bus-stat-book1

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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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