Paper 4: Fundamentals of Business Mathematics & Statistic

5.52 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

Then ( )

2

i i

i

f x x

f

σ = ∑ −

∑

.... (2) Where, x = weighted A. M.

Note : If variates are all equal (say K), then σ= 0, as x = K and ∑(x x− )=^0

Example 49: For observations 4, 4, 4, 4, s = 0 as x 4 and= ∑(4 4) 0− =

Short cut method for calculating s.d.

If x (A. M.) is not an integer, in case (1), (2) ; then the calculation is lengthy and time consuming. In such

case, we shall follow the following formulae for finding s.d.

(c) For simple observations,

d^2 d^2

n n

σ = − 

  

 

∑ ∑ .... (3)

Where, d = x – A, A is assumed mean.

(d) For simple (or group) frequency distribution

fd^2 fd^2

,

f f

σ = − 

 

 

∑ ∑

∑ ∑ Where, d = x – A

(e) For group frequency distribution having equal class interval

fd^2 fd^2

f f i

′  ′

σ = −  ×

 

∑ ∑

∑ ∑

.... (5) where, d′=x A−i

(This is known as step deviation method)

Observation

(x xi )^2 x^2 x^2

n n n

σ = − = − 

  

 

∑ ∑ ∑ .... (6)

(The proof is not shown at present)

Note : Formula (3) may be written as, for step deviation where d′=x A−i