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.
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