276 Part 4: The State of the World
The Centers
One of the ways you can represent a data set is by identifying a central tendency. A central
tendency is the center value or a typical value of a particular data set. Identifying this value gives
you a sense of the result you might get if you did the experiment again or asked the question
again. Knowing this measure of center begins to give you a sense of the typical result, what you
can expect. That expectation is approximate, of course. Every time you do the experiment or ask
the question you will probably get a different value, but the more you do that, the better your
sense of what to expect will become.
There are three different measures of center in common use. They’re called the mean, the
median, and the mode. The mean requires the most calculation, but unless you have an
extremely large set of numbers, the calculation isn’t difficult. The median only asks you to put
numbers in order and the mode only requires you to count.Mean
The mean is the number most people think of when you say “average.” It finds the center by
balancing out the highs and lows of the numbers. The mean is found by adding all the data items
and dividing by the number of items.DEFINITION
The mean of a set of data is a measure of center found by adding all the data values
and dividing by the number of values.If you take three tests and earn grades of 84, 91, and 77, you find your average grade, or mean
grade, by first adding up your three test scores. 84 + 91 + 77 = 252. Then you divide that total
by 3 because it represents three tests. 252 z 3 = 84. Your mean score is 84. The mean will not
always be the same as one of the values, but it will be in the middle of the values. Your high score
of 91 and your low score of 77 balance each other out, and the average ends up being the same as
your middle score of 84.
If one or more of the values you’re averaging are much higher or much lower than most of the
group, the mean will be pulled toward that extreme value. Suppose you accidently copied that
grade of 77 as just a 7. That would make that score significantly lower than your other grades.
When you found the average, you’d get (84 + 91 + 7) z 3 = 182 z 3 = 60.67. That gigantic drop
in your average is caused by that extremely low value.