Ssanemax wrote:'on our Mock SATS we ran, half our pupils are only average or below. I want us to make sure next time we do better than that'

'Ummmmmmmm'

They could make a start on that with better teaching of statistics.

It is quite possible, indeed common, for more than half of a population to be above or below average if you're talking about the arithmetic mean (which is what most people think about as "average"). The median (50th centile) is something different, by definition half the population is above and half below.

For example it's said more than 99% of the population in Norfolk have more than the average number of fingers on their hands. It's true, but not how you may think. The numbers of people with missing fingers make the average 4.99 whatever. Everyone with 5 fingers on their right hand is above average.

Another example is wages, 50% of UK full time workers earn around £30,000 or below, 50% above (the median). But the mean wage (average) is up near £37,000. It's quite a bit higher than the median because relatively small numbers of really high earners skew the distribution.