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Mean: Definition & Sample Problems

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  • 0:04 What is the Mean?
  • 0:39 How to Find the Mean
  • 0:51 Sample Problems
  • 1:53 Real-Life Examples
  • 4:28 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

The arithmetic mean of a group of numbers is the technical term for the average of those numbers. This lesson tells you how to compute the mean and shows you how to do it with some real-world examples.

What is a Mean

Anyone who has ever been to school knows the value 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.

How to 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 equal to the quantity of numbers you added together.

This result is your mean, or average.

Let's see how to find the mean with an actual example.

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 in the set, divide the sum by 5: 27/5 = 5.4

The mean of 2, 4, 9, 5, 7 is 5.4

Let's try another problem that more closely follows our example of figuring out school grades.

Say you have received the following grades on the last 6 math exams:

92, 84, 90, 78, 94, 88

What is the 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 6 test scores, and round to the nearest tenth:

526/6 = 87.7

87.7 is the average test score.

Real-Life Examples

Grades are not the only instance in which knowing how to find 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

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 Joe 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

Joe has run an average of 188.2 yards.

Let's look at another example.

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