Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 6.13

Example 8 :
The following data gives the distribution of the total population and those who are totally or partially blind
among them. Find out Karl Pearson’s coefficient of correlation.

Age (in Years) No. of persons (in’000) Blind

15 80 12

16 100 30

17 120 48

18 150 90

19 200 150

20 250 200

Solution:
As we have to find out the correlation between the age of persons and the number of persons who are
blinds, we find out percentage of blinds (i.e. blinds per 100 persons of population).
Taking age as X and blinds per 100 persons as Y
Table : Calculation of correlation coefficient
X Y x = X – 17.5 y = Y – 50 xy x^2 y^2
15 15 -2.5 -35 87.5 6.25 1225
16 30 -1.5 -20 30 2.25 400
17 40 -0.5 -10 5 0.25 100
18 60 0.5 10 5 0.25 100
19 75 1.5 25 37.5 2.25 625
20 80 2.5 30 75 6.25 900
∑X 105= ∑Y 300= X 0= ∑y 0= ∑Xy 24= ∑X 17.5^2 = ∑y 3350^2 =

X X^105 17.5

= N 6= =

∑

Y Y^30050

= N 6= =

∑

2 2

r xy

x y

= ∑

∑ ∑

r^240 0.99

17.5x3350

= =

There is very high positive correlation between the age of a person & blindne s.
Example 9:
Calculate the Karl Pearson’s coefficient of correlation from the information given below-

• Covariance between two variables X and Y = -15


• Coefficient of variation of X = 25%