of the weights explicit.

A 50% answer can hide a 26% overall rate

In our invented example, group A has 8 successes in 10 cases: 80%. Group B has 18 in 90: 20%. The simple average of the two rates is 50%, but pooling cases gives (8+18)/(10+90)=26%. We checked both calculations.

Tell AI which question to answer

Suggested input: “Calculate the success rate across all cases. Show each group’s numerator and denominator, then the summed numerator and denominator. Do not give each group equal weight unless I ask for an average group rate.” This is a suggested prompt, not a tested AI response.

Only combine comparable counts

Our example assumes the same success definition and time period, with every case in exactly one group. Check those conditions in a real report. Repeated cases, different definitions or rounded rates without counts can prevent a valid pooled calculation.

Missing counts should stay missing

If AI has only percentages and no group sizes, ask it to state that the pooled rate is not established. Equal group weighting may be a deliberate reporting choice, but it should be named rather than silently substituted for the all-case rate.

Published October 14, 2026. Only the invented arithmetic was tested locally. No real report, survey weighting method or AI service was evaluated; sample-size pooling is not a universal recipe for every weighted metric.

Sources: NIST · Weighted mean.