How is this? There are a very few Australians with no legs, few Australians who only have one leg and far more with two legs. Adding up the total number of legs in Australia, and dividing by the number of Australians, the average number of legs that an Australian might have is roughly 1.999. This means that someone fully equipped with the usual compliment of legs is likely to have more than the average.
A statistician goes out duck hunting. He sees a duck flying in the sky towards him, reaching for his double-barreled shotgun he takes aim and fires the first barrel. Too low! He misses.
As it gets closer to him he aims again and fires the second barrel. Too high! He has missed again.
Confidently he puts the shotgun back in its case. His companion asks him, “What are you doing? We came out duck hunting, and you havent got one yet but are going home?“. The statistician replied, “Ah, the first time I shot it went above the duck, the second time it went too low. This means on average that I hit it.”
Back at work on Monday morning the statistician has to go to a conference in York. He lives in London so goes in the morning to Kings Cross train station to catch a train to York. He gets on the train but doesn’t get off at York, the train passes on and continues all the way to the end of the line at Edinburgh. He gets off the train, confident that even though he isn’t actually in York, given that he started in London and ended up in Edinburgh, on average he is in York.
I can’t stand averages. This isn’t a joke. The ones above probably weren’t funny enough to be called jokes either, but given that I found them funny, and you probably didn’t, on average they are funny half the time. Or funny for the average amount of people. Or only funny if you are average. As I said, I hate averages.
The average is a measure of central tendency. Central Tendency isn’t a republic in Eastern Europe, it is a place or position in a group of numbers that is, according to the different calculation used, where the central value is. This is used to help us picture a group of numbers without having to listen to the whole bally lot read out to us.
A lot of indicators, especially ones specified for reporting purposes, are averages and this is a bad thing. Average number of days to process a Housing Benefit claim for example. It might take 30 days on average to process a claim. People will hear “30 days” and “process a claim” and now they have in their heads “It takes 30 days to process a claim”, but it doesn’t. It doesn’t necessarily even mean that a claim is more likely to take 30 days to process than any other time.
It means that if you add up some numbers, divide by another number, you get 30.
There is no such thing as an average anything, other than as a short cut label to describe “I added a characteristic up and divided by the total of items”. This word “average” is a handy short cut for saying that, but don’t mistake it FOR anything. You’ve manipulated some aspects of the data of a group and are using the figure you obtain to describe that group. Don’t kid yourself that you are describing something ABOUT that group.
Or don’t bother. Don’t hide reality behind an average. What is the average Beatle? Ringo or John? What is the average country, France or China? What is the average time of day, 11:26am or quarter to two in the afternoon? The average food, hot dog or paella?
There are other and better ways of describing, showing or summarizing data such as individual data in control charts or other graphs, pick one and you’ll be better off.
On average anyway.