The term “average” is not used in statistics. Statisticians will choose what they mean by the term “average” depending on the way they are going to use their data. Instead, they use the terms mean, median and mode to express an “average” for numeric data.

**Mean**

The mean of a set of numbers is the average you are probably most familiar with. The mean is calculated by adding all the numbers together and dividing by the total number of numbers.

For example, let’s take a set of test scores from a math class of nine students. The scores were:

**65, 95, 73, 88, 83, 92, 74, 83, and 94**

To find the mean, add all these scores together.

65 + 95 + 73 + 88 + 83 + 92 + 74 + 83 + 94 = 747

Divide this value by the total number of tests (9)

747 ÷ 9 = 83

The mean score on the test was a score of 83.

**Median**

The median of a set of numbers is the number which appears in the center of a set of numbers when they are placed in numerical order.

Find the median of the above test scores. First sort them in increasing numerical order:

**65, 73, 74, 83, 83, 88, 92, 94, 95**

Find the number in the middle of this sequence. This number will be the median.

**65, 73, 74, 83, 83, 88, 92, 94, 95**

The median test score is 83.

This worked out nice because there were an odd number of test scores. If the number of tests were even there would be two test scores in the middle of the set. The median would be the mean of both numbers.

Let’s take the same test scores, but remove the low one. Now we have 8 test scores. The sequence becomes:

**73, 74, 83, 83, 88, 92, 94, 95**

Identify the middle numbers

**73, 74, 83, 83, 88, 92, 94, 95**

Find the mean of these two numbers. First add them together:

83 + 88 = 171

Divide by the number of numbers (in this case, 2)

171 ÷ 2 = 85.5

The median of the new set of test scores is 85.5.

**Mode**

The mode of a set of numbers is the number that occurs most often in the set.

Find the mode of our test scores.

**65, 73, 74, 83, 83, 88, 92, 94, 95**

Notice the score of 83 occurs twice. The mode of this set of test scores is 83.

An important thing to remember about finding the mode of a set of numbers is there may not be a mode at all. If no number repeats in the set, there is no mode. On the other hand, if a set of data can have multiple modes if there are the same number of duplicate values. Let’s say our test scores were:

**65, 74, 74, 83, 83, 88, 92, 92, 95**

There are three scores that occur twice in this set of scores: 74, 83, and 92. This means there are three modes for these scores: 74, 83, and 92.

Mean, median and mode are basic calculations in introductory statistics to express average values of a set of data. Which one you use will change on a case to case basis. It is best to learn how to do all three before identifying which one you will need.

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