# Numbers

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ARE girls cleverer than boys? Last year, according to a study by the Office for Standards in Education, 43 per cent of girls passed five or more GCSE subjects with grades A to C, while only 34 per cent of boys did so. The 9 per cent difference argues powerfully, but before we all join the chorus of 'Nya-nya- nya; boys are thick' let's indulge in some statistical fantasy.

Suppose, for example, all girls secure four, five or six passes, with an equal number in each group, while boys range equally from one to nine passes. Both average five passes, but in the 'five or more' category we have 66.7 per cent of girls compared with 55.6 of boys: a massive 11.1 per cent lead for the girls. Yet a criterion of 'six or more' would have left the boys themselves 11.1 per cent ahead.

Statistically, this happens because the two groups have widely different standard deviations (the average divergence from the mean). And when that occurs, a well-chosen cut-off point can 'prove' whatever you like.

Sadly for the boys' cause, the Ofsted survey shows that girls have on average more passes than boys anyway. While arguments based on distribution are not exhausted, the figures reveal another intriguing result: there is a strong negative correlation between any school's exam performance and the percentage of its pupils who have school dinners. The more children eat a school's food, the worse its exam results.

Statistics rarely answer questions, but they should indicate which further questions to ask. Do the girls take sandwiches?