2013 (November)
Commerce (General/Speciality)
Course: 303
Full Marks: 80
Pass Marks: 32
1. (a) Answer the following
questions: 1x5=5
(i)
Which average is considered to be best for the
construction of index numbers?
(ii)
Which is the GM of 5, 10, 20, 0 and 100?
(iii)
Write the relationship among AM, GM, and HM.
(iv) When
rank correlation used?
(v)
Write the relationship among Fisher’s index,
Laspeyre’s index and Paasche’s index.
(b) Fill up the blanks: 1x3=3
(i)
The index number for the base year is taken as
_______.
(ii)
When r = ± 1, the number of regression line is
_____.
(iii)
Flood in Assam is an Example of ______ in time
series.
2. (a) (i) State the features of
a good measure of average. 3
(ii) If the AM of the following
distributions is 67.45, find the value of the missing frequency: 5
|
Height
|
Frequency
|
|
60-62
|
5
|
|
63-65
|
54
|
|
66-68
|
----
|
|
69-71
|
81
|
|
72-74
|
24
|
(iii) Calculate the coefficient
of variation of the following data: 5+2=7
|
Weight
|
No. of
persons
|
|
155-125
|
4
|
|
125-135
|
5
|
|
135-145
|
6
|
|
145-155
|
3
|
|
155-165
|
1
|
|
165-175
|
1
|
Or
(b) (i) For any two values, prove that AM≥GM≥HM. 3
(ii) Calculate mode and median
for the data given below: 5
|
Marks Less than
|
(No. of
students)
|
|
10
|
15
|
|
20
|
35
|
|
30
|
60
|
|
40
|
100
|
|
50
|
150
|
|
60
|
220
|
|
70
|
245
|
|
80
|
270
|
(iii) An analysis of the monthly
wages paid to the works in two departments A and B f a company gave the
following result. Find the combined standard deviation of the wages of the
workers of the company as a whole: 7
|
|
Department
A
|
Department
B
|
|
No. of
persons
|
60
|
20
|
|
Average
wages
|
Rs. 648
|
Rs. 584
|
|
Standard
deviation
|
4
|
5
|
3. (a) (i) Prove that the
correlation coefficient is the GM of the two regression coefficients. 3
(ii) Explain why there should be
two lines of regression. 5
(iii) Calculate the coefficient
of correlation from the following data: 7
∑X = 125, ∑Y=
100, ∑X2
=650, ∑Y2
=460, ∑XY
=508, N=25.
Or
(b) (i) Write the two regression
equations. 3
(ii) Regression equations of two
correlated variables X and Y are 5X – 6Y + 90=0 and 15X – 8Y – 130=0. Find
which equation is the regression equation of Y on X and Which one is for X on
Y. Also find means of X and Y. 5
(iii) Find out the value of Y
when X = 36 from the data given below: 7
|
|
X
|
Y
|
|
Mean
Standard Deviation
|
30
4
|
45
10
|
|
Correlation coefficient = +0.8
|
||
4. (a) (i) Discuss the relative
merits and demerits of Laspeyre’s and Paasche’s indices. 3
(ii) During a certain period
when the cost of living index goes up from 110 to 200, the dearness allowance
of an employee was also increased from Rs.325 to Rs.500. Does the worker really
gain? If so, by how much? 4
(iii) Using Fisher’s formula,
calculate price index number from the data given below: 7
|
|
2005
|
2012
|
||
|
Items
|
Price
|
Quantity
|
Price
|
Quantity
|
|
A
B
C
D
|
12
18
21
25
|
5
4
3
2
|
15
22
18
20
|
6
5
4
3
|
Or
(b) (i) Describe the various
types of Index numbers. 3
(ii) The following series of
index numbers were constructed with the year 2000 as base year. Form a new set
of index number with the year 2005 as base year: 4
|
Year
|
2001
|
2002
|
2003
|
2004
|
2005
|
2006
|
|
Index No.
|
105
|
118
|
125
|
130
|
150
|
156
|
(iii) Calculate Cost of Living
Index number from the data given below and hence suggest what should be the
salary of a person whose salary in the base year was Rs.500 to maintain his
living status: 5+2=7
|
Items
|
Index No.
|
Weight
|
|
Food
Clothing
Fuel and
lighting
House Rent
Miscellaneous
|
360
295
287
110
315
|
60
5
7
8
20
|
5. (a) (i) Discuss the uses of
studying time series. 3
(ii) From the following data,
calculate trend values by using the method of 3-yearly moving averages: 4
|
Year
|
2001
|
2002
|
2003
|
2004
|
2005
|
2006
|
2007
|
|
Production
|
100
|
120
|
95
|
105
|
108
|
110
|
120
|
(iii) What do you mean by trends
in a time-series analysis? What are the factors responsible for the occurrence
of trends? What are the uses of studying trends? 7
Or
(b) (i) Write the two models
used for analysis of time series. 3
(ii) What is seasonal variation
in a time series? Discuss the uses of studying seasonal variation in business. 4
(iii) Using the method of least
squares, find the trend values for the following data: 7
|
Year
|
2001
|
2002
|
2003
|
2004
|
2005
|
2006
|
2007
|
|
Income
|
67
|
53
|
43
|
61
|
56
|
79
|
58
|
6. (a) (i) State the assumptions
under which business forecasting is carried out. 3
(ii) Discuss how forecasting is
done by regression analysis method. 4
(iii) Prepare a note why a
business manager should use forecasting methods. 7
Or
(b) (i) Discuss the limitations
of business forecasting. 3
(ii) Discuss the economic models
of business forecasting. 4
(iii) Discuss the qualities of a
good method of forecasting. 7
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