# How to Find an Average

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In mathspeak, what people usually call the "average" is properly known as the "mean" or the "mean number." There are actually two other types of averages – the "mode" and "median" – that you'll learn about when you study statistics. But for most mathematical applications, the term "average" tells you to seek out the mean, which can be calculated with basic addition and division.

#### TL;DR (Too Long; Didn't Read)

To calculate an average, add up all the terms, and then divide by the number of terms you added. The result is the (mean) average.

## How and Why to Calculate the Average

What does it mean to calculate the average or mean? Technically, you're dividing the sum of the values you're working with by the count (or quantity) of number in that set. But in real-world terms, it's more like distributing the value of the entire set evenly among each of its numbers, and then stepping back to see what value the numbers all ended up at.

This type of average is useful for making sense of large data sets or estimating where an entire group stands. For example, you might be asked to calculate the average percentage grade in your class, the average GPA among your fellow students, the average salary for a certain job, the average amount of time it takes to walk to a bus stop and so on.

#### Tips

• What about those other types of averages? If you list all the numbers in your data set from smallest to largest, the "median" is the middle value in that list, and the "mode" is the value that's repeated most often. (If no numbers are repeated, there is no mode for that set of data.)

## Examples of the Average Formula

Does the idea of how to find averages make sense? The formula is a little clunky to write out in words, but working through a few examples will bring the concept home.

Example 1: Find the average grade in your math class. There are 10 students, and so far their cumulative percentage grades are: 77, 62, 89, 95, 88, 74, 82, 93, 79 and 82.

Start by adding up all of the students' scores:

77 + 62 + 89 + 95 + 88 + 74 + 82 + 93 + 79 + 82 = 821

Next, divide that total by the number of scores you added. (You could count them, or you could just take note that the original problem tells you there are 10.)

821 ÷ 10 = 82.1

The result, 82.1, is the average score in your math class.

Example 2: What is the average of 2, 4, 6, 9, 21, 13, 5 and 12?

You aren't being told what real-world context these numbers might exist in, but that's okay. You can still perform the mathematical operations to find their average. Start by adding them all together:

2 + 4 + 6 + 9 + 21 + 13 + 5 + 12 = 72

Next, count up how many numbers you added together. There are eight, so your next step is to divide the total (72) by the quantity of numbers involved (8):

72 ÷ 8 = 9

So the average of that data set is 9.

Example 3: Of the students in your class, seven take the bus to and from school. (The others are driven by their parents.) All told, those seven students spend a total of 93 minutes walking to and from the bus each day. What is the average walk time for the students in your class?

Normally your first step would be to add all the students' walk times together, but that's already been done for you; the problem tells you that the total of their walk times is 93 minutes.

The problem also tells you how many pieces of data you're dealing with (seven – one for each student). So if you read the problem carefully, all you have left to do to find the average is divide the sum or total of the data (93 minutes) by the number of data points (7):

93 minutes ÷ 7 = 13.2857142857 minutes

Most people don't care about whether you've walked 13.2857142857 minutes or 13.2857142858 minutes, so in a case like this you'll almost always round your answer to make it more useful.

If rounding is allowed, your teacher will tell you what decimal place to round to. In this case, let's round to the tenths place, which is one spot to the right of the decimal. Because the number in the next place (the hundredths place) is greater than 5, you'll round the number in the tenths place up when you truncate the decimal.