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Thanks for the links, just a minor nitpick:

From the article (first link), he said "condemned the fact that one in five pupils are leaving primary school without reaching the "national average" in English".

You made that into "half", possibly confusing median and average, something that that person did not do, judging by the quote.

Sure, original quotes:

> one in five children in primary schools at the age of 11 are leaving primary school without the national average

> "good" requires pupil performance to exceed the national average, and all schools must be good

I'm sure there was a certain minister who stood up in parliament declaring it to be an outrage that 50% of our children scored below average but I'm struggling to find a reference, partly because politicians keep making this same gaffe.

My point with the original "quote" ('"quote"' is not a quote either) was to illustrate the absurdity of these types of headlines. They're made all the time and they're always ridiculous.

I have seen that quote attributed to Bush, but it sounds like it could've been a made-up anecdote to make him look bad.

Yeah, I see this type of confusion all the time.

When most non-mathematicians (yep, SWEs included) use the word "average" sometimes the concept they intend to convey is "mean", and sometimes it is "median" (because of a commonplace implicit assumption that the distribution, even if not normal, is at least roughly symmetrical).

So I try not to use the word "average" at all (unless defined), and to only use "median" and "mean".

I think mentioning "half" here was just an exaggeration to make a point.

On a related note, I think it is perfectly possible that 70 % of all drivers are "better than average". It's a mathematical tautology that only 50 % are better than median, but the distribution of driver skill does not need to be a symmetric distribution, so median and average can be significantly different.

With things like IQ, the distribution is symmetrical by definition.

I was taught at school that "mean", "median" & "mode" were different averages.

Oh how we all love ambiguity in language!

Yes, sure. I'm not native English speaker but I think also in English, in colloquial use "average" is the same as "arithmetic mean".

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