318 MATHEMATICS
File Name : C:\Computer Station\Maths-IX\Chapter\Appendix\Appendix–2 (03–01–2006) PM65
A2.5 Summary
Year Enrolment Values Difference Values Difference
(in %) given between given between
by (2) values by (4) values
0 41.9 41.90 0 41.9 0
1 42.6 42.12 0.48 42.3 0.3
2 42.7 42.34 0.36 42.52 0.18
3 42.9 42.56 0.34 42.74 0.16
4 43.1 42.78 0.32 42.96 0.14
5 43.2 43.00 0.2 43.18 0.02
6 43.5 43.22 0.28 43.4 0.1
7 43.5 43.44 0.06 43.62 – 0.12
8 43.6 43.66 – 0.06 43.84 – 0.24
9 43.7 43.88 – 0.18 44.06 – 0.36
10 44.1 44.10 0 44.28 – 0.18
As you can see, many of the values that (4) gives are closer to the actual value
than the values that (2) gives. The mean of the errors is 0 in this case.
We will stop our process here. So, Equation (4) is our mathematical description
that gives a mathematical relationship between years and the percentage of enrolment
of girls of the total enrolment. We have constructed a mathematical model that describes
the growth.
The process that we have followed in the situation above is called
mathematical modelling.
We have tried to construct a mathematical model with the mathematical tools that
we already have. There are better mathematical tools for making predictions from the
data we have. But, they are beyond the scope of this course. Our aim in constructing
this model is to explain the process of modelling to you, not to make accurate predictions
at this stage.
You may now like to model some real-life situations to check your understanding
of our discussion so far. Here is an Exercise for you to try.