D x where n fi merits it is rigidly defined and based

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Thus, s.d. ( x ) = = where n = fi Merits: It is rigidly defined and based on all observations. It is amenable to further algebraic treatment. It is not affected by sampling fluctuations. It is less erratic. Demerits: (1) It is difficult to understand and calculate. (2) It gives greater weight to extreme values. Note that variance V(x) = and and s. d. ( ? x ) = and Then V ( x ) = Co-efficient Of Variation (C.V.) To compare the variations (dispersion) of two different series, relative measures of standard deviation must be calculated. This is known as co-efficient of variation or the co-efficient of s. d. Its formula is C. V. = Thus it is defined as the ratio s. d. to its mean.
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61 Remark: It is given as a percentage and is used to compare the consistency or variability of two more series. The higher the C. V. , the higher the variability and lower the C. V., the higher is the consistency of the data. Example: Calculate the standard deviation and its co-efficient from the following data. A 10 B 12 C 16 D 8 E 25 F 30 G 14 H 11 I 13 J 11 Solution: No x i (x i - x) ( x i - x ) 2 A 10 -5 25 B 12 -3 9 C 16 +1 1 D 8 -7 49 E 25 +10 100 F 30 +15 225 G 14 -1 1 H 11 -5 16 I 13 -2 4 J 11 -4 16 n= 10 150 446 Calculations: i) ii) iii)
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62 Example: Calculate s.d. of the marks of 100 students. Marks No. of Students (f i ) Mid-values (x i ) f i x i f i x i 2 0-2 10 1 10 10 2-4 20 3 60 180 4-6 35 5 175 875 6-8 30 7 210 1470 8-10 5 9 45 405 n = 100 500 2940 Solution 1) 2) Example Calculate s.d. of the marks of 100 students. Marks No. of Students (f i ) Mid-values (x i ) f i x i f i x i 2 0-2 10 1 10 10 2-4 20 3 60 180 4-6 35 5 175 875 6-8 30 7 210 1470 8-10 5 9 45 405 n = 100 500 2940 Solution 1) = 2.21 7.4. REVISION POINTS S.D ( x ) = M. D. =
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63 Range (R) = L - S 7.5. INTEXT QUESTIONS 1) Explain the importance of measure of dispersion in decision making. 7.6. SUMMARY By the end of this lesson, you should be able to understand what is reange, mean deviation and standard deviation. 7.7. TERMINAL EXERCISES Standard deviation usually more useful and easier to understand than the variance Explain How? 7.8. SUPPLEMENTARY MATERIALS 1) - levin-and-rubin-solution-manual 2) =MsQKG4Cu3xwC 7.9. ASSIGNMENTS For the following data calculate mean, median and mode Marks 20 30 40 50 60 70 No of Students 8 12 20 10 6 4 7.10. REFERENCE BOOKS 1) Agarwal, B.L. ‘Basic Statistics’, Wiley Eastern Ltd., New Delhi. 2) Chance, W., ‘Statistical methods for Decision’ Irwin Inc., Homewood. 3) Gopikuttam, G., ‘Quantitative Methods and Operations Research’, Himalaya Publishing House, Bombay. 4) Gupta, S.P., ’Statistics Methods’, Sultan Chand and Co., New Delhi. 5) Levin, R., ‘Statistics for Management’, Prentice Hall of India, New Delhi, 1984. 6) Reddy, C.R., ‘Quantitative Methods for Management Decision’, Himalaya Publishing House, Bombay, 1990. 7.11. LEARNING ACTIVITIES 1) Explain the relationship between variance and standard deviation can either be negative.
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