Thursday, October 16, 2014

Dibrugarh University Question Paper - Business Statistics (Nov' 2013)

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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