(b) Calculate standard deviation for the following data :
MidValue :

15

25

35

45

55

65

Frequency :

18

22

40

32

18

10

Or
(c) A test in algebra is given to 400 high school children of whom 150 were boys and 250 were girls. The mean score of boys was 72 and that of girls was 73. Find the mean score of the combined group.
(d) What is primary data and secondary data? Discuss any two methods of collecting primary data.
2. (a) Prove that Karl Pearson’s coefficient of correlation is independent of change of origin and change of scale.
X :

52

63

45

36

72

65

47

25

Y :

62

53

51

25

79

43

60

33

Or
(c) What are the properties of coefficient of correlation? Explain the importance of statistics in Banking and Finance.
(d) Calculate Karl Pearson’s coefficient of correlation from the data given below :
X :

78

89

99

60

59

79

68

61

Y :

125

137

156

112

107

136

123

108

3. (a) “Index numbers are economic barometers.” Explain it.
(b) What is the difference between a price index and a quantity index? How do the following stand as problems in the process of construction of index numbers – (i) selection of items, (ii) price quotations and (iii) selecting of formula?
Or
(c) Mention the two uses of cost of living index number and show that Fisher’s index satisfies time reversal test.
(d) Calculate price indices for the year 2003 from the following using – (i) Laspeyre’s method, (ii) Paasche’s method and (iii) Fisher’s method :
Commodity

2002

2003
 
Price

Quantity

Price

Quantity
 
A
B
C
D

2
5
4
2

8
10
14
19

4
6
5
2

6
5
10
13

4. (a) Discuss the utility of the study of time series.
(b) Calculate trend using least square method from the following data :
Year

1997

1998

1999

2000

2001

2002

2003

Sells (in lakh)

125

128

133

135

140

141

143

Or
(c) Calculate seasonal indices from the following (use simple average method) :
Production (Tons)
 
Year

Ist Qtr

II Qtr

III Qtr

IV Qtr

2000

3.7

4.1

3.3

3.5

2001

3.7

3.9

3.6

3.6

2002

4.0

4.1

3.3

3.1

2003

3.3

4.4

4.0

4.0

d) Write short notes on :
(i) Least square method
(ii) Simple average method
(iii) Moving average method
5. (a) A coin is tossed four times. What is the probability of getting two heads?
(b) Discuss the steps of forecasting.
Or
(c) Explain the time series analysis and regression analysis method of forecasting.
(d) Explain any three theories of forecasting