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.
