Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.51

M.D.

f|d| 91.70

= f = 50

∑

∑ = 1.834 = ` 1.83

Coeff. Of dispersion (about A.M.) =M.D. 1.824A.M.= 8.18= 0.223 = 0.22

Coeff. Of dispersion (about median) =MedianM.D. =1.8348.13 = 0.225 = 0.23

Advantages of Mean Deviation :
(1) It is based on all the observations. Any change in any item would change the value of mean deviation.
(2) It is readily understood. It is the average of the deviation from a measure of central tendency.
(3) Mean Deviation is less affected by the extreme items than the standard deviation.
(4) It is simple to understand and easy to compute.
Disadvantages of Mean Deviation :
(1) Mean deviation ignores the algebraic signs of deviations and as such it is not capable of further
algebraic treatment.
(2) It is not an accurate measure, particularly when it is calculated from mode.
(3) It is not popular as standard deviation.
Uses of Mean Deviation :
Because of simplicity in computation, it has drawn the attention of economists and businessmen. It is useful
reports meant for public.

5.3.2.3. Standard Deviation :
In calculating mean deviation we ignored the algebraic signs, which is mathematically illogical. This
drawback is removed in calculating standard deviation, usually denoted by ‘σ’ (read as sigma)
Definition : Standard deviation is the square root of the arithmetic average of the squares of all the deviations
from the mean. In short, it may be defined as root-mean-square deviation from the mean.
If x is the mean of x 1 , x 2 , ......., xn, then σ is defined by

n^1 {(x 1 −x)^2 +......+(xn−x)^2 }

 ^ ( )

2

i

(^1) x x
n
= ∑ −
Different formulae for computing s. d.
(a) For simple observations or variates.
If be A.M. of x 1 , x 2 ........, xn, then σ = n^1 ∑(x xi− )^2
(b) For simple or group frequency distribution
For the variates x 1 , x 2 , x 3 , ......., xn, if corresponding frequencies are f 1 , f 2 , f 3 , ....., fn