Paper 4: Fundamentals of Business Mathematics & Statistic

5.14 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

9. A.M. of the following frequency distribution is 5.6. Find the missing frequency.
   x f
   2 4
   4 2
   6 ––
   8 3
   10 2
   [Ans. 4 ]


10. A.M. of the distribution is 56.46. Find missing frequencies. Daily Wages () Frequency
    45 5
    50 48
    55 f 3
    60 30
    65 f 5
    70 8
    75 6
    Total 150
    [Ans. 41, 12]

5.1.2. GEOMETRIC MEAN (G. M.)

Definition. : The geometric mean (G) of the n positive values x 1 , x 2 , x 3 .............xn is the nth root of the

product of the values i.e. G=nx. x ....., x 1 2 n It means, G = (x 1. x2,......... xn )1/ n

Now taking logarithms on both sides, we find

1 2 n 1 n

logG^1 log (x. x .........,x )^1 (logx ..... logx )^1 log x.....(1)

=n =n + + =n∑

∴G = antilog

(^1) log x
n

 

 ∑ 

Thus, from formula (1) we find that the logarithm of the G. M. of x 1 , x 2 ....., xn = A.M. of logarithms of x 1 , x 2 ,

......, x n.

Properties :

1. The product of n values of a variate is equal to the nth power of their G. M. i.e., x 1 , x 2 , ......, xn = Gn
   (it is clear from the definition)]


2. The logarithm of G. M. of n observations is equal to the A.M. of logarithms of n observations. [Formula
   (1) states it]