Paper 4: Fundamentals of Business Mathematics & Statistic

5.60 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

Solution:

Table : Calculation of Coefficient of Variation

Marks f fx d fd fd^2

= x – 61

62 3 186 1 3 3

74 4 296 13 52 676

58 4 232 –3 –12 36

61 5 305 0 0 0

44 2 88 –17 –34 578

Total 18 1107 9 1293

Weighted mean percentage

fx 1107

= f = 18

∑

∑ = 61.5 marks

s.d. (s)

fd^2 fd^22

(^12939) 71.83 0.25
f f 18 18
   
= −  = −  = −
   
∑ ∑
∑ ∑
= 71.58=8.46
Coeff. of variation =A.M.s.d ×^100 =61.58.46×100 13.76%.=
Example 58 : The A.M. of the following frequency distribution is 1.46. Find f 1 and f 2.
No. of accidents : 0 1 2 3 4 5 total
No. of days : 46 f 1 f 2 25 10 5 200
Also find coefficient of variation.
Solution:
Putting these values of f 1 and f 2 we find the following distribution :
Table : Calculation of Coefficient of Variation
x f d fd fd^2
0 46 –2 –92 184
1 76 –1 –76 76
2 38 0 0 0
3 25 1 25 25
4 10 2 20 40
5 5 3 15 45
Total 200 – –108 370