{iii} 1I.l'-'leasures of dispersion and skewness are complimentary to one another in understanding a frequency distribution.' Elucidate the statement. {iv} Calculate Karl Pearson's coe cient of skewness from the following data: Weekly Sales (shi 13-12 12-1414-13 13-13 13-23 2322 22-24 2423 Number of Companies 12 13 35 42 53 33 3 4 iv} Why is the standard deviation the most widely used measure of dispersion? Explain. {vi} The following data shows the daily sales of a certain manufacturing company in hundred thou sand US dollars. Use the data to answer the following questions. 33 33 35 34 31 T3 T3 T3 33 33 33 33 35 33 33 T3 T5 T2 33 33 33 33 35 32 33 T3 T5 T1 3? 53 33 3T 34 32 T3 TT T4 T3 34 5T 31 33 34 31 T3 TT T4 T3 33 54 {a} Make a frequency distribution table where the width of each class is 5. {b} Using table in {a}, compute the coe_cient of variation (CV) for the distribution and provide an interpretation. {c} Calculate the _rst four moments about the mean from the following data. id] calculate the values of _1 and _2 and provide interpretation to each. {vii} Suppose the mean monthly return on a T-Elill is 3.533 with a standard deviation of 3.53%. Sup- pose we have another investment '1" with a 1.533 mean monthly return and standard deviation of 3%. Which of the two investments o_ers less risk in terms of investment. Question three ii} A proofreader is interested in _nding the probability that the number of mistakes in a page will be less than 13. From his past experience he_nds that out of 3333 pages he has proofedr 233 pages contained no errors. 1233 pages contained 5 errors, and 2233 pages contained 11 or more errors. Can you help him in _nding the required probability?II {iii The odds that A speaks the truth are 3:2 and the odds that 3 does so are T:3. In what percentage of cases are they likely to {a} contradict each other on an identical point? lb] agree each other on an identical pointiII {iii} A and 3 play for a prize of Rs. 13333. A is to throw a die _rst and is to win if he throws 1: If A falls, 3 it to throw and is to win if he throws 2 or 1. If 3 fails. A is to throw again and to win if he throws 3. 2 or 1: and so on. Find their respective expectations