Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 6.17

Example13 :
Calculate Karl Pearson’s coefficient of correlation from the following information and comment on the
result:
Standard deviation of X series 10
Standard deviation of Y series 12
Arithmetic mean of X series 25
Arithmetic mean of Y series 35
Summation of product of deviations from
actual arithmetic means of two series 24
Number of observations 20

Solution:

x y

r xy

=Nσ σ

∑

where
r = coefficient of correlation

∑xy = Summation of product of deviations from
actual arithmetic means of two series
σx = Standard deviation of X series
σy = Standard deviation of Y series

r^2424 0.01

=20x10x12 2400= =

Example14 :
Calculate the coefficient of correlation by Pearson’s method between the density of population and the
death rate.
Area in Sq. Km Population in ‘000 No. of deaths
A 300 60 600
B 360 180 2880
C 200 80 1120
D 120 84 1680
E 240 144 2448
F 160 48 624

Solution:
Using formula

Density(X) populationand death rate(Y) No.ofdealth

= area = population