At 08:58 10/10/2013 +0000, Galbraith, Jane wrote:
>It may not be his grasp of mathematics but his undue optimism that is at
>fault. ... It appears that the Secretary of State believes that continual
>improvement is possible.
>Then it would be possible for all schools to perform better than the
>current average. This would lead to perpetual improvement, each year the
>average being higher than the year before! On the other hand if enough
>schools performed badly then the average would go down and some schools
>would suddenly become good without any improvement.[/quote]
All true, but I don't think that is what was said, or even implied, was
it? If one says "good means above the national average", that surely
implies that one is comparing individual schools with the _contemporaneous_
national average (whatever sort of 'average' one is talking about). If one
defined "good" as being above some historical average, then an awful lot of
things in this world would be "good" when they probably didn't deserve to
be! Is it not probable that the fact that he responded to the question
about whether it was possible for all schools to be 'above average' by
talking about 'continual improvement' indicates that the asking of the
first question led him to suddenly realise the mathematical 'problem' that
it posed?
As for the maths, I don't think there is any (sensible) sort of 'average',
with any sort of distribution, that can be below every one of the values
which have been 'averaged', is there?
Kind Regards,
John
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