How to Calculate the Mean of a Statistical Data Set
The most common way to summarize a statistical data set is to describe where the center, or mean, is. One way of thinking about what the center of a data set means is to ask, What’s a typical value? Or, Where is the middle of the data? The center of a data set can actually be measured in different ways, and the method chosen can greatly influence the conclusions people make about the data.
For example, NBA players make a lot of money, right? You often hear about players like Kobe Bryant or LeBron James who make tens of millions of dollars a year. But is that what the typical NBA player makes? Not really (although you probably shouldn’t feel sorry for the others, given that they still make more money than most of us will ever make). Tens of millions of dollars is the kind of money you can command when you are a superstar among superstars, which is what these elite players are.
So how much money does the typical NBA player make? One way to answer this is to look at the average (the most commonly used statistic of all time).
The average, also called the mean of a data set, is denoted
The formula for finding the mean is:
where each value in the data set is denoted by an x with a subscript i that goes from 1 (the first number) to n (the last number).
Here’s how you calculate the mean of a data set:
Add up all the values in the data set.
Divide by the number of values in the data set, n.
The mean discussed here applies to a sample of data and is technically called the sample mean. The mean of an entire population of data is denoted with the Greek letter µ and is called the population mean. It’s found by summing up all the values in the population and dividing by the population size, denoted N (to distinguish it from a sample size, n). Typically the population mean is unknown, and you use a sample mean to estimate it (plus or minus a margin of error).
The following table shows salary data for the 13 players on the 2010 NBA Champion Los Angeles Lakers.
The mean of all the salaries on this team is $91,378,064 ÷ 13 = $7,029,082. That’s a pretty nice average salary, isn’t it? But notice that Kobe Bryant really stands out at the top of this list, and he should — his salary was the second highest in the entire league that season (just behind Tracy McGrady). If you remove Kobe from the equation (literally), the average salary of all the Lakers players besides Kobe becomes $68,343,689 ÷ 12 = $5,695,307 — a difference of around 1.3 million.
This new mean is still a hefty amount, but it’s significantly lower than the mean salary of all the players including Kobe. Bottom line: The mean doesn’t always tell the whole story. In some cases it may be a bit misleading, and this is one of those cases. That’s because every year a few top-notch players (like Kobe) make much more money than anybody else, and their salaries dramatically pull up the overall average salary.