Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 6.7

METHOD II WHEN DEVIATIONS ARE TAKEN FROM ASSUMED MEAN

This method is generally used when actual mean of X series or of Y series or both are in decimals, in which
case using method I becomes tedious; in such a case deviations are taken from assumed mean to simplify
the calculations.

( )( )

( ) ( )

dx yd

d d -x y

r= N

2 2

2 dx 2 dy

d -x d -y

N N

Where
dx = Deviations taken from assumed mean of X series = (X - Ax)
dy = Deviations taken from assumed mean of Y series = (X - Ay)
Sdx = Sum of deviations of X series from its assumed mean
Sdy = Sum of deviations of Y series from its assumed mean
Sdx^2 = Sum of squares of deviations of X series from its assumed mean
Sdy^2 =^ Sum of squares of deviations of Y series from its assumed mean
Sdxdy = Sum of the product of deviations of X and Y series from an assumed mean
N = number of observations
r = Correlation coefficient

Example 2 :

Calculate coefficient of correlation from following data

X 0 15 15 14 10 12 10 8 16 15

Y 20 15 12 10 8 5 6 15 12 18

Solution:

Table : Calculation of coefficient of correlation

X Y dx = x-Ax dy = y-Ay dx^2 dy^2 dxdy

0 20 -10 5 100 25 -50

15 15 5 0 25 0 0

15 12 5 -3 25 9 -15

14 10 4 -5 16 25 -20

10 8 0 -7 0 49 0

12 5 2 -10 4 100 -20

10 6 0 -9 0 81 0

8 15 -2 0 4 0 0

16 12 6 -3 36 9 -18

15 18 5 3 25 9 15

ΣX=115 ΣY= 121 Σdx = 15 Σdx = -29 Σd^2 = 235 Σd^2 = 307 Σdx dy= -108