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Mean: Definition & Sample Problems

Instructor: Jennifer Beddoe
The arithmetic mean of a group of numbers is the technical term for the average of a group of numbers. This lesson will tell you how to compute the mean, give some examples and provide a quiz at the end so you can practice.

What is a Mean

Anyone who has ever been to school knows the importance of keeping up with their grades; it's important to know where you stand. The usual way to determine just how well you're doing in a class is to take the arithmetic mean, or average, of the test scores, homework and other graded materials. Obviously, every teacher will do things a bit differently, but taking the average of your test scores is not a bad way to get a close approximation of your grade. It can, at the very least, let you know if you need to study harder for the next test to improve that average. You can even go so far as to figure out what grade you need on the next test to raise your grade from a B to an A.

Find the Mean

The process for finding the mean of a group of numbers is as follows:

  1. Add together all the numbers for which you need to find the average.
  2. Divide this sum by the number of terms you added together

This number is your mean, or average.

Sample Problems

Find the mean of the following numbers:

2, 4, 9, 5, 7

First add the numbers together: 2 + 4 + 9 + 5 + 7 = 27

Then, because there are 5 numbers, divide the sum by 5: 27/5 = 5.4

Let's try another problem that more closely follows our grading example above. Say you have received the following grades on the last 6 math exams:

92, 84, 90, 78, 94, 88

What is my average test score, rounded to the nearest tenth?

Add all the scores together

92 + 84 + 90 + 78 + 94 + 88 = 526

Divide that number by 6, because there are six test scores, and round to the nearest tenth:

526/6 = 87.7

87.7 is my average test score.

Real-Life Examples

Grades are not the only instance in which finding the average is important. There are many other applications where this skill is necessary. Here are some real life examples in which you might need to find the mean.

Sports

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In sports, determining the mean of a group of numbers occurs almost to excess - they have stats for everything! Say Joe is trying to calculate the average number of yards he's run during the first half of the football season. Here are his rushing yards from each game:

124, 118, 97, 140, 112

What is the average number of yards he has run?

The first step is to add up the numbers from each game

124 + 118 + 97 + 140 + 112 =591

Now divide the sum by the number of games, which is 5.

591/5 = 118.2

Census

Every country keeps statistics about its residents. Each state and city in America does the same thing. This can be useful information when deciding where to distribute money or what to build in certain areas. Here is a list of ages of people that live in the fictional city of Shelby:

5, 7, 2, 21, 24, 26, 33, 45, 67, 72, 38, 42, 77, 28, 55, 40

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