Average<>Median

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I am always amazed (annoyed?) at the innumeracy of the American (ok, the world’s) populace.  It’s one of the ways polemicists can convince folks of certain “facts”– even when there is no logic behind their words.

One of the biggest teases is the “average” concept.  Once we hear that this is average, we assume that things are ok- maybe not great, but ok, nevertheless.  But, that assumes that the distribution of outcomes follows the “bell-shaped” curve, so that most of the items really are average, and there are only a few outliers.

When you think of average, is this it?
So, is this the average you had in mind?

But, I recall when I moved to Charlottesville long ago (nearly four decades, now).  While I don’t recall the exact financial values, I do remember the basics.  I believe that the average income for the area was $ 25K.  That number sounded pretty reasonable.  But, the median income (that means that ½ the folks make more and ½ the folks make less) was about $ 14K.   What, you say?  How can that be?  It’s because there were a few very, very wealthy and a fair number of fairly wealthy people who blew up the average income numbers.

But, what did it mean?  Well, if you were trying to start a slightly upscale retail establishment, you might have considered that most of the folks could afford to frequent your shop, based upon that average income.  But, when you realized that most of the folks made less than you thought, your total potential market share dropped precipitously- perhaps, even leading to the failure of your enterprise.

We also know that most children of divorce are not really much different than those who are raised by married parents.  But, there are more than a few children of divorce who really have problems- and then when one considers the “average” affects, it is critical to recognize that we have just skewed the impacts of divorce upon child-rearing.

The same applies when professors “curve” grades.  Which is a problem, if you are a graduate program admissions officer or an employer expecting your “chosen ones” to have mastered certain subject matters.  Would you want your physician to have done real well when compared with his peers at institution XYZ (and much worse than those at the rest of the higher learning establishments)?  Would that render his/her ability to treat your ailment adequately?

Or, when we hear that the charitable deduction on our tax forms is critical to maintain our beneficial establishments.  And, then, we hear that the richest 20% give much lower percentages of their income to charity than we originally thought?  As a matter of fact, that top echelon only provides 1.3% of their income (not their wealth- which is an even lower percentage) to charity- while the poorest (the bottom 20%) give about thrice that- 3.2%.  And, those poor don’t have enough deductions to deduct those donations from their tax computations.

So, remember that there are vast differences between averages (the total number of X divided by those involved) and the median (the value where ½ are above and ½ are below a certain value).  The bigger the skew, the less likely the information can be used for any inferences.

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10 thoughts on “Average<>Median”

    1. Actually, the typical person understands the post, Lisa. It’s just that most of us want to hear from people with the same point of view. Which is why certain folks watch Fox News, others watch MSNBC. Where is a Walt Cronkite (that’s way too old) or even a Peter Jennings (more recent) that can garner the respect and audience?

  1. One of the reasons I don’t chose to debate much of anything with anyone is that depending on what they or I have read/heard from some report you just know that the numbers are being spun one way or another. Qualifying words like “almost” or other exclusions/inclusions just make it so very hard to even know what you are arguing about. But, what do I know? I am just of average intelligence 🙂

    1. That’s the same comment I just made to Ann. We tend to only want to hear one point of view- our own. And, that does not make for an intelligent populace.
      One of the key joys I have are friends with a wide range of opinions that afford interesting discussions.

    1. Ann:
      You said a mouthful. One of the issues in today’s society is that we tend to only want to watch or read the news sources that agree with our biases. Which means that we don’t get all the facts, we just feed our bias. That does not make an educated populace.

  2. I didn’t know the fact about the charitable donation percentage differences between the wealthy and the poor. How sad is that? I guess numbers can be spun just as easily as facts can.

  3. This is a very good point, Roy. In itself, the average doesn’t really mean anything, but for some reason it is always used to make a point. It is all about tweaking the numbers to make them say what you want, isn’t it? What we need is a bit more intellectual honesty!

    1. That’s a great point, Muriel. The average only makes sense, when the distribution is what we call “normal” (the bell-shaped curve). Once there is a different distribution- binormal, for example, then using terms like average provides little benefit to the discussion. You know- if we have ten people in a company, with three of them earning $20K, 2 earning $ 200K, 1 earning $ 500K, and the rest earning between 30 and $ 40K, does the average salary of $106K provide any idea of what the group really makes?

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