5.16 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICSMeasures of Central Tendency and Measures of Dispersion
- Find f log x and divide it by f, i.e., calculate
f logx
f
.- Now antilog of the quotient thus obtained is the required G. M. The idea given above will be clear
from the following example.
Example 16 : Find (weighted) G. M. of the table given below : ––
x f
4 2
12 4
18 3
26 1
Solution :
Table : Calculation of G.M
x f log x f log x
4 2 0.6021 1.2032
12 4 1.0792 4.3168
18 3 1.2553 3.7659
26 1 1.2553 1.4150
Total 10 ––– 10.7019
∴ log G =f logx
f10.7019 1.07019
= 10 =∴ G = antilog 1.07019 = 11.75
Advantages Geometric Mean
(i) It is not influenced by the extreme items to the same extent as mean.
(ii) It is rigidly defined and its value is a precise figure.
(iii) It is based on all observations and capable of further algebraic treatment.
(iv) It is useful in calculating index numbers.
Disadvantages of Geometric Mean :
(i) It is neither easy to calculate nor it is simple to understand.
(ii) If any value of a set of observations is zero, the geometric mean would be zero, and it cannot be
determined.
(iii) If any value is negative, G. M. becomes imaginary.
[Use. It is used to find average of rates of changes.]
SELF EXAMINATION QUESTIONS- Find G.M of the following numbers :
(i) 3, 9, 27 [Ans.9]
(ii) 3, 6, 24, 48 [Ans. 12]