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
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
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.