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# Descriptive statistics

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• 1. Descriptive statistics "Study little but study very thoroughly,because it is thoroughness in work which pays in the long run." PROBLEMS
• 2. Q1 If there are 7 observations4,6,8,12,10,20,24, then the sum of å ( x - x) =? deviation of the observations from their AM is ?
• 3. Q2 If a variable assumes the values 1,2, 3 ... 5 with frequencies as 1, 2, 3 ... 5, then what is the AM?
• 4. Q3 The average salary of a group of unskilled workers is Rs.10000 and that of a group of skilled workers is Rs.15,000. If the combined salary is Rs.12000, then what is the percentage of skilled workers?
• 5. Q4 The weighted arithmetic mean of the four numbers 26, 128, 12 and 4 is 10.4.If the weights of the first three numbers are 1, 3 and 4 respectively, find the weight of the fourth number?
• 6. Q5 The weighted AM of 3, 5 and 10 with weights x, y and z respectively is known to be 8.What is the weighted AM if the weights are changed to 2x, 2y and 2z respectively?
• 7. Q6 The algebraic sum of the deviations of 25 observations measured from 45 is – 55 find the A.M. of the observations?
• 8. Q7 The weighted arithmetic mean of first n natural numbers whose weights are equal to the corresponding numbers is equal to?
• 9. Q9 The average weight of the following frequency distribution is 17. Find the value of p X 8 20 26 29 F 3 2 p 1
• 10. Q10The mean age of a group of 50 persons was found to be 48 Later, it was discovered that age 40,34,56 was misread as 30,43,52 Then the correct mean is?
• 11. Q11 The numbers 3.2, 5.8, 7.9 and 4.5 have frequencies x, x+2, x–3 and x+6respectively, If the arithmetic mean is 4.876, find the value of x?
• 12. Q13  What is the GM for the numbers 8, 24 and 40?  If A.M. = 25; H. M. = 9, then GM =? Calculate geometric mean of the four numbers 5,8,6,1 with frequency 3,2,4,1
• 13. Q14 If the AM of two unequal positive real nos a and b (a>b)be twice as that of its GM for two numbers then the ratio a : b ?
• 14. Q15 If there are two groups with 75 and 65 as harmonic means and containing 15 and 13 observation then find the combined HM ?
• 15. Q16 An, aero plane flies from A to Bat the rate of 500 km/hour and comes back from B to A at the rate of 700 km/hour. The average speed of the aero plane is?
• 16. Q17 A motor car covered a distance of 50 miles four timesThe first time at 50 mph, the second at 20 mph, the third at 40 mph and the fourth at 25 mph. Calculate the average speed.
• 17. Q18“MOI” travelled some distance by cycle at a speed of 15 km per hour. On return journey he travelled the same distance at a speed of 10 km per hour. What was his average speed per hour during the entire journey?
• 18. Q19 Find the Harmonic mean of the following numbers: 1, 1 , 1 ,........, 1 . 2 3 n Find the Harmonic mean of the following numbers: 1 1 1 1, , ,......, 3 5 2n − 1
• 19. Q20 What is the H.M of the following data relating to the age distribution of 72 persons? Age (Year): 20 30 40 No. of people: 13 28 31
• 20. Q21 Find the H.M of the following data Class Frequency 10 – 15 4 15 – 20 8 20 – 25 12 25 – 30 20 30 – 35 11 35 – 40 6 40 – 45 5
• 21. Q22The median of the following observation 22,24,33,37,x+1,x+3,44,47,51,58 arranged in ascending order is 42 find x?
• 22. Q23 You are given below a certain statistical distribution. Calculate the most suitable average. Value Frequency Less than 100 40 100 – 200 89 200 – 300 148 300 – 400 64 400 and above 39
• 23. Q24 If x and y are related by 2x – ½y =10 and mode of x is known to be 7.5, then the mode of y is?
• 24. Q25 For the given data find the three quartiles 23, 14, 24, 45, 23, 34, 43, 12, 34, 45, 23, 23, 45, 56, 43, 42
• 25. Q25 The average American spends \$65.88 per month dinning out (the Des Moines register). a sample 25 of young adults provided the following dining out expenditures( in dollars) over the past month. 253 101 245 467 131 0 225 80 113 69 198 95 129 124 11 178 104 161 0 118 151 55 152 134 169
• 26. ANSWER THE FOLLOWING? 1. COMPUTE THE MEAN MEDIAN AND MODE. 2. CONSIDERING THE RESULTS ABOVE DO THESE YOUNG SEEM TO SPEND ABOUT SAME AS AN AVERAGE AMERICAN EATING OUT. 3. COMPUTE THE FIRST AND THIRD QUARTILE. 4. COMPUTE THE RANGE AND THE I.Q.R.5. COMPUTE THE VARIANCE AND THE SATANDRAD DEVIATION. 6. THE SKEWNESS MEASURE FOR THE DATA IS -1.54? 7. CHECK THE ACCURACY OF THE ABOVE STATEMENT.
• 27. Q26Find the standard deviation of first n natural numbers?If the quartile DEVIATION is 30 and median 22, find the coefficient of quartile deviation, assuming the distribution to be symmetrical.
• 28. Q27 The quartile deviation of the following distribution is: Weights (Kg) No. of men 40 – 45 10 45 – 50 22 50 – 55 28 55 – 60 20 60 – 65 12 65 – 70 8
• 29. Q28If the relation between x and y is 5y – 3x =10 and the mean deviation about mean for x is 12, then the mean deviation of y about mean is? Karl Pearson coefficient of skewness is 0.32.Its standard deviation is 6.5 & mean is 29.6, find the mode and median?
• 30. Q29 What is the value of mean deviation about mean for the following observations? 50, 60, 50, 50, 60, 60, 60, 50, 50, 50, 60, 60, 60, 50.
• 31. Q30 The mean deviation about mode for the numbers 4/11, 6/11, 8/11, 9/11, 12/11, 8/11If the SD of the 1st n natural numbers is 2, then the value of n must be?
• 32. Q31Prices of a particular commodity in five years in two cities are given below. Find from the data the city which had more stable prices Prices in city A Prices in city B 20 10 22 20 19 18 23 12 26 15
• 33. Q32What is the standard deviation from the following data relating to the age distribution of 200 persons? Age (Year): 20 30 40 50 60 70 80 No. of people:13 28 31 46 39 23 20
• 34. Q33 The mean and SD of a sample of 100 observationswere calculated as 40 and 5.1 respectively by a CA student who took one observations as 50 instead of 40 by mistake. The correct value of SD would be?
• 35. Q34 The standard deviation calculated from a set of 32 observations is 5. If the sum of the observations is 80, what is the sum of the squares of these observations?
• 36. Q35 For a group containing 100 observations, the A.M. and S.D. were 8 and 10.For 50 observations selected from these 100 observations the A.M and S.D are 10 and 2 respectively. Find the A.M. and S. D. of the other half.
• 37. Q36 Find the coefficient of variation of the following data: Marks No of Students 0 – 10 4 10 – 20 10 20 – 30 16 30 – 40 12 40 – 50 8
• 38. Q37 The following data relates to the salary of workers of two factories Factory A Factory BNo. of workers 80 110Mean Rs 2320 Rs 2160SD Rs 120 Rs 122 In which factory is variation in salary more?
• 39. Q38 For 2 values of a variable x, the mean and the standard deviation are 10 and 2 respectively. What are the values of x?
• 40. Q39For a set of ungrouped values the following sums are found: N = 15, å X = 480, å X = 15735. 2 Find the mean and standard deviation of the values.
• 41. Q40 The INTER QUARTILE RANGE of the following distribution is: Weights (Kg) No. of men 400–450 10 450–500 22 500–550 28 550–600 20 600–650 12 650–700 8
• 42. Q42Wageweb conducts surveys of salary data and present the summaries on its website. Assume the following data come from a sample of annual salaries for 20 marketing executives (data are in thousands) 145,140,145, 173,116,127, 155,134,138, 114,951,621,271, 131,781,439,316,516,157 184 CALCULATE PEARSON COEFFICENT?
• 43. Q43Find mean deviation and its coefficient for the data wages No of workers 0 – 1000 4 1000 – 2000 10 2000 – 3000 16 3000 – 4000 12 4000– 5000 8
• 44. Q45 Prove that the standard deviation calculated from two values a and b is equal to half of their difference
• 45. Q46The following table gives the earned run averages (eras) for the 2002 season for the pitching staffs of the 16 baseball teams in the national league. Arizona 3.92 Milwaukee 4.73 Atlanta 3.13 Montreal 3.97 Chicago 4.29 New York 3.89 Colorado 5.20 Philadelphia 4.17 Cincinnati 4.27 Pittsburgh 4.23 Florida 4.36 St. Louis 3.70 Houston 4.00 San Diego 4.62 Los Angeles 3.69 San Francisco 3.54
• 46. CALCULATE mean (eras) median and mode variance of the data standard deviation and its coefficient comment on skewness of the data calculate I.Q.R
• 47. ANALYSEYou are given the data of a factory before and after the settlement of industrial dispute. comment on the gain or losses from the point of the workers and the management BEFORE AFTER NO OF 2440 2359 WORKERSMEAN WAGES 45.5 47.5MEDIAN WAGES 49.0 45.0 STANDARD 12.0 10.0 DEVIATION
• 48. ANALYSE From the data given below state Which series is more consistent? Variable Series A Series B 10-20 20 13 20-30 18 22 30-40 32 40 40-50 40 32 50-60 22 18 60-70 18 10