Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 6.11

= 1 – 0.205

= 0.795

Example 6 : Find the coefficient of correlation between price and sales from the following data :

Prices (X) 103 98 85 92 90 88 90 94 85

Sales (Y) 500 610 700 630 670 800 570 700 680

Solution: Let the value of assumed mean for X(AX) be 90
Let the value of assumed mean for Y(Ay) be 700
Table : Calculation of correlation coefficient

X Y dx=X A− 1 x dy=Y A− 10 Y d^2 x dxdy

= X–90/1 = Y – 700/10 d^2 y

103 500 13 -20 169 400 -260

98 610 8 -9 64 81 -72

85 700 -5 0 25 0 0

92 630 2 -7 4 49 -14

90 670 0 -3 0 9 0

88 800 -2 10 4 100 -20

90 570 0 -13 0 169 0

94 700 4 0 16 0 0

95 680 5 -2 25 4 -10

d 25x= d 44y= − d 307x^2 = d 812y^2 = d d 376x y= −

Note : As r is a pure number, change of scale does not affect its value. Hence the values are divided by 10 in
column 4 to make the calculations simple. The following formula can be applied to all the problems.

( )( )

( ) ( )

y

x y

x y

2 2

(^2) x x 2 y
d d
d d N
r
d d
d N d N

−

=

− −

∑ ∑ ∑

∑ ∑

∑ ∑

( )

( )^2 ( )^2

376 25x 44

10

307 25 812 44

10 10

− − −

=

− − −

3 76 110

307 62.5 812 193.6

= − +

− −^

266

244.5 618.4

= −

266

13.64 24.88

= −

×

266

389.12

= −

r = 0.684