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Comment by sgregnt | Hacker News Reader

> Half of the public is below average, in fact.

Not necessary

When it comes to refinancing at a bank, they certainly are. It's a very specific subject that few ever come in contact with. It's like kernel programming, also a topic that indirectly affects most people but is truly understood by very few.

I mean, it depends on the average. We can (and often do) select an average where it is necessarily so.

Please name an average that necessarily has "half of the population is below average", because that is not true for median, mode or the traditional average.

Not an average, but their argument is salvageable:

In a perfect world, exactly half of a population will be (equal to or) below any average when frequency is a normal distribution. Like IQ scores. So when they say "half of the population is below average [IQ]", it's not complete nonsense.

Yes, there are absolutely many distributions where the assertion is correct. It is that fact, that the truth is contingent on the nature of the distribution, which prompts the comment that "half are below average" is not necessarily true but only true contingent on the distribution of "level of expertise".

While that is a very vaguely defined term which is hard to measure accurately, it seem likely that it does not follow a normal distribution but is rather has a bulge at the lower end and have a long tail at the upper end. If this hand-wavey distribution is accepted, that would likely mean that fewer than half are above average. But again, that is contingent on the distribution and not a necessary truth.

This is the definition of median, surely?

That, uh...is true for the median. That's pretty much the definition of the median.

> the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution

So what is the median of the set (5,1,1,1,1,1), does half of that set have a value below the median?

Is that not what the median is?

Yep

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