How clever are you?

[HeadingNorth]

Surely there should be a 50/50 split between below average and above average.....:huh:

 

That depends what is being used as "average." There are three, entirely different, mathematical terms, any one of which could be used.

 

MEAN; this is what most people think of as "the average." Add up every score involved, then divide by the total number of scores.

 

MEDIAN: Arrange all the scores in numerical order, and the median is the one that falls exactly halfway along the list. By definition, exactly half the population will be below the median IQ score and the other half above it.

 

MODE: the score which occurs the most often. This is likely to be a fairly central score, but in extreme conditions it may not be.

 

 

 

To show how these figures can vary quite widely, imagine a cricket team containing Geoff Boycott and ten utter incompetents. Boycott scores a hundred and ten runs; the other ten batsmen are all out for 0.

 

The mean is (110 plus ten lots of zero, divided by eleven batsmen): 11 runs. Nobody scored 11.

 

The median is zero (0,0,0,0,0,0,0,0,0,0,110). The mode is also zero (ten scores of nil and one score of 110.) But if you declare that the average score was zero, how on earth has the team ended up at 110 all out?

 

Anything which fits the model of a Normal Distribution (mentioned by BritPat above, and it's amazing how many things do so), will most likely see all three "averages" giving the same result. IQ measurements would certainly fit this pattern, but cricket scores and other things involving a small sample, often do not.

[Gormenghast]

Surely there should be a 50/50 split between below average and above average.....:huh:

 

I've got an above average number of fingers, as have most people......

[esme]

I'm not seeing "duuuuuurrrr" up there, that would be my choice

 

that or "stares vacantly at the wall while drooling"

[Moosey]

I've got an above average number of fingers, as have most people......

 

Absolutely right. And an above average number of legs and arms.

[HeadingNorth]

Absolutely right. And an above average number of legs and arms.

 

Based on the mean, true; on the median or the mode, definitely false.

[Moosey]

Based on the mean, true; on the median or the mode, definitely false.

 

By and large, for most calculations, mean is taken as the "average" though. In the everyday world that is.

 

Ask an accountant to work out your average salary over 10 years, and he'll most likely use the mean I'd say. When I do salary calculations I certainly do.

[Frazer1974]

That depends what is being used as "average." There are three, entirely different, mathematical terms, any one of which could be used.

 

MEAN; this is what most people think of as "the average." Add up every score involved, then divide by the total number of scores.

 

MEDIAN: Arrange all the scores in numerical order, and the median is the one that falls exactly halfway along the list. By definition, exactly half the population will be below the median IQ score and the other half above it.

 

MODE: the score which occurs the most often. This is likely to be a fairly central score, but in extreme conditions it may not be.

 

 

 

To show how these figures can vary quite widely, imagine a cricket team containing Geoff Boycott and ten utter incompetents. Boycott scores a hundred and ten runs; the other ten batsmen are all out for 0.

 

The mean is (110 plus ten lots of zero, divided by eleven batsmen): 11 runs. Nobody scored 11.

 

The median is zero (0,0,0,0,0,0,0,0,0,0,110). The mode is also zero (ten scores of nil and one score of 110.) But if you declare that the average score was zero, how on earth has the team ended up at 110 all out?

 

Anything which fits the model of a Normal Distribution (mentioned by BritPat above, and it's amazing how many things do so), will most likely see all three "averages" giving the same result. IQ measurements would certainly fit this pattern, but cricket scores and other things involving a small sample, often do not.

 

That doesn't necessarily follow, because it's the England cricket team.

 

What would probably happen is that Boycott would be out for single figures, while the numpty who we got in to make the teas would score a century. Then the following match, the numpty would be out for a duck and Boycott would be out with stress. Then the next match another middle-order nobody would be made captain in place of Boycott and score a century. Then the next match he would score nothing while a faceless wonder would score a century etc, etc, etc.... you get the picture.

[HeadingNorth]

By and large, for most calculations, mean is taken as the "average" though. In the everyday world that is.

 

 

In most situations and calculations, it is the most sensible choice. When calculating the "average" number of fingers, toes, arms and legs, I don't think it is. The average person has two arms, two legs, two thumbs, eight fingers and ten toes.

 

A small percentage are missing some of the full complement due to accidents or illness, and a still smaller percentage are born with extra digits, but the median, and the mode, both say "2,2,2,8,10" and I think most people would agree that this constitutes the "average person."

[HeadingNorth]

That doesn't necessarily follow, because it's the England cricket team.

 

 

Admittedly, you can't expect anything remotely average with the England cricket team. I prefer to imagine an Invitation XI consisting of Boyks, and ten people about as good at cricket as I am.

 

(Actually they'd have to be better than me, or they'd all ten of them be out before Boyks had time to reach double figures.)

[Moosey]

In most situations and calculations, it is the most sensible choice. When calculating the "average" number of fingers, toes, arms and legs, I don't think it is. The average person has two arms, two legs, two thumbs, eight fingers and ten toes.

 

A small percentage are missing some of the full complement due to accidents or illness, and a still smaller percentage are born with extra digits, but the median, and the mode, both say "2,2,2,8,10" and I think most people would agree that this constitutes the "average person."

 

Absolutely.

 

The point that was made isn't that "most people have 1 leg", because they don't. The point was that statistics can and are easily manipulated to suit a headline or purpose.