Three Averages

Baseball is one activity that’s consumed by averages.  There are batting averages, earned run averages, slugging percentages, on-base percentages, runs with runners in scoring position (an average), stolen base percentages and many more.  Most professional baseball players are average.  Yet even a Major League Baseball position player (not a pitcher or designated hitter), possessing just a so-so batting average of .260, made more than $3,000,000 in salary in 2008.  Most actors are average.  Most actors don’t make nearly that much money. 

Think of the Bell Curve where the large hump in the middle represents average.  Most of any category that has variation is average.  Incomes, scores, performance, prices, sizes and so on.  Students of math are wary of average, for they know that average is a tricky term.  That’s because there are three types of averages:  mean, median, and mode.  When we talk about average, we usually intend the mathematical mean average.  Mean average is the sum of all the parts divided by the number of parts.  Like this:

1+2+2+3+4+7+9 = 28 divided by 7 = 4

Four is the mean average of these seven numbers.  However the median average separates the lower half of all the numbers from the upper half.  In this example that number is 3 because three of the numbers, 1, 2 and 2, are lower than 3 and three numbers, 4, 7 and 9, are higher than 3.   The mode is the average that includes the number that appears most frequently.  In the series above that number is 2. 

When it comes to those characteristics that cannot be measured, the concept of an average is simply speculation.  However when characteristics or behaviors can be measured or counted, then the three averages, mean, median and mode, have meaning.

From Threes, Chapter 2, “Threes in Math”