How To Calculate The Percentage Of Something From A Data Set

Percentages are useful in today's world. The are just another way of expressing fractions, but they are always fractions of 100. Understanding how to find a percentage from a data set can make using percentages more meaningful, and it can be a helpful skill in itself.

When you compile a data set, each value (x) can be expressed as a percentage of the entire set. To calculate this you first start by summing up all the values in the set (∑x₁...x_n) and make this sum the denominator of a fraction. The number for which you want the percentage becomes the numerator. Convert to decimal form and multiply by 100 to get the percentage.

In mathematical notation:

\(x\% = \frac{x}{(∑x_1...x_n)} × 100\)

The following is an outline of the procedure:

Step 1

Suppose you would like to know information about your shoe collection. You have three pairs of white shoes, two pairs of red shoes, two pairs of gray shoes and five pairs of black shoes – 12 pairs total. If you would like to find out what percentage of your shoes are black, first write the percentage fraction as the number 5 above the number 12, with a line drawn between the two horizontally.

Step 2

Divide using the calculator to find the percentage in decimal form. Divide the top number – the number of pairs of black shoes – by the total number of shoes, 12. The answer, when rounded, is 0.42.

Step 3

Multiply the decimal by 100, since 12 is 100 percent of the total. This will bring your decimal answer to whole-integer form, 42.

Step 4

Place a percentage sign behind the answer, as this is your percentage of black shoes out of a total of 12 pairs – 42 percent.