Average Percentage Calculator (simple vs weighted average of percentages)

Understanding the average percentage calculator — concept and principle

This calculator averages percentages correctly. Enter each percentage with the size of its group, and it gives the weighted (pooled) average, which is the true overall percentage, next to the simple average of the percentages, so you can see how far apart they are. Use it for pass rates of classes, survey results from different regions or conversion rates of several campaigns.

How it is calculated

Weighted average P = Σ(pᵢ × nᵢ) ÷ Σnᵢ

Simple average = Σpᵢ ÷ k

Total count = Σ(pᵢ × nᵢ ÷ 100)

• pᵢ is a group's percentage, nᵢ its size and k the number of groups.
• Each line is "percentage, group size". Without sizes, only the simple average is shown.

The principle

A percentage is a count divided by a group size. To get the overall percentage you must go back to the counts: add up all the "yes" items and divide by all the items. That is the same as weighting each percentage by its group size. The simple average gives every group the same say, so a small group with an extreme percentage pulls it as hard as a large group. The two averages agree only when all groups are the same size.

Worked example

Default inputs: 80 % of 50, 60 % of 150, 90 % of 20.

1. Counts: 0.80 × 50 = 40, 0.60 × 150 = 90, 0.90 × 20 = 18; total 148.
2. Total group size = 50 + 150 + 20 = 220 across 3 groups.
3. Weighted average = 148 ÷ 220 = 67.27 %.
4. Simple average = (80 + 60 + 90) ÷ 3 = 76.67 %.
5. Difference = 67.27 − 76.67 = −9.39 percentage points; the weighted average is shown first because it is the true overall percentage.

How to read the result

Use the weighted average when you want the share of all items or people together. Use the simple average only when you want the typical percentage of a group and every group should count equally, such as comparing schools as units. A large gap between the two means group sizes are very uneven and the large groups have different rates from the small ones.

Common mistakes

• Averaging percentages from groups of different sizes without weights.
• Weighting by something other than the base of the percentage.
• Entering counts instead of percentages in the first column.
• Mixing percentages that have different bases, such as share of visitors and share of orders.

Frequently asked questions

Can I just average percentages?

Only if every group has the same size; otherwise weight each by its group size.

How do I average percentages with different totals?

Multiply each percentage by its total, add these, and divide by the sum of the totals.

What is a pooled percentage?

The overall percentage found from all the counts together, the same as the size-weighted average.

Sources: Standard formulas for the weighted mean Σ(wᵢxᵢ)/Σwᵢ and the arithmetic mean