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It should be rigidly defined 2 it should be based on

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Unformatted text preview: ute measure of dispersion gives the variation in rainfall in mm. On the other hand relative measures of dispersion are free from the units of measurements of the observations. They are pure numbers. They are used to compare the variation in two or more sets, which are having different units of measurements of observations. The various absolute and relative measures of dispersion are listed below. Absolute measure Relative measure 1. Range 1.Co-efficient of Range 2.Quartile deviation 2.Co-efficient of Quartile deviation 3.Mean deviation 3. Co-efficient of Mean deviation 4.Standard deviation 4.Co-efficient of variation 7.3 Range and coefficient of Range: 7.3.1 Range: This is the simplest possible measure of dispersion and is defined as the difference between the largest and smallest values of the variable. In symbols, Range = L – S. Where L = Largest value. S = Smallest value. 142 In individual observations and discrete series, L and S are easily identified. In continuous series, the following two methods are followed. Method 1: L = Upper boundary of the highest class S = Lower boundary of the lowest class. Method 2: L = Mid value of the highest class. S = Mid value of the lowest class. 7.3.2 Co-efficient of Range : L −S Co-efficient of Range = L+S Example1: Find the value of range and its co-efficient for the following data. 7, 9, 6, 8, 11, 10, 4 Solution: L=11, S = 4. Range = L – S = 11- 4 = 7 L −S Co-efficient of Range = L+S 11 − 4 = 11 + 4 7 = 0.4667 = 15 Example 2: Calculate range and its co efficient from the following distribution. Size: 60-63 63-66 66-69 69-72 72-75 Number: 5 18 42 27 8 Solution: L = Upper boundary of the highest class. = 75 143 S = Lower boundary of the lowest class. = 60 Range = L – S = 75 – 60 = 15 L −S Co-efficient of Range = L+S 75 − 60 = 75 + 60 15 = = 0.1111 135 7.3.3 Merits and Demerits of Range : Merits: 1. It is simple to understand. 2. It is easy to calculate. 3. In certain types of problems like quality control, weather forecasts, share price analysis, et c., range is most...
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