## Wednesday, December 05, 2012

### Eleven Plus Marks

Your child is waiting impatiently for 11+ results. By now you know the actual scores – but want to delve a little deeper into possible reasons for failing the examination. “How did this happen? We were doing so well!”

Part of the thinking behind the arrival at the pass or fail scores is the presumption that some children will be above the pass level, others around the pass/fail level and some, poor souls, in the fail band. This suggests a spread or scattering of numbers – and these numbers can be examined mathematically.

A little explanation may help. Eleven plus parents, and their children, know how to work out a mean.

What is the mean of 2, 3, 7, 4 and 9?

You would have worked this out very quickly to be:  5.

Now the statisticians among you would give the deviations from the mean.

 Numbers Mean Deviation from the Mean 2 5 -3 3 5 -2 7 5 2 4 5 -1 9 5 4

If you add the -3, -2, 2, -1 and 4 your answer should be 0. (So who passes or who fails?)

What now happens is that the deviations from the mean are squared. Eleven plus candidates take note: a minus times a minus is a plus!

 -3 -3 times – 3 = 9 -2 - 2 times minus 2 = 4 2 2 times 2 = 4 -1 -1 times – 1 = 1 4 4 times 4 = 16

This then leads to finding the square root of the variance.  (The square root of 9 is 3, the square root of 16 is 4 and so on.)

We now arrive at a definition that the standard deviation is the positive square root of the variance.

If you do happen to arrive before an appeal board – someone may comment on how far your child was from the cut-off point. You don’t really want to know, however, that he or she was two or three marks below – what you want to know is how far your child was from the pass mark. I hope the feed-back is positive.