Mean standard deviation
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The document contains 10 problems related to statistics concepts like mean, median, standard deviation, variance, etc. The problems involve calculating these measures from data provided in tables and using formulas to derive new statistics based on existing statistics. For example, problem 1 asks to calculate the average bonus paid to workers based on salary groups and bonus amounts provided. Problem 5 asks to calculate the average speed of an airplane flying around a square based on its speeds on each side.
Mean standard deviation
- 1. ASSIGNMENT-2 1. The following are the monthly salaries (in Rs.) of 30 employees in firm: 140 139 126 114 100 88 62 77 99 103 108 129 144 148 134 63 69 148 132 118 142 116 123 104 95 80 85 106 123 133 The firm gave bonus of Rs. 10, 15, 20, 25, 30, and 35 for individuals in the respective salary groups: ‘exceeding Rs 60 but not exceeding Rs 75’ ; ‘exceeding Rs.75 but not ExceedingRs.90’; and so on up to ‘exceeding Rs.135 but not exceeding Rs.150’. Find the average bonus paid worker. 2 Find out the missing frequencies of the following data, given that A.M. IS 67.45 inches Height (inches) 60-62 No. of students 5 63-65 18 66-68 f1 69-71 f2 72-74 8 Total 100 3.The G.M. of 4 observations is 47, and the G.M. of 6 others is 40. Find the G.M.of all the observations. 4. The geometric mean of six numbers is 75. If the geometric mean of four of them is 67,what is the geometric mean of the other two? 5. An aeroplane flies around a square the sides of which measure 100 Kms. each. The aeroplane covers at a speed of 100Kms.per hour the first side, at 200 Kms.per hours the second side, at 300 Kms. per hour the third side, and at 400Kms. per hour the fourth side. Use the correct mean to find the average speed round the square. 6. The G.M., H.M. and A.M. of three observations are 3.63,3.27 and 4 respectively. Find the observations. 7.Using a suitable formula calculate the median value from the following data: Midvale Frequency 115 6 125 25 135 48 145 72 155 116 165 60 175 38 185 22 195 Total 3 390 8. In a group of 1000 wage earns the monthly wages of 4% are below Rs.60 and those of 15% are under Rs. 62.50. 15% earned Rs95 and over, and 5% got Rs.100 and over. Find the median wage. ASSIGNMENT-3 1.Find out the range of the following data: Height (inches) 40-49 50-59 60-69 70-79 80-89
- 2. No, of. Students 3 5 7 8 9 2.Calculate mean deviation from median from the following: Class Boundary Frequency 2-4 3 4-6 4 6-8 2 8-10 1 3.Find mean and standard deviation of ‘n’ natural numbers. 4. The mean and standard deviation of a group of 100 observations were found to be 20 and 3 respectively. After the calculations were made it was found that three of the observations were incorrect which were recorded as 21, 21, and 18. Find the mean and s.d. if the incorrect observations are omitted. 5. Ā is the mean of A1, A2, and A3. If a1, a2, a3 are the deviations of A1,A2, A3 from Ā respectively, prove that a12 +a22 + a32 = A12 +A22 + A32 – 3Ā 2. 6. If d2= mean square deviation about x, σ =standard deviation, and x-x = a, then show that d2 = a2 + σ2. 7. Compute the s.d. of income from the following: Income (Rs.) No.of earners: Below 200 25 200-399 72 400-599 47 600-799 22 800-999 13 1000-1199 7 8.Out of 400 observations, 100 observations have the value one and the rest of the observations are zero. Find the mean and s.d. of 400 observations together. 9. The mean and the variance calculated from a group of 80 observations are 63.2 and 25.93 respectively. If 60 of these observations have mean 64.8 and s.d. 4, find the mean and the s.d. of the remaining 20 observations. 10. The mean life in days and standard deviation for two types of electric bulbs are given below: Mean life in days Standard deviation in days Type I 310 9 Type II 260 14