Why this pooled completion rate is 72.7% while the branch mean is 60%

Two branches report completion rates of 80% and 40%. Their combined rate is not necessarily 60%. If one branch handled more cases, the pooled result must account for that different denominator.

Here is a complete invented dataset. It represents disjoint cases from the same reporting period, with the same definition of completion. It is a teaching example, not a claim about a customer or business.

Calculate the pooled answer

Add completed cases: 72 + 8 = 80. Add eligible cases: 90 + 20 = 110. Divide the first total by the second: 80 / 110 = 0.72727…, or 72.7% to one decimal place.

To a whole percentage point, the result rounds to 73%. Use one display precision consistently across the summary and table so a reader does not mistake rounding for a disagreement.

Why 60% answers a different question

The arithmetic mean of the two branch rates is (80% + 40%) / 2 = 60%. That gives each branch equal weight. It answers “What is the average of these two branch percentages?”

The pooled rate answers “What share of all eligible cases was completed?” Each eligible case has equal weight, so North contributes more because it handled 90 of the 110 cases.

This is a weighted mean of the branch rates, using eligible-case counts as weights: (90 × 0.8 + 20 × 0.4) / 110. NIST documents the weighted-mean formula as the sum of weighted values divided by the sum of weights. NIST weighted mean reference

Publish the denominator with the result

For a public table, keep the completed and eligible counts available alongside the rate. A reader can then check the calculation and understand why the two branches contribute differently. A column containing only percentages cannot recover those missing counts.

Use a label such as “Completed cases / eligible cases, same reporting period.” If the question instead gives each branch equal importance, publish the 60% mean with that explicit definition. Neither calculation should silently borrow the other’s label.

Check whether pooling is justified

Before adding counts, confirm that the populations do not overlap, the periods align and the eligibility rules agree. If the same case appears in both branches, the calculation above counts it twice. If the definitions differ, an apparently precise pooled number can conceal a mismatch.

Do not reconstruct counts from rounded percentages when exact counts are available. Keep the underlying division precise and round only for display. If the total denominator is zero, report the pooled rate as unavailable rather than forcing it to zero.

For this example, the final summary is 80 completed cases out of 110 eligible cases: 72.7%. That sentence carries the result, denominator and interpretation together, so readers do not have to guess what the average means.

When exporting the result, distinguish the numerical fraction from its display format; the percentage-versus-decimal guide covers that separate step.