Median

Whenever you find yourself writing the words, "the average worker" this, or "the average household" that, you don't want to use the mean to describe those situations. You want a statistic that tells you something about the worker or the household in the middle. That's the median.

Again, this statistic is easy to determine because the median literally is the value in the middle. Just line up the values in your set of data, from largest to smallest. The one in the dead-center is your median.

For the World Wide Widget Co., here are the worker's salaries:

$100,000
$50,000
$50,000
$15,000
$15,000
$15,000
$15,000
$9,000
$9,000

That's 9 employees. So the one halfway down the list, the fifth value, is $15,000. That's the median.

Comparing the mean to the median for a set of data can give you an idea how widely the values in your dataset are spread apart. In this case, there's a somewhat substantial gap between the CEO at WWW Co. and the rank and file. (Of course, in the real world, a set of just nine numbers won't be enough to tell you very much about anything. But we're using a small dataset here to help keep these concepts clear.)

Statisticians have a value, called a standard deviation, that tells them how widely the values in a set are spread apart. A large SD tells you that the data are fairly diverse, while a small SD tells you the data are pretty tightly bunched together. If you'll be doing a lot of work with numbers or scientific research, it will be worth your time to learn a bit about the standard deviation.

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