Average marks not enough to decide the better school
The Sunday Nation
Nairobi,
24 November 2013
Suppose you wanted to
hire a private tutor for your child and two candidates presented the
following records. The first one, Anne, tutored three pupils last year
and they scored: 90, 50 and 55 marks respectively – an average of 65.
The second tutor,
Ben, also presents the scores of three pupils from last year with the
following marks: 60, 65, and70 – the average is also 65. If you were to
make your choice based on the marks only, which of the two would you
pick: Anne or Ben?
My opinion is that
Ben is probably the better tutor. Anne’s results are only high because
one of her pupils was quite intelligent and managed a very high score
which pulled up the average for the group. Thus I conclude that it was
not the tutor’s effort that is responsible for high average score but
one pupil’s exceptional intelligence.
This is an important
consideration that parents must always make when choosing schools for
their children. How much of the average exam score can be attributed to
the teachers’ efforts and how much is from the pupils’ intelligence?
It is a difficult
question but the example above provides a possible way of making the
decision. Anne’s scores appear quite widely spread from the average
while Ben’s are all very close to it.
Mathematically, the
magnitude of this spread from the average is expressed in a quantity
known as the standard deviation. It is calculated in a four step process
as follows:
Step 1 in to subtract
each data value from the average. In Anne’s scores, we get: 90 – 65 =
25; 50 – 65 = -15; and 55 – 65 = -10. Now some of the answers are
positive and some negative, therefore we go to strep 2 which is to
square each of them as follows: 25 squared = +625; -15 squared = +225;
and -10 squared = +100 – all are now positive quantities.
The third step is to
get the average of these squared values; that is (625 + 225 + 100)
divided by 3. In other words 950/3 = 316.7.
The final step is to
find the square-root of 316.7 and this comes to 17.8. Now this is just a
numerical answer, but what does it mean?
The standard
deviation tells us how far the majority of the data is from the average
value. Two thirds of the scores will be found somewhere between 65 –
17.8 and 65 + 17.8; that is from 47.2 to 82.8.
In tutor Ben’s scores
the standard deviation is 4.1. That is the majority of his students’ are
closer to the average (65) than Anne’s. For this reason, I think Ben is
a better tutor.
So, when deciding
which school to take your child to, do just look at the average exam
scores; find out what the standard deviation is. For schools with
similar mean marks, the lower the standard deviation, the better.
 |
 |