Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 6.15

Example 11 :
Calculate Karl Pearson’s coefficient of correlation between variables X and Y using the following data:

X 25 40 30 25 10 5 10 15 30 20

Y 10 25 40 15 20 40 28 22 15 5

Solution: Table : Calculation of coefficient of correlation

X Y x X 21= − y Y 22= − x^2 y^2 xy

25 10 4 -12 16 144 -48

40 25 19 3 361 9 57

30 40 9 18 81 324 162

25 15 4 -7 16 49 -28

10 20 -11 -2 121 4 22

5 40 -16 18 256 324 -288

10 28 -11 6 121 36 -66

15 22 -6 0 36 0 0

30 15 9 -7 81 49 -63

20 5 -1 -17 1 289 17

∑X 210= ∑Y 220= ∑X 0= ∑y 0= ∑x 1090^2 = ∑x 1228^2 = ∑xy 235= −

X X^210

= N 10=

∑

= 21

Y Y^220

= N 10=

= 22

r^235

1090x1228

= −

235

1156.94

= −

= – 0.203

(‘Hint - First calculate mean of X series and Y series. If they are in integer then use Method I. If they are in
points then use short cut method ie. Method II)