NCERT Class 9 Mathematics

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.