Calculating percentages is a standard mathematical procedure. A percent is a ratio that you write as a fraction of 100. In this article, learn why percentages are crucial summary measures and how to calculate them.
What are Percentages?
Percentages express a ratio as a fraction of 100. In other words, they always use 100 in the ratio’s denominator. The word “percent” combines the Latin words “per” (for) and “cent” (hundred). Hence, it’s the amount for every 100.
For example, if 25% of the students ate oatmeal for breakfast, interpret that as 25 out of every 100 students ate oatmeal.
Percentages simplify relative proportions and group comparisons. They standardize ratios on a common scale by expressing a quantity as a fraction of 100, making it easier to compare proportions between groups of different sizes.
For example, the United States and the small country of Belgium have vastly different population sizes (331 million vs. 11.5 million). Suppose 40% of Belgians list pizza as their favorite food, while only 10% of Americans do. The percentages indicate that Belgians have a stronger pizza preference per person despite the population size difference.
In fact, you don’t even need to know the populations of the U.S. or Belgian to understand either percentage.
Percentages are a valuable tool in descriptive statistics. As a relative frequency, they provide a way to understand and summarize the distribution of data.
Learn more about Relative Frequencies and Their Distributions.
Finding percentages involves identifying a subgroup with a property of interest and comparing it to the size of the entire group. In other words, it’s a relative frequency. For example, we might define a subgroup as red balloons and the full group as the number of balloons in the bag.
To calculate a percentage, follow these steps:
- Determine the number of items in the subgroup of interest for the numerator.
- Determine the total group size for the denominator.
- Divide the numerator by the denominator.
- Multiply the decimal by 100 to find the percentage.
Here is how to find a percentage as a formula.
For example, we are interested in red balloons. Our bag contains 18 red balloons, and there are a total of 120 balloons in the bag.
18 / 120 = 0.15
0.15 X 100 = 15%
Therefore, 15 percent of the balloons are red. In other words, there are 15 red balloons for every 100 balloons.
How to Calculate a Percentage of a Number
Now, suppose you know the percentage and the total amount and need to calculate how many items have the property of interest.
To calculate a percentage of a number, do the following:
- Convert the percentage to a decimal by dividing by 100.
- Multiply the decimal by the total amount.
We know that 15% of the balloons are red, and this time we have a bag that contains 360 balloons. Let’s calculate 15% of 360 to find the number of red balloons.
0.15 X 360 = 54.
15% of 360 is 54. Hence, the bag contains 54 red balloons out of a total of 360 balloons.
To learn how to calculate relative changes, read Percent Change: Calculation Steps.