So far, we’ve got a lot of information: spreadsheets filled with data that we arranged into variables and observations. But what do we do with all this? Unless you’re really special, you probably can’t learn a lot from looking at a list of one thousand numbers. You probably know even less from looking at a thousand observations for each of four different variables. Sets of data in business and science are usually larger than this, so we need to think of something fast.
The key is to take it slowly. Rather than look at the entire set of data, we want to look at the data one variable at a time in order to find out what that one variable tells us about the situation about which we collected data. To make things even easier, we want to reduce the data down to one number that represents the ”typical” data point for that variable. In general, a number used to represent an entire variable is called a statistic. If that statistic is meant to represent the typical data point, we call it an average.
Watch out, though, the word ”average” doesn’t really mean what you probably think it does. It has a much more general meaning than ”add up the data and divide by the number of data points.” That’s only one method of computing an average. There are many others. In this chapter, we’re interested in the three most common averages: the mean, the median, and the mode.
Another way to think of an average comes from the phrase central tendency. This refers to the middle of the data. You’ll always have some data above the average and some below it. The average is a way of talking about the middle of the data. The three described here (mean, median, mode) are the most commonly used ways to compute the middle. Each has a different meaning and has different applications. All are correct ways to compute the middle; it’s just that sometimes one is more appropriate than the others. When you go about computing an average you may need to check all three statistics (mean, median, and mode) of these in order to determine which of these will be the most appropriate measure of the typical data point.
If you’ve understood the ideas above, you might be amused by the statement below, which was issued by Joan Barb Briggs, the president of Generic University, in a moment of administrative desperation:
By the end of the next academic year, I want all of our instructors to have above average course evaluations.