Mean and Median for Statistical Dummies

Measures of central tendency

Here at the Antisocial Network, we're in the habit of calling out people for exposing their lack of experience, knowledge or common sense in hopes of making money; often while answering (or pretending to answer) questions or providing how-to "instructions." Every once in a while, however, we run across a bit of dumbassery that wasn't published  at a content farm. Today is one of those times: our DotD awardee is Keryn Newman, a NIMBY blogger trying to stop a power line in West Virginia. No matter how honorable – or self-serving, we didn't read through the entire blog – Keryn's cause may have been, it's pretty clear that she never took a class in statistics (she must've been one of those damned journalism majors...). All you need do to figure out that deficiency is to take the time to read her post "Median vs. Midpoint" carefully.

It appears that the evil power line company intended to use eminent domain to take the property of landowners along the route. According to Newman, the method the company would use to determine the purchase price is "unfair." That's because the purchase price would be determined as follows:

"...TrAILCo [will] purchase the property at a fair market value based on the median [emphasis Keryn's] of three appraisals..."

Keryn goes on to "explain," based on an article she found online, that "...median is a popular mathematical trick favored by shysters..." She says that because the example in the article compares median and mean salaries: You add one filthy-rich person's salary to a population, and the median only changes a little (if at all) but the mean goes way up. So, Keryn "explains," that her reference clearly proves that using the median to determine the purchase price is a rip-off, because the median is always lower than the mean.

But wait: as Keryn correctly stated previously in her own post,  "You're probably all familiar with 'average' and how to calculate it -- you add up all the figures in your series and then divide by the number of figures to find the average or 'midpoint'.  Median is a slightly different animal and can result in a lower figure.  To calculate median, you sort your figures in numerical order and then select the middle number." And there's where Ms Newman goes all wonky: first, that's not how you calculate "midpoint," that's how you calculate "mean." Second, she actually admits that median isn't always less than mean: she says it "can be a lower figure" -- which clearly means it can also be a higher figure. But Keryn wants to imply that it's always lower, the better to stir up her readers. That's not so: statistically speaking, in any set of three numbers, the mean has a 0.50 probability of being less than the median, and a 0.50 probability of being greater. Some examples:

2, 6, 28 (mean 12, median 6) 5, 11, 20 (mean 12, median 11) 4, 14, 18 (mean 12, median 14) 2, 17, 17 (mean 12, median 17)

So in her zeal to push her cause, Newman not only misinterprets some pretty simple statistics, she also pretty much libels those PATH representatives she calls Randy and Monique. You know what that makes Keryn? You are correct: Our Dumbass of the Day! What's perhaps saddest is that although a couple of people tried to call her on her dumbassery in the comment section, they both got it wrong, too...

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MM - STATISTICS