## Monday, July 25, 2022

• Monday, July 25, 2022

Time: 3 Hours] [Max. Marks: 80

Note: - Attempt any four questions from Section A carrying 5 marks each and attempt any two questions from Section B and Section C each, carrying 15 marks each.

Section-A

(Attempt any four questions)

1. What are the properties of a good measure of dispersion?

2. A person is known to hit the target in 3 out of 4 shots, whereas another person is known to hit the target in 2 out of 3 shots. Find the probability of the target being hit at all when they both try.

3. Calculate arithmetic mean by direct method from the following data: 3

Marks            No. of Student

0-10               5

10-20             10

20-30             25

30-40             30

40-50             20

50-60             10

4. Write a note on the graphic method of measuring trends.

5. A coin is tossed six times. What is the probability of obtaining four or more heads?

6. Calculate mean deviation from the following series:

x:         10       11       12       13       14

F:         3          12       18       12       3

Section-B

7. From the following data calculate the missing value when the mean is 115.85:

Wages (Rs.)                                     No. of Workers

110                                                     25

112                                                     17

113                                                     13

(x)                                                      14

125                                                     8

128                                                     6

130                                                     2

8. Calculate the Standard Deviation of the following frequency distribution of marks:

Marks       No. of Student 0-10

1-10               5

10-20             12

20–30            30

30-40             45

40-50             50

50-60             37

60-70             21

9. (a) Define correlation. What are the various types of correlation?

(b) Calculate Spearman's coefficient of correlation between marks assigned to ten students by judges X and Y in a competition.

S. No.     Marks by Judge X                      Marks by Judge Y

1                      52                                           65

2                      53                                           68

3                      42                                           43

4                      60                                           38

5                      45                                           77

6                      41                                           48

7                      37                                           35

8                      38                                           30

9                      25                                           25

10                   27                                           50

10. (a) What is the difference between correlation and regression?

(b) In a correlation study following values were obtained:

X                     Y

Arithmetic Mean                65                   67

Standard Deviation            2.5                  3.5

Coefficient of correlation r = 0.8

Find the two regression equations that are associated with above values.

Section-C

11. A man wants to marry a girl having qualities: White complexion the probability of getting such a girl is one in twenty; handsome dowry-the probability of getting this is one in fifty; Westernised manners and etiquettes, the probability here is one in hundred. Find out the probability of his getting married to such a girl when the possession of these three attributes is independent.

12. Fit a straight line trend for the following series.

Estimate the value for 2008 :

Year                           Production of steel (m. tonnes)

2001                          60

2002                          72

2003                          75

2004                          65

2005                          80

2006                          85

2007                          95

13. Calculate Fisher's Ideal Index from the given data. Does it satisfy the time reversal and factor reversal tests ?

14. Define Normal Distribution. What are the properties of Normal Distribution? Write the importance of normal distribution.