Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.53

d^2 d^2

i

n n

σ = ′ − ′ ×

 

 

∑ ∑ .... (7)

5.3.2.3.1. Computation for Standard Deviation :
(A) For individual observations computation may be done in two ways :
(a) by taking deviations from actual mean. Steps to follow––
(1) Find the actual mean, i.e. x.
(2) Find the deviations from the mean, i.e., d.
(3) Make squares of the deviations, and add up, i.e. ∑d.^2
(4) Divide the addition by total number of items, i.e., find d / n^2 and hence make square root
of it.
(b) by taking deviations from assumed mean. Steps to follow––
(1) Find the deviations of the items from an assumed mean and denote it by d find also ∑d.
(2) Square the deviations, find ∑d.^2
(3) Apply the following formula to find standard deviation.

( )

d^2 d^2

S.D.

n n

σ = − 

  

 

∑ ∑

Example 50 : Find s.d. of (`) 7, 9, 16, 24, 26. Calculation of s.d. by methods (a) Taking deviations of Sum (b)
Taking deviations from Assumed Mean

Method (a) : Taking deviation from A.M. Method (b) : Taking deviation from assumed mean
Variate Variate
() A.M. (16.4) () A.M. (16)
x d d^2 x d d^2
7 –9.4 88.36 7 –9 81
9 –7.4 54.76 9 –7 49
16 –0.4 0.16 16 0 0
24 7.6 57.76 24 8 64
26 9.6 92.16 26 10 100
Total –– 293.20 – 2 294

For method (a) : x A.M.( )=^825 = 16.40

σ =( s.d)= n^1 ∑(x x− )^2 =^1 n∑d^2 =^15 ×293.20= 58.64 = ` 7.66