The average of a set of numbers is also known as the arithmetic mean or average value. It’s simple to calculate. Read on to find out how to calculate the average of a set of numbers, and whether it’s always useful.
What Is the Average?
The average of two or more numbers is the sum of those numbers divided by the count, or how many numbers you want to average. It’s also known as the arithmetic mean.
Is There More than One Kind of Average?
The arithmetic mean isn’t the only average. Below are a few other types:
- Geometric mean
- Harmonic mean
- Weighted mean
However, the arithmetic mean is usually the only kind referred to simply as average.
How to Calculate the Average of a Set of Numbers
Here’s how to calculate the average of a sum of numbers:
- Add the numbers
- Divide the sum by the number of values you just added
Say you want to find the average of five numbers: 7, 11, 15, 21, and 22. Going by the above formula, here’s how to do it.
First, add the numbers:
7 + 11 + 15 + 21 + 22 = 76
Second, divide the sum by the number of values you just added:
76 ÷ 5 = 15.2
The average or arithmetic mean is 15.2
Why is the Average Useful?
The average gives you an overall picture of a situation. Say you’re a coffee drinker who’s going to spend a weekend house-sitting for a friend who doesn’t drink coffee. You want to get a general idea of how much coffee you drink so you can buy enough beans to last you there.
In order to do this, you keep a record for the entire preceding week then add up the numbers.
Now you divide 16 by the number of days:
16 ÷ 7 = 2.3
Your average is 2.3 cups of coffee a day. Now you can plan accordingly to make sure you don’t run out of coffee during your stay.
When is the Average Misleading?
Certain situations or groups of numbers have a few wildly different values or outliers. These can skew the result if you calculate the average, giving you a misleading overall picture.
For instance, say you want an overall idea of the allowance each of the 20 students in your kid’s class gets. Ten of them get an allowance of $12 a week, eight get $15, whereas the remaining two get $75. Here’s how these two outliers will skew the whole equation.
Add all the allowances and divide by the number of students:
390 ÷ 20 = 19.5
The average, 19.5, misrepresents the group. In this case, the median should be used instead.
So there you have it: To measure the average or arithmetic mean, simply add up all the numbers, divide them by the number of numbers, and you’ve got your average.