It is rigidly defined and its value is always

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Unformatted text preview: possible for further algebraic treatment. 5. It is less affected by the fluctuations of sampling and hence stable. 6. It is the basis for measuring the coefficient of correlation and sampling. = Demerits: 1. It is not easy to understand and it is difficult to calculate. 2. It gives more weight to extreme values because the values are squared up. 3. As it is an absolute measure of variability, it cannot be used for the purpose of comparison. 166 7.6.7 Coefficient of Variation : The Standard deviation is an absolute measure of dispersion. It is expressed in terms of units in which the original figures are collected and stated. The standard deviation of heights of students cannot be compared with the standard deviation of weights of students, as both are expressed in different units, i.e heights in centimeter and weights in kilograms. Therefore the standard deviation must be converted into a relative measure of dispersion for the purpose of comparison. The relative measure is known as the coefficient of variation. The coefficient of variation is obtained by dividing the standard deviation by the mean and multiply it by 100. symbolically, σ Coefficient of variation (C.V) = × 100 X If we want to compare the variability of two or more series, we can use C.V. The series or groups of data for which the C.V. is greater indicate that the group is more variable, less stable, less uniform, less consistent or less homogeneous. If the C.V. is less, it indicates that the group is less variable, more stable, more uniform, more consistent or more homogeneous. Example 15: In two factories A and B located in the same industrial area, the average weekly wages (in rupees) and the standard deviations are as follows: Factory A B Average 34.5 28.5 Standard Deviation 5 4.5 No. of workers 476 524 1. Which factory A or B pays out a larger amount as weekly wages? 2. Which factory A or B has greater variability in individual wages? Solution: Given N1 = 476, X1 = 34.5, σ1 = 5 167 N2 = 524, X 2 = 28.5, σ2 = 4.5 1. Total wages pai...
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