Paper 4: Fundamentals of Business Mathematics & Statistic

5.62 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

Solution :

Table : Calculation of Coefficient of Quartile Deviation and Cofficient of Variation

Marks m.p.n No. of m-50 fd fd^2 cf

students 20

(d)

0-20 10 8 -2 -16 32 8

20-40 30 12 -1 -12 12 20

40-60 50 30 0 0 0 50

60-80 70 20 +1 +20 20 70

80-100 90 10 +2 +20 40 80

n=80 fd 12= fd^2 = 104

Mean:

X A fd C

N

= +Σ ×

50 12 20

= + 80 ×

= 50 + 3 = 53

Standard deviation

fd^2 fd^2

= ΣN −^ ΣN ×C

104 12 2

= 80 −^80 × 20

= 1.3 (0.15)−^2 × 20

= 1.3 0.0225 20− ×

= 1.2775 20 1.13 20 22.6× = × =

C.V. 2 = σλ×^100

22.6 100

= 53 ×

= 42.64%

Co-efficient of Q.D.^3311

Q Q

Q Q

= −

+

Q 1 = Size of N/4th item

= Size of 80/4 = 20th item