How Do You Find The Mean Of A Data Set

The about mutual way to summarize a statistical information gear up is to describe where the center, or mean, is. One way of thinking most what the mean of a data set ways is to ask, "What's a typical value?" Or, "Where is the middle of the data?" The center of a information set can actually be measured in unlike ways, and the method called can greatly influence the conclusions people make nearly the data.

For example, NBA players make a lot of money, right? Yous often hear about players similar Kobe Bryant or LeBron James who make tens of millions of dollars a year. Only 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 always 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 aristocracy players are.

And then how much coin does the typical NBA player make? One way to reply this is to look at the average (the most unremarkably used statistic of all fourth dimension).

The average, likewise called the hateful of a data gear up, 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 ane (the first number) to n (the concluding number).

Hither's how y'all 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, due north.

The mean discussed here applies to a sample of information and is technically called the sample mean. The hateful of an entire population of data is denoted with the Greek letter µ and is chosen the population hateful. It's plant by summing up all the values in the population and dividing by the population size, denoted N (to distinguish information technology from a sample size, n). Typically the population mean is unknown, and you use a sample hateful to estimate information technology (plus or minus a margin of error).

The post-obit table shows salary data for the 13 players on the 2010 NBA Champion Los Angeles Lakers.

Salaries for L.A. Lakers NBA Players (2009–2010)
Player	Bacon ($)
Kobe Bryant	23,034,375
Pau Gasol	sixteen,452,000
Andrew Bynum	12,526,998
Lamar Odom	7,500,000
Ron Artest	5,854,000
Adam Morrison	five,257,229
Derek Fisher	five,048,000
Sasha Vujacic	5,000,000
Luke Walton	iv,840,000
Shannon Brown	2,000,000
Hashemite kingdom of jordan Farmar	1,947,240
Didier Ilunga-Mbenga	959,111
Josh Powell	959,111
Total	91,378,064

The mean of all the salaries on this squad is $91,378,064 ÷ 13 = $7,029,082. That's a pretty nice average salary, isn't it? But discover 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 backside Tracy McGrady). If you lot remove Kobe from the equation (literally), the average salary of all the Lakers players besides Kobe becomes $68,343,689 ÷ 12 = $five,695,307 — a divergence of around ane.three 1000000.

This new mean is still a hefty corporeality, just it's significantly lower than the hateful salary of all the players including Kobe. Bottom line: The mean doesn't ever tell the whole story. In some cases it may exist a bit misleading, and this is one of those cases. That's because every year a few tiptop-notch players (like Kobe) make much more than money than anybody else, and their salaries dramatically pull up the overall average salary.