Take deviation of the items from the mean x x 3 find

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Unformatted text preview: l mean( x-x)2 / N 4. Sum the squares of the deviations ( x-x)2 Sikkim Manipal University Page No. 198 Research Methodology Unit 11 5. Find the average of the squares of the deviations ( x-x)2 / N 6. Take the square root of the average of the sum of the deviation Problems 1. Calculate the standard deviation of the following data 49 50 65 58 42 60 51 48 68 59 Standard deviation from actual mean = x/N = 550 /10 = Arithmetic mean 55 Values (x-55) (x-55)2 49 -6 36 50 -5 25 65 10 100 58 3 9 42 -13 169 60 5 25 51 -4 16 48 -7 49 68 13 169 59 4 16 (x-x)2 614 550 = (x-x) 2 / N = 614 /10 = 61.4 = S.D 7.836 Standard deviation from assumed mean Assumed mean = Sikkim Manipal University 50 Page No. 199 Research Methodology Unit 11 Values (x-55)2 (x-50) 49 -1 1 50 0 0 65 15 225 58 8 64 42 -8 64 60 10 100 51 1 1 48 -2 4 68 18 324 59 9 81 550 ( x-x) = 50 (x-x)2 =864 = (x-x) 2 / N - {(x-x) / N} 2 = 864 /10 – 50/10 = 86.4 - 52 = 81.4 - 25 = 61.4 = S.D 7.836 Discrete Series Standard deviation can be obtained by three methods. 1. Direct method 2. Short cut method 3. Step deviation Direct method Under this method formula is S.D = (fx) 2 / N - {(fx) / N}2 Sikkim Manipal University Page No. 200 Research Methodology Unit 11 Calculate standard deviation for the following frequency distribution. Marks : 20 30 40 50 60 70 Frequency : 8 12 20 10 6 4 Marks Frequency X2 fx Fx2 20 8 400 160 3200 30 12 900 360 10800 40 20 1600 800 32000 50 10 2500 500 25000 60 6 3600 360 21600 70 4 4900 280 19600 2460 112200 60 = (FX) 2 / N - {(FX) / N} 2 = 112200/60 - {2460 / 60}2 = 1870 - 2 = 1870 – 1681 = 189 = S.D 13.747 11. 13. 3 Correlation Analysis Economic and business variables are related. For instance, demand and supply of a commodity is related to its price. Demand for a commodity increases as price falls. Demand for a commodity decreases as its price rises. We say demand and price are inversely related or negatively correlated. But sellers supply more of a commodity when its price rises. Supply of the commodity decreases when its price falls. We say supply and pric...
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