Question

The following table gives the distribution of the total

population and those who are blind among them. Find out

if there is any relation between age and blindness :

Age Population (’000) No. of Blinds

0—10 150 90

10—20 90 63

20—30 50 50

30—40 32 40

40—50 20 30

50—60 12 30

60—70 5 20

70—80 2 12​

Answer 1

Given : distribution of the total  population and those who are blind among them

To Find :  is there  any relation between age and blindness

Solution:

Age   Population (’000)   No. of Blinds           Blinds %

0—10         150                   90                           0.06

10—20       90                    63                            0.07

20—30      50                     50                           0.1      

30—40        32                   40                           0.125

40—50         20                30                             0.15      

50—60           12                30                            0.25

60—70           5                 20                              0.4          

70—80         2                      12​                           0.6    

Linear

y = 0.007x - 0.061

R² = 0.816   ( not Bad  but not very good)

Quadratic

y = 0.000x² - 0.005x + 0.108

R² = 0.983  

R² value is close to 1. for Quadratic function  

hence Quadratic relation exist between age and Blind %

We can further go for cubic relations as well that would be much closer.

y = 3E-06x³ - 0.000x2 + 0.004x + 0.040

R² = 0.998

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