An Average Story
All my life I have been defined as an average kid. Not a normal one; just average! Average by looks, built, smartness and pathetic in terms of coolness. But I never let it get to my heart. I worked hard and showed them that they were right.
I got myself thinking, what exactly people mean when they called me average? Do they mean that I was the sum of the total human beings divided by the total number of human beings? Or was I the most frequently occurring human being that they know of? Or somehow I had all the traits found in human beings? Or maybe that everyone was exactly like me. As usual, I wen’t to the great reddit library where all the masterminds of the internet come to discuss useless ideas. I came up with the following information:
Average = Total of elements/No. of elements
or Average (geometric mean)= nth root of product of n numbers
or Average (harmonic mean) = Number of elements/sum of reciprocals of elements
or Average (median) = The middlemost value in a sorted array
or Average (mode) = The most frequently occurring value in a sample
Not sure where to proceed with that, I logged out of my account and decided to have a nap. But as usual, I stared at the ceiling for a few hours thinking up some clever idea to have fun with ‘mean’. Consider a case of marks of 10 students in an exam : 10,8,7,7,6,7,6,8 ,8 and 7 (the teacher wont give marks in decimals and there was a point for trying). The average of these values comes out as:
Arithmetic mean: 7.4 Geometric Mean: 7.32 Mode:7 Median:7 Harmonic Mean:7.24
Here, the means gave me no means to make sense of the data. I mean none of the students got 7.4, 7.32 or 7.24 marks. I am pretty sure if there was a different set of data, I wouldn’t have gotten proper values for the median as well as mode.
Majority of the people got lower than 7.4, 7.32 or 7.24 marks (a total of 6). This might imply that majority of the people are below average (contradictory to what you might believe).
The median did not divide the population strictly into halves. Only two people were below and four were above the median. If there were no duplicate marks, it’d have done that.
The geometric mean and harmonic mean would have failed miserably when even one of the students got zero marks (just consider it for my sake this time).
The closest I’ve come to a real explanation is here. But they say that the term geometric mean is the arithmetic mean of graphs and I lost my mind (actually I think I lost it long back).
I think the average is just a mathematical concept, not existing in real life. You might never meet the average person, the average score of a player doesn’t give you any useful information except that he/she is a regular at scoring high. The “average ” person has lesser than two eyes, the average good weather can definitely ruin an outdoor picnic. The whole concept of ‘mean’ makes very less sense to me.The statistics and percentage figures leave me with a sense of bewilderment.
The ‘means’ are definitely mean. Perhaps some of you would care to explain the concepts to me.