11-Unit11

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Unformatted text preview: stical and algebraic treatment. 5. It should have sampling stability 6. It should not be unduly affected by extreme values. Sikkim Manipal University Page No. 186 Research Methodology Unit 11 Measures of Dispersion 1. Range 2. Quartile deviation 3. Mean deviation 4. Standard deviation 5. Lorenz curve Range, Quartile deviation, Mean deviation and Standard deviation are mathematical measures of dispersion. Lorenz curve is a graphical measure of dispersion. Measures of dispersion can be absolute or relative. An absolute measure of dispersion is expressed in the same unit of the original data. When two sets of data are expressed in different units, relative measures of dispersion are used for comparison. A relative measure of dispersion is the ratio of absolute measure to an appropriate average. The following are the important relative measures of dispersion. 1. Coefficient of range 2. Coefficient of Quartile deviation 3. Coefficient of Mean deviation 4. Coefficient of Standard deviation Range Range is the difference between the lowest and the highest value. Symbolically, range = highest value – lowest value Range = H–L H = highest value L = lowest value Relative measure of dispersion is co-efficient of range. It is obtained by the following formula. Coefficient of range = Sikkim Manipal University (H – L) / (H + L) Page No. 187 Research Methodology Unit 11 1. Calculate of range of the following distribution, giving income of 10 workers. Also calculate the co-efficient of range. 25 37 40 23 58 75 89 20 81 Range = H–L H = highest value = 95 L = lowest value = 20 Range = 95 –20 = 75 Coefficient of range = (H – L) / (H + L) = (95 –20) / (95 +20) = 75/ 115 = 95 .6521 Range is simple to understand and easy to calculate. But it is not based on all items of the distribution. It is subject to fluctuations from sample to sample. Range cannot be calculated for open-ended series. Quartile Deviation Quartile deviation is defined as inter quartile range. It is based on the first an...
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