Monday, December 6, 2010

On Average

Every day we read about  “average” interest rates, “average” gas prices, batting “averages,” “average” SAT scores, and the iconic Dow Jones Industrial “Average”—among dozens of other numerical indexes that purport to denote the general state of affairs in many aspects of life.  But what, exactly, is an “average”?

One of the more appealing dictionaries (its cover is bright red) tells us that an average is “a single value that summarizes or represents the general significance of a set of unequal values.”  Ten bucks says you didn’t know it derives from an Arabic word used to describe a proportional allocation of costs arising from cargo damaged in shipping.  

If you read further, and at this point, you might as well, you will learn that there are three basic kinds of averages, and they do not necessarily produce the same result.  They are the arithmetic mean, the median, and the mode.  The mean is the quotient of the sum of a set of values, divided by the number of values in the set.  The median is the value at which there are an equal number of greater and lesser values.  And the mode is the single value with the largest number of instances in the set. (I knew I should have taken a math course in college.) 

For example, suppose you wanted to find the “average” hourly legal fee charged by attorneys in your town. (Don’t ask me why.) Let’s assume there are 11 lawyers; 5 charge $500 an hour, 1 charges $300, 4 charge $200, and 1 poor guy who barely passed the bar exam charges just $100 an hour and is lucky to get it when he does, which is seldom. What’s the average hourly legal fee? (I knew I should have become a lawyer.)

The mean would be the sum of the 11 lawyers’ fees ($3,700) divided by the 11 lawyers, or an average of $336.36 an hour (check the math if you don’t believe me).  The median, however, would be just $300, since there are an equal number of values below and above it.  Finally, if you preferred, you could say the average hourly rate is $500—since that is the mode, the value that is represented by the largest number of instances. 

Ergo, when someone quotes an “average” to you, be sure you know what is meant.

There is no way of knowing what is meant by the Bard of Buffalo Bayou, whose poems have defied the most assiduous explication de texte.

            The average man is not too smart--
            He’s ignorant of modern art,
            Klee, Kandinsky and de Kooning
            Send him into fits of groaning.
            Grand opera he cannot abide,
            When Valkyries ride, he’ll hide.           
            Chamber music to him brings
            The sound of scraping on the strings.

            Modern novels are a bore,
            And poetry is even more.
            He won’t attend solo recitals
            Or watch a film that has subtitles.

            The average man’s a Philistine,
            His lack of learning is obscene,
            He shuns high culture when he can--
            Good grief! I am that average man!

1 comment:

  1. OY. You just brought back all sorts of horrid memories of my second/junior year at UST, when Her Majesty insisted that I skip second-year French and dive directly into 3rd- and 4th-year classes ... one of which was Explication de texte, which kicked my not-so-callipygian. I got my first [and, luckily, ONLY] D from her on the first assignment in that class, and I haven't yet -- 29 years ex post facto -- recovered. Thanks awfully!
    [Oh, and memories of calculus, through which I suffered as a high-school senior, will also haunt me now. For which I am ALSO grateful -- NOT.]