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Comment by bigmattystyles | Hacker News Reader

This reveals itself with the Carlin joke about the average person being dumb and that by implication 1/2 of the population is even dumber. Carlin and people who eagerly repeat it don’t know about distributions and that intelligence is not a standard distribution. Mea culpa, I used to parrot and believe the joke…

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I suspect Carlin understood averages and the diversity of intelligence better than your comment implies. He probably was just having fun with the idea. After all, it is a good joke.

Intelligence, as measured, shows a normal distribution. Just like height, grip strength, BMI, and many other human metrics.

Hence the name of a rather notorious book by Charles Murray.

The median is also an average.

Only in a standard distribution right?

No, the word average is a place holder for measures of central tendencies (like mean, median and mode).

Any symmetrical distribution will have the mean equal the median.

Not exactly. This pathological distribution has no mean. https://en.wikipedia.org/wiki/Cauchy_distribution

You got me—funny thing is I took a couple analysis courses in school so I should have been more careful making such a strong statement.

But that’s the definition of a standard distribution? Intelligence is not, at least I think.

AFAIK "standard distribution" is not a defined mathematical term; usually it's shorthand for standard normal distribution.

Can't comment on intelligence distributions.

"standard normal distribution" is a normal distribution with mean 0 and s.d. 1.

To talk about whether intelligence follows a (one-dimensional) normal distribution we have to assign a number to it. That number is usually IQ, but by design the raw score is transformed to make IQ scores follow a normal distribution.

So it is trivially true.

If we want to go beyond that, what does it even mean to say, for example, "twice as smart"?

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