[nostromo95]

Any symmetrical distribution will have the mean equal the median.

[ackfoobar]

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

[nostromo95]

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.

[bigmattystyles]

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

[nostromo95]

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

Can't comment on intelligence distributions.

[ackfoobar]

"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"?