Paper 4: Fundamentals of Business Mathematics & Statistic

5.54 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

Here the average or A.M. 16.40 and the variates deviate on an average from the A.M. by ` 7.66.

For method (b) : Let A (assumed mean) = 16

( )

d^2 d^2

s.d. n n ,

 

σ = = −  

 

∑ ∑ by using formula (3)

( )

294 2 2 2

= 5 −   5 = 58.8−0.4 = 58.8 0.16−

  = ` 7.66.

Note : If the actual mean is in fraction, then it is better to take deviations from an assumed mean, for

avoiding too much calculations.

(B) For discrete series (or Simple Frequency Distribution). There are three methods, given below for computing

Standard Deviation.

(a) Actual Mean, (b) Assumed Mean, (c) Step Deviation.

For (a) the following formula are used.

This method is used rarely because if the actual mean is in fractions, calculations take much time.

f x x( )^2 or fd^2 ;

f f

σ = ∑ − ∑

∑ ∑

d = x −x

(In general, application of this formula is less)

For (b), the following steps are to be used :–

(i) Find the deviations (from assumed mean), denote it by d.

(ii) Obtain ∑fd.

(iii) Find ∑fd ,^2 i.e. (fd × d and then take ∑, and hence use the formula.

fd^2 fd^2

f f

= −

Example 51 : Find the Standard deviation of the following series :

x f

10 3

11 12

12 18

13 12

14 3

Total 48