Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.59

Solution :
(a) For firm A : total wages = 586 × 52.5 = 30,765. For firm B : Total wages = 648 × 47.5 = 30,780. i.e. Firm B pays largest amount.
(b) For firm A : σ^2 = 100 ∴ σ = 10

Now, v=Meanσ ×^100 =52.5^10 ×100 19.04=

For firm B : σ^2 = 121 ∴ σ = 11

V^11 100 23.16

=47.5× =

∴ Firm B has greater variability, as its coefficient of variation is greater than that of Firm A.

(c) Here, n 1 = 586, x 1 =52.5,σ = 1 10

n 2 =648, x 2 =47.5σ = 2 11

12 1 1 2 2

1 2

x n x n x 586 52.5 648 47.5 30,765 30,780

n n 586 648 1234

∴ = + = × + × = +

+ +

6 1,545 49.87

=1,234 = = ` 49.9

Again, d 1 =x 1 −x 2 =52.5 49.9 2.6 ;− = d 2 = 47.5 – 49.9 = – 2.4

1 1^2 2 2^2 1 1^2 2 2^2

(^1212)
n n n d n d
n n
∴ σ =  σ + σ + + 
 + 
 

586 10( )^2 648 11( )^2 586 2.6( )^2 648 2.4( )^2

586 648

 + + + − 

=  + 

 

58600 78408 3962 3733

1234

=  + + + 

 

144703

1234

= = 10.83 (Calculation by log table)

Example 57 : In an examination a candidate scores the following percentage of marks :
English 2nd language mathematics Science Economics
62 74 58 61 44
Find the candidates weighted mean percentage weighted of 3, 4, 4, 5 and 2 respectively are allotted of
the subject. Find also the coefficient of variation.