Great comments on left blog of our time

‘half the public are below average intelligence’ Seems like a statistical impossibility to me, unless the other half are 50% above the average intelligence.

steveb at Liberal Conspiracy.

20 thoughts on “Great comments on left blog of our time”

  1. steveb’s right, isn’t he? Most people use ‘average’ to mean ‘mean’. 50/50 would be right if he meant ‘median’.

    Because only 10% of the population could be above average intelligence if they were sufficiently clever to drag up the average that far.

  2. As RT
    half are below the median by definition.
    Whether or not half are below the mean or the mode depends on the distribution. Assuming a normal distribution then half are below average on those definitions- but is the distribution in fact normal?
    Not that I suppose steveb would have understood a word of that.

  3. When last I read about it, the distribution of IQ was reported to be normal, at least for the first two or three SDs from the mean. How they handled people too impaired even to test I don’t know. But this is all too subtle; the Portugeezer is right – the twit was being very dim.

  4. Let me expand: Steveb is, IMHO, correct in two ways, one in his incredulity that 50% of the population are “above the average” and he is also right in saying that if that were the case 50% must be below (and NOBODY at precisely the average, one might also assert).

  5. “NOBODY at precisely the average, one might also assert”


    Given the large size of the population and the fact that intelligence most likely (I’ve also seen research on this) follows a standard distribution there would be a large number of people with an intelligence very close to the average and it is also likely that many of them will be precisely on the average – why shouldn’t they be?

  6. Bound to be, Emil, you’re right. since IQ is a continuous distribution, albeit treated as a discrete one (We don’t measure it beyond the decimal point, but if we could, we’d find people on 100.01, 02, 03….[somevalue of n]. And since IQ appears to be very close indeed to a normal distribution (bell curve), mean, median and mode will be, for practical purposes equal.

  7. Emil, save your incredulity and read what Roger wrote. He was saying that IF the 50/50 split were as precise as was being postulated, then … Ex hypothesi he must be right.

    All Roger and I are saying is that the steveb comment is far, far from being as stupid as I think Tim is trying to sell it as.

  8. If you treat the distribution as a mathematical abstraction, it’s a symmetrical continuous distribution. Therefore no-one has precisely the average (=mean=mode=median) IQ; 50% are above the average and 50% below. That’s the nature of a continuous distibution: any particular IQ is a point on the curve and the area under that point is zero. Thanks to the wonders of the Integral Calculus, however, the area under the curve for any finite range of IQ is finite, so that you can report the proportion of the population with IQ in the range, say, 99-101, or 99.5 – 100.5, or 145-150, or whatever. If you’d prefer to think of a histogram instead of a continuous distribution, go right ahead, but if you want to think of a continuous distribution, then the chap’s remark was stupid. That’s that.

  9. “How they handled people too impaired even to test I don’t know.”

    The size of this subset is 646 and it was decided best to confine them to a large institution on the north bank of the Thames in the belief they couldn’t cause any trouble there.

  10. There are calls for Parliament to be representative of the people as well as represent the people (it is claimed that we can’t do the latter if we don’t do the former). I was the person who first made the “half the public are below average intelligence” comment in the LC thread. It’s odd that it has been taken so seriously – it was intended as a little joke to make a point about representativeness vs. merit or suitability. Perhaps the LC commenters who didn’t get it are from the bottom half of the distribution.

  11. “Almost everybody has an above-average number of feet.”

    Ah yes but then the number of feet doesn’t follow a normal distribution

  12. Near the mean IQ is roughly normally distributed (and is in fact usually scaled to have mean 100, S.D. 15.) Out in the right-hand tail it looks a bit more like log-normal. A long way out simple statistical models break down.

    But it is nonetheless true that about 68% of the population lie in the 85-115 IQ range. This is uncontentious, and maybe even meaningful, as long as we bear in mind that what IQ tests measure is how good people are at doing IQ tests.

  13. Emil, it is not about normal distribution, it is about what was said.

    The example of feet is precisely it. Most people have above the average (Sum(f)/n) and nobody has the average (unless missing toes count!).

  14. Roger,

    The reason why no one has the average number of feet is that you can have either 1 or 2 feet, it is therefore physically impossible to have 1.x feet. IQ however (closely) follows a normal distribution which means that you will have a lot of people having average IQ if this is represented as a discrete distribution but not if treated as a continous distribution (as rightly pointed out above).

  15. No – the comment is completely nonsensical and Tim’s counter comment is also wrong.

    Steveb did not say “unless the other half are above the average intelligence” – which would make relevant all the discussion above about continuous versus non-continuous sets, distributions and whether anybody could have an IQ of exactly 100.

    He said “unless the other half are 50% above the average intelligence”.

    If he meant median or modal, he is simply wrong – the actual shape of the distribution simply doesn’t matter (except to compare the values of the three different ‘averages’) – you pick the middle value or the most common value. If he meant mean, then he is more interestingly innumerate – you can get 50% above and 50% below mean with any balanced distribution or an infinitely large variety of strange distributions. Can you get the balance if 50% are 50% above the mean? Only if the data points below the mean are also (in aggregate) 50% below the mean.

    Assuming the limiting case for his contention that the upper group is a point cluster at IQ=150, that gives you a mean IQ of 50 for the lower cluster. This is “trainable mentally retarded” under the current US definition. Definitely the political class!

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