(b) Calculate mean and variance from the following data:
X :

010

1020

2030

3040

4050

F :

1

4

10

22

30

OR
(c) What is the difference between absolute and relative measure of dispersion? Find the missing frequency from the following distribution when median is 32.5 marks:
Marks :

1020

2030

3040

4050

5060

No. of students:

3

5



3

1

(d) Calculate from the following (i) Geometric mean (ii) Median and (iii) Mode:
5,2,2,3,4,4,1
(b) Calculate Karl Pearson’s coefficient of correlation from the following:
N=10 ∑X=140 ∑Y=150
∑(X10)^{2}=180 ∑(Y15)^{2}=215
∑(X10) (Y15) =60
Or
(c) Write down the difference between correlation and regression.
(d) Calculate coefficient of correlation from the following data:
Value of X:

1

2

3

4

5

6

7

8

9

10

Value of Y:

46

42

38

34

30

26

22

18

14

10

3. (a) Define index number and state its uses.
(b) Why is Fisher’s index number called ideal index number? Calculate Fisher’s index number? Calculate Fisher’s index number from the following data:
Commodity

Price
2003

Quantity
2003

Price
2005

Quantity
2005

A
B
C
D
E

8
10
5
4
4

10
12
8
14
5

10
12
8
14
5

12
8
5
3
25

Or
(c) State the limitations of index number.
(d) Calculate (i) price index (according to Laspeyres’ formula) and (ii) quantity index (according to Paasche’s index) using the following table:
Commodity_{}

P_{0}

q_{0}

P_{1}

q_{1}

A
B
C

4
2
6

6
4
2

6
4
2

4
2
6

4. (a) From the following table, calculate trend values by 3yearly weighted moving averages
With weight 1, 2, 2 respectively:
Year:

1

2

3

4

5

6

7

Sales(Rs.)

2

4

5

7

8

10

13

(b) Discuss the components of a time series.
Or
(c) Find the trend values by 3yearly moving average method from the following data:
Year:

1960

1961

1962

1963

1964

1965

1966

1967

1968

Sales:

5

7

9

12

11

10

8

12

13

(d) Discuss the methods of measuring trends.
5. (a) Mention the purpose and assumptions of business forecasting.
(b) Discuss any three methods of forecasting.
Or
(c) Explain the concept of business forecasting.
(d) Explain sales forecasting and demand forecasting.
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