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What Is an Average?

The question arises in part because although everyone has a rough idea about what it is, many people don't know how to calculate it. Then there is the fact that "average" has several meanings when used in statistics. There are several ways to calculate it then.

Because of this it's easy to mislead people or "lie" with statistics that are perfectly accurate from a technical standpoint--a good reason to understand just what is meant by the word. First, we need to know that an average can be a "mean," "median," or "mode." To understand these we'll use an example that will explain the calculations and also show how perceptions can be influenced by choosing which average to use.

Let's suppose there are 17 employees in a company, with the following annual incomes:

\$22,000, \$22,000, \$22,000, \$28,000, \$32,000, \$32,000, \$33,000, \$35,000, \$36,000, \$42,000, \$44,000, \$45,000, \$48,000, \$52,000, \$106,000, \$122,000, \$480,000

The average used least commonly is perhaps the mode. This is simply the value which occurs most often in a group (not all groups have a mode, and some may have multiple modes). In this case that would be \$22,000, since that occurs three times, which is more than any other.

The calculation used most is the mean. This is the total of all values added up and divided by the number of values. In this case all the incomes add up to \$1,201,000, which, when divided by the 17 salaries we just added together, gives us an average wage of \$70,647.

Also commonly used is the median. This is simply the middle value in the case of an odd number of values, or the mean of the two middle values if there is an even number. In our example, \$36,000 is the middle value, with eight higher and eight lower.

Now let's look at what happens if we use one or the other of these calculations. To start with, if you were asked what an employee makes on average at this company, you could accurately answer \$22,000, \$36,000, or \$70,647. That's quite a range, isn't it?

Why might a person choose one or the other of these averages? Because each presents a picture that could be useful to someone.

For example, a company recruiter might like wages to appear higher to attract better employees, and so he could say that the average is \$70,64. A union organizer could complain that the most common salary is \$22,000, in order to negotiate for a raise for all employees.

Now, many people feel that the most commonly used measure, the mean, is generally the most accurate, but is it? In this case, even that can be very misleading. It shows the average salary as \$70,647, yet only 3 of 17 employees make more than that. In fact of all the other 13 employees, the highest salary is \$52,000. We can mislead ourselves--or even lie--very easily with statistics, and answering the question "what is an average?" in different ways to suit our purposes is just one way to do that.

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