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 103108 129 144 148 134 63 69 148 132 118142 116 123 104 95 80 85 106 123 133The firm gave bonus of Rs. 10, 15, 20, 25, 30, and 35 for individuals in the respectivesalary groups: ‘exceeding Rs 60 but not exceeding Rs 75’ ; ‘exceeding Rs.75 but notExceedingRs.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 63-65 66-68 69-71 72-74 TotalNo. of students 5 18 f1 f2 8 100

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 115 125 135 145 155 165 175 185 195 Total Frequency 6 25 48 72 116 60 38 22 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

No, of. Students 3 5 7 8 9

2.Calculate mean deviation from median from the following: Class Boundary 2-4 4-6 6-8 8-10

Frequency 3 4 2 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 a1

2 +a22 + a3

2 = A12 +A2

2 + 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.) Below 200 200-399 400-599 600-799 800-999 1000-1199No.of earners: 25 72 47 22 13 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 daysType I 310 9Type II 260 14