88 n 60 example 4 following is the distribution of

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Unformatted text preview: sons Solution: Income C.I 0-10 10-20 20-30 30-40 40-50 50-60 60-70 0-10 6 10-20 8 Number of Persons (f) 6 8 10 12 7 4 3 50 20-30 10 Mid X 5 15 25 A 35 45 55 65 97 30-40 40-50 50-60 60-70 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 open-end 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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