Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 6.5

METHOD I — WHEN DEVIATIONS ARE TAKEN FROM ACTUAL ARITHMETIC MEAN

(A) WHEN STANDARD DEVIATIONS ARE GIVEN IN THE QUESTION.

( x y)

xy

r

Nσ σ

=^

Where x = Deviations taken from actual mean of X series

Y = Deviations taken from actual mean of Y series

N = Number of items

σx = Standard deviation of X series

σy = Standard deviation of Y series

(B) WHEN STANDARD DEVIATIONS ARE NOT GIVEN IN THE QUESTION

2 2

xy

r

x y

=

×

∑

∑ ∑

Where Σxy = Sum of product of deviations of X and Y series from actual mean

Σx^2 = Sum of squares of deviation of X series from its mean

Σy^2 = Sum of squares of deviation of Y series from its mean

Example: 1
Find correlation between marks obtained by 10 students in mathematics and statistics
X 2 4 6 6 8 9 10 4 7 4
Y 12 12 16 15 18 19 19 14 15 10
Solution:
Calculation of coefficient of correlation
X Y X y X^2 y^2 xy
2 12 -4 -3 16 9 12
4 12 -2 -3 4 9 6
6 16 0 1 0 1 0
6 15 0 0 0 0 0
8 18 2 3 4 9 6
9 19 3 4 9 16 12
10 19 4 4 16 16 16
4 14 -2 -1 4 1 2
7 15 1 0 1 0 0
4 10 -2 -5 4 25 10
SX = 60 SY = 150 SX = 0 Sy = 0 Sx^2 = 58 Sy^2 = 86 Sxy = 64