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al Vi is here 10:12 PM @ 51% O Done Probability And Statistics Tutorial... frequency 5 18 42 27 8 6 The first four moments of a distribution about x =2 are 1, 2.5, 5.5 and 16. Find first four central moment and also find , and 2 also give your conclusion about distribution. COLLEGE OF ENGINEER . L. D. CO L. D. College of Engineering, Ahmedabad B.E. Sem. III (BM/CE/EC/IT) AHMEDABAD Probability and Statistics(3130006) Q.7 For a group of 10 items, 2 x = 452 , _ x = 24270 and mod e = 43 .7. Find Karl Pearson's coefficient of skewness. Q.8 In a distribution, the mean =65, median = 70, coefficient of skewness = - 0.6. Find the mode and coefficient of variation. Q.9 From the following data calculate Karl Pearson's coefficient of skewness. Marks 0-10 10-20 20-30 30-40 40-50 50-60 No. of students 4 6 10 20 6 4 Q.10 Calculate the Bowley's coefficient of skewness for the following data. Class interval 0-10 10-20 20-30 30-40 40-50 Frequency 10 14 19 17 131 of 2 L. D. College of Engineering, Ahmedabad B.E. Sem. III (BM/CE/EC/IT) AHMEDABAD Probability and Statistics(3130006) Tutorial :8 Moments and Skewness Q.1 The first four moments of a distribution about the value 4 of the variable are -1.5, 17, -30 and 108. Find the moments about the mean 1-2 and comment on their values. Also find the moment about the point x = 2. Ans (14.75, 39.75, 142.3125 and 0.4926, 0.6543) Q.2 Calculate the first four moments of the following distribution about a = 40.5 and hence find the moments about the mean of distribution: Hours worked 30-32.9 33-35.9 36-38.9 39-41.9 42-44.9 45-47.9 No. of Industries 2 26 47 15 Ans. (-0.39,8.91,-13.23,294.03) & (0, 8.75, 8.98) Q.3 Find the first four moments (a) about the origin (b) about the mean for a random variable x having density function f (x ) = 4x(9-x2) 81 otherwise Ans. (8/5,3,216/35,27/2) & (0,11/25,-32/875,3693/8750) Q.4 Compute the first four moments about the mean of the observations 4, 7, 10, 13, 16, 19, 22. Ans. (0, 34.71, 0, 2256.42) Q.5 For a distribution of 250 heights, calculations showed that the mean, standard deviation B, and B2 were 54 inches, 3 inches, 0 inches and 3 inches. It was however, discovered on checking that two items 64 and 50 in the original data were wrongly written in place of the correct values 62 and 52 inches respectively. Calculate the correct frequency constant. Ans. (mean=54, Variance= 8.81, B, = .0070 and B2 = 2.81 ) Q.5 Compute the coefficient of skewness by using Karl Pearson and Bowley's method for the following data. Class 0-2 2-4 4-6 6-8 8-10 frequency 5 18 42 27 8 The first four moments of a distribution about x =2 are 1, 2.5, 5.5 and 16. Find first four central moment and also find S, and 2 also give your conclusion about distribution. COLLEGE OF ENGINER HEERING L. D. College of Engineering, Ahmedabad B.E. Sem. III (BM/CE/EC/IT) AHMEDABAD Probability and Statistics(3130006) Q.7 For a group of 10 items, 2 x = 452 , _ x2 = 24270 and mod e = 43 .7. Find Karl Pearson's coefficient of skewness. Q.8 In a distribution, the mean =65, median = 70, coefficient of skewness = - 0.6. Find the mode and coefficient of variation. Q.9 From the following data calculate Karl Pearson's coefficient of skewness
