Unformatted text preview: sons Solution:
Income
C.I
010
1020
2030
3040
4050
5060
6070 010 6 1020 8 Number of
Persons (f)
6
8
10
12
7
4
3
50 2030 10 Mid
X
5
15
25
A 35
45
55
65 97 3040 4050 5060 6070 7 4 3 12 d= x−A
c
3
2
1
0
1
2
3 Fd
18
16
10
0
7
8
9
20 Mean = x = A +
= 35 – ∑ fd
N 20
50 × 10 = 35 – 4
= 31
Merits and demerits of Arithmetic mean :
Merits:
1. It is rigidly defined.
2. It is easy to understand and easy to calculate.
3. If the number of items is sufficiently large, it is more
accurate and more reliable.
4. It is a calculated value and is not based on its position in the
series.
5. It is possible to calculate even if some of the details of the
data are lacking.
6. Of all averages, it is affected least by fluctuations of
sampling.
7. It provides a good basis for comparison.
Demerits:
1. It cannot be obtained by inspection nor located through a
frequency graph.
2. It cannot be in the study of qualitative phenomena not
capable of numerical measurement i.e. Intelligence, beauty,
honesty etc.,
3. It can ignore any single item only at the risk of losing its
accuracy.
4. It is affected very much by extreme values.
5. It cannot be calculated for openend classes.
6. It may lead to fallacious conclusions, if the details of the
data from which it is computed are not given.
Weighted Arithmetic mean :
For calculating simple mean, we suppose that all the values or
the sizes of items in the distribution have equal importance. But, in
practical life this may not be so. In case some items are more
98 important than others, a simple average computed is not
representative of the distribution. Proper weightage has to be given
to the various items. For example, to have an idea of the change in
cost of living of a certain group of persons, the simple average of
the prices of the commodities consumed by them will not do
because all the commodities are not equally important, e.g rice,
wheat and pulses are more important than tea, confectionery etc., It
is the weighted arithmetic average which helps in finding out the
average value of the series...
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 Winter '08
 Moshiri
 Business, Statistics

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