Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.61

AM x( )= + 2 − 200108 = −2 0.54 1.46=

370 108 2

200 200

σ = −− 

 ^ = 1.85−(0.54)^2

= 1.85 0.2916− = 1.5584
= 1.248 = 1.25 (app.)

Now coeff. of variation =^1 1.46.25×100 85.62%= (app.)

Advantages of Standard Deviation :

1. Standard deviation is based on all the observations and is rigidly defined.


2. It is amenable to algebraic treatment and possesses many mathematical properties.


3. It is less affected by fluctuations of sampling than most other measures of dispersion.


4. For comparing variability of two or more series, coefficient of variation is considered as most appropriate
   and this is based on standard deviation and mean.
   Disadvantages of Standard Deviation :


5. It is not easy to understand and calculate.


6. It gives more weight to the extremes and less to the items nearer to the mean, since the squares of the
   deviations of bigger sizes would be proportionately greater than that which are comparatively small.
   The deviations 2 and 6 are in the ratio of 1 : 3 but their squares 4 and 36 would be in the ratio of 1 : 9.
   Uses of Standard Deviation :
   It is best measure of dispersion, and should be used wherever possible.

5.4 COEFFICIENT QUARTILE & COEFFICIENT VARIATION

Example 59:
Calculate co-efficient of quartile deviation and co-efficient of variation from the following data:
Marks No. of student
Below 20 8
” 40 20
” 60 50
” 80 70
” 100 80