This online Average of Percentages Calculator performs calculation of the average of a number of percentages. One can choose the case when all the percentages to be averaged correspond to samples of the same size or different sizes. To add or subtract a percentage in the list of percentages click the “+” symbol or the “–” symbol respectively.
How to calculate average percentages
Percentage is a proportion or ratio that indicates the number of parts per 100. For example, if 40 percent of the pencils in a box of 100 pencils are red, that means 40 pencils are red. If there are 60 pencils in another box, then 40 percent means that only 24 pencils are red.
Unlike other numbers, averaging of percentages is rarely a matter of adding and then dividing them. Since the numbers represented by each percentage can be different – for example, 10 percent for a large sample versus 15 percent for a small sample – you need to consider the base numbers to find the average percentage.
Let’s take two boxes of pencils from the above example. Suppose that the box of 100 pencils contains 40 percent of red pencils, and the second box of 60 pencils contains 80 percent of red pencils.
The average percentage of red pencils in two boxes is obviously calculated as the ratio of the sum of red pencils to the total number of pencils in two boxes multiplied by one hundred. In other words: (40% * 100 + 80% * 60) / (100 + 60) = 55%. A simple arithmetic mean of these two percentages would give us the wrong result: (40% + 80%) / 2 = 60%.
So we come to the general formula for the average of percentages:
$$\bar{p} = \frac{p_{1}s_{1}+p_{2}s_{2}+p_{3}s_{3}+…}{s_{1}+s_{2}+s_{3}+…},$$
where:
\(\bar{p}\) is the average of percentages;
\(p_{i}\) is the percentage in the sample number \(i\);
\(s_{i}\) is the size of the sample number \(i\).
Note, that in case when all the samples are of the same size we get the formula for a simple arithmetic mean and we don’t actually need to know the sample size.
Our Average Percentage Calculator is the easiest way to find the average in question for an arbitrary series of data samples of the same or different sizes.
Related calculators
Check out our other percentage calculators such as Percent Error Calculator or Percentage Increase Calculator.