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Bell curve in human performance questioned
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Bell curve in human performance questioned

  #21 (permalink)
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There is an easy way to find out whether a distribution could be represented by a bell curve.

A bell curve is symmetrical.

Let us take the first question of the number of publications. Let us assume that the average number of publications of a researcher during a given time period is 100. The minimum number is obviously a positive number greater than zero. If the distribution is symmetrical, there should be no values greater than 200. However, there is no upper limit on the number of publications. It therefore cannot be symmetrical and cannot be described by a Gauss distribtution (bell curve).

Another example is the distribution of the height of men. Here the odds are much better that the distribution will fit a curve similar to a bell curve. If the average height of men is about 5 feet 8, I would not be astonished if somebody finds out that there are as many men that with a height of 6 feet 8 as there are men with a height of 4 feet 8. This could be more or less symmetrical.

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  #22 (permalink)
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Fat Tails View Post
There is an easy way to find out whether a distribution could be represented by a bell curve.

A bell curve is symmetrical.

Let us take the first question of the number of publications. Let us assume that the average number of publications of a researcher during a given time period is 100. The minimum number is obviously a positive number greater than zero. If the distribution is symmetrical, there should be no values greater than 200. However, there is no upper limit on the number of publications. It therefore cannot be symmetrical and cannot be described by a Gauss distribtution (bell curve).

I don't have a good math back round. Just a couple comments below though.

In reality there is actually an upper limit to the number of publications that could be published.
It's limited by the human life span. It might be
6,000 but there must be a limit. If there's one publication per week then that's more than 100 years of work.

There is a
upper limit on the maximum number of terms that someone can serve in the House of Representatives. Even if
we say it's 60 terms (in the U.S. that's 2 years per term). That's more than 100 years obviously.

I think what the authors are saying, if I understand them, is that even if there was an upper limit on
whatever (publications, terms, Grammy awards etc.) that wouldn't matter. There would be just a few
individuals that would have contributed greatly. Just a few that stand out by how much they've done.

- Stephen

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Lornz View Post
OCD is the nearest full-blown crazy a sane person can be.

Post below is off-topic and can be skipped.

First, I know what I call OCD. If there is a range of disorders, then it's not what I'm
thinking of.

There is this forum below (and I'm sure there are other forums). The cliche is: "You don't
have to suffer." Unfortunately in our lives, some things can't be fixed (without a miracle).

I heard once that low serotonin levels can cause OCD, but low serotonin is blamed on
depression as well. Serotonin levels can be raised, but that may not help you.




OCD Forums - Powered by vBulletin

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  #24 (permalink)
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stephenszpak View Post
I don't have a good math back round. Just a couple comments below though.

In reality there is actually an upper limit to the number of publications that could be published.
It's limited by the human life span. It might be
6,000 but there must be a limit. If there's one publication per week then that's more than 100 years of work.

There is a
upper limit on the maximum number of terms that someone can serve in the House of Representatives. Even if
we say it's 60 terms (in the U.S. that's 2 years per term). That's more than 100 years obviously.

I think what the authors are saying, if I understand them, is that even if there was an upper limit on
whatever (publications, terms, Grammy awards etc.) that wouldn't matter. There would be just a few
individuals that would have contributed greatly. Just a few that stand out by how much they've done.

- Stephen

For a bell curve upper and lower limit should be symmetrical with respect to the mean. This is not the case with publications. You can also take the number of posts by each member of Big Mike's, calculate the mean number of posts and the see whether the active posters exceed the double of the mean (the minimum being zero). If that is the case, then you know that it cannot be a bell curve, because it is asymmetrical.

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  #25 (permalink)
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@stephenszpak

I'm sure you mean well, but it's borderline offensive to assume I know nothing about the condition that is devouring my mind. Thankfully, I never get offended; I am far too arrogant to even consider the opinion of others...

Let's not derail this thread any further...

Cheers!

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  #26 (permalink)
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I cant recall the book, but there's an interesting example of just how distorted our perception of what we assume to be normally distruibuted data can be.

The example considers the distribution of wealth of 30,000 spectators in a sports stadium, and how the average wealth would be effected by adding or subtracting just one more individual to the crowd.

Adding in the total wealth of practically anyone you find at random walking down the street makes practically no difference at all to the average wealth, which remains approxiately normally distributed.

Adding the assetts of a high paid celebrity, or sports star to the crowd, increase the average wealth, but only by a little, and the distribution remains unchanged.

However, if the person you add is Bill Gates with assets of 100 billion dollars, then the effect on the average is significant !

These kinds of statistical outliers are exceedingly rare, and therefore most people cant comprehend just how asymetric the distribution can be.

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The Hare View Post
I cant recall the book, but there's an interesting example of just how distorted our perception of what we assume to be normally distruibuted data can be.

The example considers the distribution of wealth of 30,000 spectators in a sports stadium, and how the average wealth would be effected by adding or subtracting just one more individual to the crowd.

Adding in the total wealth of practically anyone you find at random walking down the street makes practically no difference at all to the average wealth, which remains approxiately normally distributed.

Adding the assetts of a high paid celebrity, or sports star to the crowd, increase the average wealth, but only by a little, and the distribution remains unchanged.

However, if the person you add is Bill Gates with assets of 100 billion dollars, then the effect on the average is significant !

These kinds of statistical outliers are exceedingly rare, and therefore most people cant comprehend just how asymetric the distribution can be.


Does the Distribution of Wealth Follow a Power Law, a Lognormal or a Gamma Distribution?

Your statement that the average wealth remains approximately normally distributed is not correct. The distribution of the average wealth follows a completely different probability distribution, which is somewhere betweem a power law, a lognormal and a gamma distribution. The upper end of the distribution has been found to be in line with the findings of Pareto, who has put forward the power law. However, this is only applicable to the upper 5-10% of the population. The rest of the population can be better fitted to a lognormal or a gamma distribution. Neither of these distributions has any similarity with a bell curve.


Bill Gates in the Sports Stadium

Your Bill Gates example is always used to show the difference between an arithmetic average and a median.

Let us assume that you have already 19,999 visitors and each has a net worth of $ 100,000. Then Bill Gates steps into the arena with a net worth of $ 60 billion. Now let us do the calculations:

(1) The average net worth of all 20,000 visitors is $ 3.1 million.
(2) The median net worth of all 20,000 visitors is $ 100,000.


Which statement, (1) or (2) best describes the 20,000 visitors?


Now you know, why I prefer a moving median to a moving average, also see anaSupertrendM11.

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