Find the missing frequencies in the following frequency distribution of 60. The arithmetic mean is given as 11.09

Class interval

Frequency

9.3 – 9.7

2

9.8 – 10.2

5

10.3 – 10.7

A

10.8 – 11.2

B

11.3 – 11.7

14

11.8 – 12.2

6

12.3 – 12.7

3

12.8 – 13.2

1

6. The pass result of 50 students who took a class test is given below. If the average marks for all the students were 51.6, find out the average marks of the students who failed.

Marks

40

50

60

70

80

90

No. of students

8

10

9

6

4

3

7. The average dividend declared by a group of 10 chemical companies was 18%. Later on, it was discovered that one correct figure 12, was misread as 22. Find the correct average dividend.

8. The mean of 200 observations was 50. Later on, it was found that two observations were misread as 92 and 8 instead of 192 and 88. Find the correct mean.

9. There are two units of an automobile company in two different cities employing 760 and 800 employees respectively. The arithmetic mean of monthly salaries paid to employees in these two units is Rs.18750/- and Rs.16950/- respectively. Find the combined arithmetic mean of salaries of the employees in both the units.

10. Find the median wage of a daily worker from the following data. Also calculate the third quartile, fourth decile and 79th percentile. The total number of daily workers employed is 6000. Out of which 5% earn less than Rs.350 per day, 1160 earn from Rs.351 to Rs.400 per day, 30% earn from Rs.401 to Rs. 450 per day, 1000 earn from Rs.451 to Rs.500 per day, 20% earn from Rs.501 to Rs.550 per day and the rest earn Rs.551 or more per day.

11. A set of adventurous MBA students decided to take up a project in Oceanography. They met the oceanographers, discussed in detail and decided to do a statistical survey in the Ocean. Each student in turns jumped into the ocean as scuba divers and found different objects and recorded the number of objects found by them each time. The total numbers of dives were 213. The number of objects found varied from zero to hundred. Calculate the modal value of number of objects found by the scuba divers. No. of objects frequency 0 – 10 1 10 – 20 6 20 – 30 24 30 – 40 37 40 – 50 49 50 – 60 38 60 – 70 23 70 – 80 18 80 – 90 12 90 – 100 5

12. The annual salaries (in rupees’ thousands) of employees in an organization is given below. The total salary of 10 employees in the class 40 and above is Rs.900000. Compute the mean salary. Every employee belonging to the top 25% of earners has to pay 5% of their salary to the workers’ relief fund. Estimate the contribution to relief fund.

Salary (Rs. In thousands)

Number of Employees

Below 10

4

10 – 20

6

20 – 30

10

30 – 40

20

40 and above

10

13. The following is the age distribution of 1000 persons working in an organization.

Age group

No. of persons

20 – 25

30

25 – 30

160

30 – 35

210

35 – 40

180

40 – 45

145

45 – 50

105

50 – 55

70

55 – 60

60

60 – 65

40

Due to continuous losses, it is desired to bring down the manpower strength to 30% of the present number according to the following scheme: Retrench the first 15% from the lower age group. Absorb the next 45% in other branches. Make 10% from the highest age group retire permanently, if necessary. Find the average age of the above three groups and the retained employees.