3 ms·

Shouldn't it be: Half of the population is dumber than the median. ??

by MR4D 7y ago

Natsu 7y ago
This is true by default, the other depends on the distribution.
- the8472 7y ago
  Since intelligence must be a one-sided distribution it's probably right-tailed, which means the mean is higher than the median. So I expect (slightly) more than half of the population to be dumber than average.
  - alasdair_ 7y ago
    >Since intelligence must be a one-sided distribution it's probably right-tailed, which means the mean is higher than the median. There are a lot of people with physical injuries or disabilities that skew things to the left.
    - the8472 7y ago
      Those are all small, independent random contributions that naively would lead to a normal distribution per the central limit theorem. But it can't be quite a normal distribution due to the lower bound of 0 (in terms of absolute intelligence, not IQ). A better candidate would be a log-normal distribution which is always right-skewed.
blululu 7y ago
Yes, it should be median though the original is true for symmetric distributions. If you apply the central limit theorem, then you could say that half of all randomly samplings of a population are, on average, dumber than the population's average.
alasdair_ 7y ago
>Shouldn't it be: >Half of the population is dumber than the median. >?? Probably not. Imagine a population of three people. The middle person is not dumber than themselves.
- saagarjha 7y ago
  That’s a very small population.
- dragonwriter 7y ago
  At least 50% must be at or under the median. Exactly half under is correct only for if none is exactly at the median, which requires (but is not necessarily the case when) there are an even number of measures.
saagarjha 7y ago
The median is one measure of central tendency, though less commonly used than the mean when referring to “average”.
dragonwriter 7y ago
The median is an average, one of many (though the most common thing people mean when they say “average” is “arithmetic mean”.)

Shouldn't it be: Half of the population is dumber than the median. ??

by MR4D 7y ago

Shouldn't it be: Half of the population is dumber than the median. ??

Natsu 7y ago

This is true by default, the other depends on the distribution.

the8472 7y ago
Since intelligence must be a one-sided distribution it's probably right-tailed, which means the mean is higher than the median. So I expect (slightly) more than half of the population to be dumber than average.
- alasdair_ 7y ago
  >Since intelligence must be a one-sided distribution it's probably right-tailed, which means the mean is higher than the median. There are a lot of people with physical injuries or disabilities that skew things to the left.
  - the8472 7y ago
    Those are all small, independent random contributions that naively would lead to a normal distribution per the central limit theorem. But it can't be quite a normal distribution due to the lower bound of 0 (in terms of absolute intelligence, not IQ). A better candidate would be a log-normal distribution which is always right-skewed.

blululu 7y ago

Yes, it should be median though the original is true for symmetric distributions. If you apply the central limit theorem, then you could say that half of all randomly samplings of a population are, on average, dumber than the population's average.

alasdair_ 7y ago

>Shouldn't it be: >Half of the population is dumber than the median. >?? Probably not. Imagine a population of three people. The middle person is not dumber than themselves.

saagarjha 7y ago
That’s a very small population.
dragonwriter 7y ago
At least 50% must be at or under the median. Exactly half under is correct only for if none is exactly at the median, which requires (but is not necessarily the case when) there are an even number of measures.

saagarjha 7y ago

The median is one measure of central tendency, though less commonly used than the mean when referring to “average”.

dragonwriter 7y ago

The median is an average, one of many (though the most common thing people mean when they say “average” is “arithmetic mean”.)