# Definition of dispersion the arithmetic mean of the

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Definition of Dispersion: The arithmetic mean of the deviations of the values of the individual items from the measure of a particular central tendency used. Thus the ’dispersion’ is also known as the " average of the second degree. " Prof. Griffin and Dr. Bowley said the same about the dispersion. In measuring dispersion, it is imperative to know the amount of variation (absolute measure) and the degree of variation (relative measure). In the former case we consider the range, mean deviation, standard deviation etc. In the latter case we consider the coefficient of range, the coefficient mean deviation, the coefficient of variation etc. Methods Of Computing Dispersion The range Mean deviation Standard Deviation Range In any statistical series, the difference between the largest and the smallest values is called as the range. Thus Range (R) = L - S Coefficient of Range : The relative measure of the range. It is used in the comparative study of the dispersion co-efficient of Range = Example (Individual Series) Find the range and the co-efficient of the range of the following items: 110, 117, 129, 197, 190, 100, 100, 178, 255, 790. Solution: R = L - S = 790 - 100 = 690 Co-efficient of Range = Example (Continuous series ) Find the range and its co-efficient from the following data. Solution: R = L - S = 100 - 10 = 90 Co-efficient of range =

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57 Mean Deviation Average deviations ( mean deviation ) is the average amount of variations (scatter) of the items in a distribution from either the mean or the median or the mode, ignoring the signs of these deviations by Clark and Senkade. Individual Series Steps: (1) Find the mean or median or mode of the given series. (2) Using and one of three, find the deviations ( differences ) of the items of the series from them. i.e. xi - x, xi - Me and xi - Mo. Me = Median and Mo = Mode. (3) Find the absolute values of these deviations i.e. ignore there positive (+) and negative (-) signs. i.e. | xi - x |, | xi - Me | and xi - Mo |. (4) Find the sum of these absolute deviations. (5) Find the mean deviation using the following formula. Note that: (i) generally M. D. obtained from the median is the best for the practical purpose. (ii) co-efficient of M. D. = Example Calculate Mean deviation and its co-efficient for the following salaries: \$ 1030, \$ 500, \$ 680, \$ 1100, \$ 1080, \$ 1740. \$ 1050, \$ 1000, \$ 2000, \$ 2250, \$ 3500 and \$ 1030.
58 Calculations : i) Median (Me) = Size of = Size of 11th item.

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59 Therefore, Median ( Me) = 8ii) M. D. = Example (Continuous series) Calculate the mean deviation and the coefficient of mean deviation from the following data using the mean. Difference in ages between boys and girls of a class. Diff. in years: No.of students: 0 - 5 449 5 - 10 705 10 - 15 507 15 - 20 281 20 - 25 109 25 - 30 52 30 - 35 16 35 - 40 4 Calculation: 1) X 2) M. D. 3) co ?? efficient of M. D. Variance
60 The term variance was used to describe the square of the standard deviation R.A. Fisher in 1913. The concept of variance is of great importance in advanced work where it is possible to split the total into several parts, each attributable to one of the factors causing variations in their original series. Variance is defined as follows: Variance = Standard Deviation (s.d.) It is the square root of the arithmetic mean of the square deviations of various Thus, s.d. ( x

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