Paper 4: Fundamentals of Business Mathematics & Statistic

5.56 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

Solution :

Table : Calculation of Standard Deviation

x f d d′= 10 d fd¢ fd¢^2

4.5 2 –30 –3 –6 18

14.5 3 –20 –2 –6 12

24.5 5 –10 –1 –5 5

34.5 17 0 0 0 0

44.5 12 10 1 12 12

54.5 7 20 2 14 28

64.5 4 30 3 12 36

∑f 50= – – ∑fd′=^21 ∑fd′^2 =^111

fd^2 fd^22

i^1112110

f f 50 50

 ′  ′    

σ =  −  × =  − ×

      

∑ ∑

∑ ∑

= (2.22 0.1764− )× 10 = 1.4295 × 10 = 14.295.

(C) For Continuous Series (or group distribution) : Any method discussed above (for discrete series) can be

used in this case. Of course, step deviation method is convenient to use. From the following example,

procedure of calculation will be clear.

Example 53 : Find the standard deviation from the following frequency distribution.

Weight (kg.) No. of persons

44–46 3

46–48 24

48–50 27

50–52 21

52–-54 5

Total 80