Saturday, April 24, 2010

Mean/Median Confusion

Updated: Columbia University Business School Professor Ray Fisman writes in this article:

"It's a sad statistical reality: Half of us are below average."

To be more precise, it should be "half of us are below the median."

HT: Chris Douglass

Thanks to Steve in his comment for providing information about
Fisman's background.


At 4/24/2010 10:33 PM, Anonymous SuhrMesa said...

nor does the editor....

At 4/24/2010 11:18 PM, Blogger Bret said...

In some fairness, since many human traits are distributed more or less normally, the median and average are pretty close and the statement is essentially true.

At 4/24/2010 11:41 PM, Anonymous Lyle said...

However the media are likley no different in this than a majority of the population. Where is anything but average taught in school, until you get to science labs and learn about standard deviations and the like? How much of this is recalled years later even by people who once knew it.
This is a bit of the larger point of the innumeracy of a large part of the population. Surveys show most don't understand compound interest and the like, let alone get to the concept of net present value. (unless they are doing business cases)

At 4/25/2010 4:11 AM, Blogger juandos said...

"However the media are likley no different in this than a majority of the population. Where is anything but average taught in school, until you get to science labs and learn about standard deviations and the like? How much of this is recalled years later even by people who once knew it"...

It is time to recognise that even the best schools under the best conditions cannot overcome the limits on achievement set by limits on academic ability

At 4/25/2010 6:56 AM, Blogger Steve said...

The author is not a journalist; he is a professor at Columbia Business School. Although, that certainly doesn't invalidate the subject of your post.

"Ray Fisman is the Lambert Family professor of social enterprise and director of the Social Enterprise Program at the Columbia Business School. He is at work on a book about the economics of office life."

At 4/25/2010 8:29 AM, Blogger juandos said...

What the heck does is Social Enterprise Program good for?

According to Fisman: All Columbia Business School graduates will be called upon to contribute to society at some point during their lives...

Why? Whose alledged society?

It sounds like European socialism being offered/pushed at a quasi American school...

At 4/25/2010 9:16 AM, Blogger John Thacker said...

I'm a probabilist, and I wouldn't assume that "average" always meant arithmetic mean. A median is a form of average. If someone says "average," and the median is the obvious sort of average meant from context, then I don't have a problem with it.

If you mean arithmetic mean, say "mean."

At 4/25/2010 9:42 AM, Blogger Marko said...

"called upon to contribute to society" - I thought the best way to do this was to go out, get a job, be productive and to spend and invest your earnings. Silly me, I guess need to take that class at Columbia, haha! (reference is made to previous discussions about how liberals are 'better' educated than 'conservatives' - if this counts as education, well all right then).

Regarding mean and median, it is true people use them rather interchangeably in casual discourse. I do recall reading with amusement a headline declaring it is a tragedy that 75% of 4th graders have below average reading skills! lol.

At 4/25/2010 11:19 AM, Anonymous Anonymous said...

I think half-below-average is an appropriate term to use when writing for a general audience (non-academic articles). A lot of people don't know what the term "median" means; you tend to lose readers if you go into too much detail with the microwave generation. Writing that no one reads is useless to anyone except the writer.

Besides, with no other details given, on a 0-100% scale, 50% would be both the average and median. If two people take a test and one gets 0% and the other gets 100%, what is the average and what is the median?

At 4/25/2010 11:29 AM, Anonymous Anonymous said...


Wouldn't the 75% of 4th graders with below average reading skills youm mentioned normally be comparing an individual class of 4th graders to a school or national average (or an externally defined standard)? That's a faily common way of measuring student perfomance. This is the type of measurement educational administrators want use to justify teacher pay-for-performance.

At 4/25/2010 6:01 PM, Blogger OA said...

I don't think the first sentence is anywhere near the worst problem with the article.

He tells about Republicans increasing usage after seemingly being below average before:

"Republicans had the opposite reaction. When told of their relative thrift, they started cranking up the thermostat and leaving the lights on more often."

He later compares the changes for Democrats with undisclosed levels of usage relative to average, liberals who were "heavier-than-average consumers", and Republicans of undisclosed, but seemingly lower than average usage originally based on his prior statement.

"Registered Democrats who give to environmental organizations and live near other liberals reduced their consumption by 3 percent. For liberals who started out as heavier-than-average consumers, the reduction was almost 6 percent. Republicans who live in conservative neighborhoods (and hence had no neighborly pressure to conserve) and had no record of giving to environmental organizations actually increased their consumption by 1 percent."

Are these distinct and comparable subsets? "Liberals" seems to be synonymous to "Democrats" as he says "Democrats who ... live near other liberals..." Or maybe Democrats is a subset of liberals. Does that 3% include that 6%? Do they overlap subsets? Completely unclear.

He states "The economists found that the 2 percent average decline in energy use..."

What does "average" mean in any of these instances? Is that "2% average decline" an average of the changes, or the decline in total units of energy for the entire population?

House A down 3%, house B down 2%, house C down 1%, for an average of 2% decline. Versus XX units of energy for all the houses total originally and 2% decline in the total after.

At 4/26/2010 9:22 AM, Blogger Marko said...

Walt G, you are correct of course. I found it amusing when it was stripped of context.


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