## Tuesday, March 19, 2013

### Eleven Plus Memories

In the eleven plus world we meet means every day. We watched a very able girl working on a `mean’ question where she was adding up a long list of numbers. She started doing the calculation in her head, then changed to breaking the long list into three parts. (One of us was checking her calculations on a calculator!)

The conversation drifted, as it does with the very bright, into other areas of means or averages. It was suggested to her that she may enjoy looking at a `working mean’ or the deviations of successive numbers from the mean. This naturally does not play a part in the eleven plus – but a deviation from a working mean can excite the imagination of a bright nine year old (nearly 10!).

Take the example where a teacher is trying to work out the ages of pupils in a class at school.

14.5, 15.2, 14.3, 13.9, 14.10, 14.11, 15.3, 14.6, 15.6, 16.1, 15.4, 14.4, 14.9 and 15.3

We asked our embryo mathematician to estimate the average age. She came up with the age of 15 years. This was very fortunate as it made subsequent calculations easier.

We wrote down two columns of numbers – one marked `+’ and the other `-‘. The deviations are written in months.

Average Age15.00

 + - 2 7 3 9 6 15 8 2 13 1 4 4 3 6 8 5 3 13 34 21

The average age is 15 years 0 months less 1.2 months which is 14 years and 10.8 months or rounded up to 14 years and 11 months.

Our eleven plus girl will certainly meet up with deviations from the mean when she is studying advanced mathematics a year early! I wonder if she will remember this lesson.