Unlike other numbers, averaging percentages is seldom a matter of just adding them together and then dividing. Because the numbers each percentage represents may be different – like 10 percent of a large group of people compared to 12 percent of a small group – you need to factor in the base numbers in order to find the percentage average.
A percentage is a proportion, or ratio, that states the number of parts per 100. For example, if 40 percent of the pencils in a box of 100 pencils are red, this means 40 of the pencils are red. If another box contains 20 pencils, then 40 percent means only eight pencils are red.
Convert Percentages to Decimals
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 percent 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 Percentages by the Numbers They Represent
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 percent 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 percent 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 Represented Numbers
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.
Next, 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
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 percent.