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Unformatted text preview: dly defined.
2. It is defined on all observations.
3. It is amenable to further algebraic treatment.
4. It is the most suitable average when it is desired to give
greater weight to smaller observations and less weight to the
larger ones.
Demerits of H.M :
1. It is not easily understood.
2. It is difficult to compute.
3. It is only a summary figure and may not be the actual item in
the series
4. It gives greater importance to small items and is therefore,
useful only when small items have to be given greater
weightage.
Geometric mean :
The geometric mean of a series containing n observations
th
is the n root of the product of the values. If x1,x2…xn are
,
observations then
G.M = n x1. x2 ... xn
H.M = = (x1.x2 … n)1/n
x 1
log(x1.x2 … n)
x
n
1
=
(logx1+logx2+…
+logxn
n
∑ log xi
=
n
∑ log xi
GM = Antilog
n log GM = 102 For grouped data ∑ f log xi GM = Antilog N Example 8:
Calculate the geometric mean of the following series of monthly
income of a batch of families 180,250,490,1400,1050
x
180
250
490
1400
1050
GM = logx
2.2553
2.3979
2.6902
3.1461
3.0212
13.5107 Antilog ∑ = Antilog log x n 13.5107
5 = Antilog 2.7021 = 503.6 Example 9:
Calculate the average income per head from the data given
below .Use geometric mean.
Class of people
Number of
Monthly income
families
per head (Rs)
Landlords
2
5000
Cultivators
100
400
Landless – labours
50
200
Money – lenders
4
3750
Office Assistants
6
3000
Shop keepers
8
750
Carpenters
6
600
Weavers
10
300
103 Solution:
Class of people Annual
income
( Rs) X Landlords
Cultivators
Landless –
labours
Money – lenders
Office Assistants
Shop keepers
Carpenters
Weavers 5000
400
200
3750
3000
750
600
300 GM = Antilog ∑ Number
of
families
(f)
2
100
50
4
6
8
6
10
186 Log x f logx 3.6990
2.6021
2.3010 7.398
260.210
115.050 3.5740
3.4771
2.8751
2.7782
2.4771 14.296
20.863
23.2008
16.669
24.771
482.257 f log x N 482.257 = Antilog 186 = Antilog (2.5928)
= Rs 391.50
Merits of Geometric mean :
1. It is rigidly defined
2. It is bas...
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 Winter '08
 Moshiri
 Business

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