How to calculate averages of percentages

A percentage is a proportion (or ratio) that states the number of parts or items per 100. For example, if 37 per cent of the pencils in a box of 100 pencils are red, this means 37 of the pencils are red. Percentages for more than one category can be averaged, but it can be a little tricky. In most cases you can’t simply add the percentages together and divide by the number of categories to find the average percentage. This is because the number of items in each category may be different.

Convert each percentage to its decimal form to make calculation easier. In decimal form it’s usually simpler to enter the numbers into a calculator. Divide each percentage by 100 to convert. For example, 37 per cent in decimal form is calculated by dividing 37 by 100 to get 0.37. Do the same for all the percentages in the problem.

Multiply the percentage for each category by the total number of items in each category to find the actual number of items represented by the percentage. For example, let’s say 37 per cent of a box of 200 red pencils has been removed from the box, which is 0.37 x 200, or 74 red pencils removed. Suppose 42 per cent of a box of 300 blue pencils has also been removed. That means 0.42 x 300, or 126 blue pencils, have been removed.

Add the actual number of items represented by each percentage together. For instance, add the number of red and blue pencils removed together. For 74 red and 126 blue pencils used, you get 200 pencils removed overall.

Add the total items in each category together. In the example, the boxes of pencils started with 200 pencils in one and 300 pencils in the other, so 200 plus 300 equals 500.

Calculate the average percentage by dividing the total items represented by percentages by the overall total of items. In the example, a total of 200 pencils were removed out of a total of 500 pencils. Divide 200 by 500, which is equal to 0.40. Convert to percentage form by multiplying 0.40 by 100. The average percentage removed equals 40 per cent.

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