Combine Percentages When Group Sizes Differ

Define the combined question

Team A reviews ten fictional forms and finds the chosen field on nine. Team B reviews thirty forms and finds it on eighteen. Each form appears once, both teams use the same criterion, and their review periods match. These assumptions make the records compatible for this exercise.

The question asks what proportion of all forty reviewed forms contained the field. It does not ask for the average team score, the quality of the entries or an official audit result. Naming the unit as a form keeps those different questions separate.

Combine the underlying counts

Add numerators and denominators separately: (9 + 18)/(10 + 30) × 100 = 67.5%. Averaging 90% and 60% gives 75%. That calculation weights each team equally despite the different numbers of forms. It answers a different question, so it needs a different label.

Check whether combination makes sense

If the teams reviewed some of the same forms, adding their counts would double-count those records. If one counted signatures while the other counted complete histories, their criteria would differ. A neat calculation would not repair either problem. Reconcile definitions and duplicates before combining.

Weights must match the reporting question. This exercise weights each form equally. It does not establish weights for an examination, certification assessment or audit. If a report is deliberately designed to weight each site equally, say so. Do not substitute one convention simply because its result looks better.

Keep the total and the component rows

Write: “Across forty distinct forms reviewed with the same criterion, twenty-seven contained the field, or 67.5%.” Retain the group rows because they show a difference the total could conceal. The combined number describes scale; the rows help identify where further inquiry belongs.

In a spreadsheet, calculate from count columns and format the result as a percentage afterward. Avoid building totals from already rounded percentages. Check that matching counts never exceed reviewed counts and that every row uses the intended period. If a denominator is unavailable, disclose the missing value rather than giving that group an invented weight.