Friday, August 18, 2017

Dibrugarh University Question Papers: Business Statistics (November' 2015)

2015 (November)
COMMERCE
(General/Speciality)
Course: 303
(Business Statistics)
The figures in the margin indicate full marks for the questions
(New Course)
Full Marks: 80
Pass Marks: 24
Time: 3 hours
1. Answer any eight questions: 2x8=16
  1. What do you mean by frequency of a class interval?
  2. Define a discrete variable.
  3. Ifbe the mean ofseries, the mean ofseries and, then show that.
  4. The coefficient of rank correlation betweenpairs of observations isand the sum of the squares of differences between the ranks is, then what will be the value of
  5. Prove that coefficient of correlation is the geometric mean of the two regression coefficients.
  6. Is it possible for two regression equations to beandExplain, with reason, why?
  7. What do you mean by cost of living index number?
  8. What do you mean by ‘base year’ in the construction of index numbers?
  9. The trend equation for publicity cost (in ‘000 Rs.) of a company is given by (Origin 1st July, 2005, ). Shift the origin to 1st July, 2012.
  10. Name the components of a time series.
  11. Write the differences between Laspeyres’ and Paasche’s indices.
  12. Given the annual trend line equation of production of a company as
2. (a) (i) Prove that for any two values. When do they become equal? 3
(ii) The mean and standard deviation of 100 observations are 50 and 5, and that of another 150 observations are 40 and 6 respectively. Find the combined standard deviation of this 250 observations. 5
(iii) Calculate the coefficient of standard deviation for the following data: 8
Marks: (less than)
80
70
60
50
40
30
20
10
No. of students
100
90
80
60
32
20
13
5


Or
(b) (i)Prove that for a variable, the sum of deviations of the observed values from their arithmetic mean is zero.   3
(ii) Find the mean daily wages from the following data: 5
Wages (Rs.)
230-240
240-250
250-260
260-270
270-280
280-290
No. of workers
8
20
40
18
10
4
(iii) Give the definition of semi-inter-quartile range. Mention one merit and one demerit of. 3
(iv) Why is standard deviation considered to be the best measure of dispersion? Explain. 5
3. (a) (i) State the properties of Karl Pearson’s coefficient of correlation. 3
(ii) What do you mean by regression lines? Explain why there should be two lines of regression. 5
(iii) Calculate Karl Pearson’s coefficient of correlation from the given data: 8
X:
35
42
20
50
72
64
Y:
40
48
24
60
84
68
Or
(b) (i) Discuss the uses of regression equations. 3
(ii) Calculate the coefficient of rank correlation from the data given below: 5
SL. No.
1
2
3
4
5
6
7
8
9
10
X:
48
33
40
9
16
65
24
18
44
20
Y:
13
10
24
6
15
4
20
9
10
19


(iii) Derive the equations of two regression lines for the following data: 8
X:
35
42
20
50
72
64
Y:
40
48
24
60
84
68


4. (a) (i) What are the different types of index numbers? Name each of them. 3
(ii) Calculate CLI from the given data: 5
Group
Index No.
Weight
Clothing
360
60
Food
298
5
Fuel and Lighting
287
7
House Rent
110
8
Miscellaneous
315
20
(iii) Using the following data prove that Fisher’s index number satisfy (1) time reversal test and (2) factor reversal test: 8
Commodity
Base Year
Current Year

Price (in Rs.)
Quantity.
Price (in Rs.)
Quantity
A
B
C
D
E
4
5
2
1
3
20
15
30
50
25
6
6
3
1
5
18
12
30
60
28
Or
(b) (i) The monthly salary of an employee in the year 2010 was Rs. 18,500 and then the cost of living index was 160. In the year 2012 the cost of living index became 200. What should be the monthly salary of the employee in the year 2012 to rightly compensate him for price rise?
(ii) Discuss the limitations of index numbers.
(iv) What is Laspeyres’ price index number? Using the following data, show that Laspeyer’s formula does not satisfy the time reversal test: 8
Commodity
Base Year
Current Year

Price (in Rs.)
Quantity.
Price (in Rs.)
Quantity
A
B
C
D
E
6
2
4
10
8
50
100
60
30
40
10
2
6
12
12
56
120
60
24
36
5. (a) (i) Write the two mathematical models used for analysis of time-series data. 3
(ii) Calculate the trend value by using 3 yearly moving averages for the following data: 5
Year:
2008
2009
2010
2011
2012
2013
Production:
77
88
94
85
91
98
(iii) Fit a straight line trend for the following data and estimate the production for the year 2010: 8
Year:
2002
2003
2004
2005
2006
2007
2008
Production (‘000 ton):
200
225
175
165
200
265
285
Or
(b) (i) What do you mean by seasonal variations? What are the uses of studying it? 3
(ii) Calculate 3 yearly weighted moving average with weights 2, 2, 1, 2, 2, 1, 2 for the following data: 5
Year:
1995
1996
1997
1998
1999
2000
2001
Value:
45
43
47
49
46
45
42
(iii) Using the method of simple averages, calculate the seasonal indices for the following data: 8
Quarter
2010
2011
2012
I
72
74
84
II
50
68
60
III
78
74
62
IV
92
90
76
(Old Course)
Full Marks: 80
Pass Marks: 32
Time: 3 hours
The figures in the margin indicate full marks for the questions
1. (a) (i) Prove that the sum of the variate values from their arithmetic mean is zero. 2
(ii) If mean and mode of a moderately skewed distribution are 36.4 and 34.6 respectively, find its median.     3
(iii) What is standard deviation? Why is it regarded as the best measure of dispersion? 4
(iv) If arithmetic mean of the following distribution is 72.5, find the missing frequency and also calculate the mode for the distribution: 4+3=7
Marks:
30-39
40-49
50-59
60-69
70-79
80-89
90-99
No. of students:
2
3
11
20
--
25
7


Or
(b) (i) Discuss about the relationship between mean, median and mode. 2
(ii) Calculate the mode and median for the following data: 3
6, 4, 3, 6, 5, 3, 3, 2, 4, 3, 4, 3, 3, 4, 3, 4, 2, 2, 4, 3, 5, 4, 3, 4, 3, 3, 4, 1, 2, 3.
(iii) Calculate the coefficient of quartile deviation for the following data: 4
Wages (Rs.):
58-62
62-66
66-70
70-74
74-78
78-82
82-86
No. of Persons
4
7
11
16
12
8
2
(iv) Calculate the standard deviation for the following distribution: 7
Marks (more than):
0
10
20
30
40
50
60
No. of students:
80
77
72
68
53
40
0


2. (a) (i) Prove that, coefficient of correlation is the geometric mean of the two regression coefficients. 2
(ii) Find the value offrom the following data: 3
anddenotes the derivations ofandseries from their AM. 3
(iii) What do you mean by regression lines? Explain why there should be two lines of regression. 4
(iv) Find the appropriate regression equation from the data given below: 7
Age:
56
42
72
36
63
47
55
49
38
Blood Pressure:
147
125
160
118
149
128
150
145
115
Or
(b) (i) What are the properties of two regression coefficients? 2
(ii) If two regression equations are andfind the values ofand.     3
(iii) From the following data, find the two regression equations: 4

X
Y
Arithmetic Mean
Standard Deviation
20
5
25
4
Correlation coefficient 0.6
(iv) Calculate the value of coefficient of correlation from the following data: 7
X:
43
44
46
40
44
42
45
42
38
40
Y:
29
31
19
18
19
27
27
29
41
30
3. (a) (i) “The wholesale price index of the year 2015 taking 2010 as base year is 165.” What information can you derive from this statement about the rise in wholesale prices? 2
(ii) Write a short note on factor reversal test. 3
(iii) Calculate the cost of living index number from the following data: 4
Commodity
Weight
Index
Food
50
241
Clothing
2
221
Fuel
3
204
House Rent
16
256
Others
29
179
(iv) Calculate Fisher’s price index number from the data given below: 7
Commodity
Base Year
Current Year

Price (in Rs.)
Quantity.
Price (in Rs.)
Quantity
A
B
C
D
E
25
20
30
12
90
30
22
54
20
15
30
22
33
15
19
35
25
64
25
18


Or
(b) (i) Write the differences between chain base and fixed base index numbers. 2
(ii) What are ‘weights’ in the construction of index numbers? Discuss the importance of weights. 3
(iii) Discuss the limitations of index numbers. 4
(iv) Calculate Fisher’s index from the data given below, and hence prove that Fisher’s index number satisfies factor reversal test: 7
Commodity
Base Year
Current Year

Price (in Rs.)
Quantity.
Price (in Rs.)
Quantity
A
B
C
D
E
5
3
4
11
7
50
100
60
30
40
10
4
6
14
10
56
120
60
24
36
4. (a) (i) Write the two mathematical models used for the analysis of time series data. 2
(ii) Write a short note about the uses of studying time series. 3
(iii) Calculate 3 yearly moving averages from the data given below: 4
Year:
1
2
3
4
5
6
7
8
9
Value:
150
200
225
175
165
200
265
285
350
(iv) Using the principle of least squares, calculate the trend line equation for the data given below: 7
Year:
1985
1986
1987
1988
1989
1990
1991
Production:
23
20
18
18
14
13
13
Or
(b) (i) Given the annual trend equationWhat is its monthly trend equation? 2
(ii) In a multiplicative model of time series analysis T = 100, S = 1.2, C = 1.04 and I = 0.9, find the value of y.    3
(iii) Discuss the limitations of time series analysis. 4
(iv) Using the method of 4 yearly moving averages, calculate the trend values for the following data: 7
Year:
1
2
3
4
5
6
7
8
9
10
Price:
20
21
23
22
25
24
27
26
28
30


5. (a) (i) What do you mean by business forecasting? 2
(ii) Write the differences between forecasting and estimation. 3
(iii) Discuss the assumptions of forecasting. 4
(iv) Write short notes on sales forecasting and demand forecasting. 7
Or
(b) (i) Discuss the uses of extrapolation as a method of forecasting. 2
(ii) What precautions are to be taken while forecasting? 3
(iii) Discuss the limitations of forecasting. 4

(iv) Discuss how regression analysis may be used for forecasting. 7

Labels

Absorption Costing (1) Accountancy (4) accounting for partnership firms (3) Accounting for Share Capital (3) accounts of non trading concern (3) advanced financial accounting (14) AHSEC (108) ahsec 11 (47) ahsec 12 (60) ahsec notes (104) AHSEC Question Papers (33) Assam Slet (10) bcfm (11) bills of exchange (6) branch accounting (3) Budgetary Control (3) Budgetary Control Notes (2) business communication (28) Business Environment Notes (12) business regulatory framewrok (49) Business Statistics Notes (25) cash flow statement (5) cbse 12 (19) cbse notes (27) commerce (13) company law (23) corporate accounting (33) corporate laws (14) cost accounting (63) cost and management accounting (34) cpt (36) cpt 200 (7) cpt notes (30) dibrugarh university (1113) dibrugarh university notes (597) dibrugarh university question paper (454) dibrugarh university solved papers (225) dibrugarh university syllabus (47) direct tax law (49) eco - 01 (4) ECO - 02 (2) ECO - 03 (2) ECO - 05 (6) ECO - 06 (1) ECO - 07 (1) eco - 08 (4) eco - 09 (1) ECO - 10 (2) ECO - 11 (3) ECO - 12 (7) ECO - 13 (2) ECO - 14 (4) entrepreneurship (14) fianancial accounting (3) financial accounting (48) Financial Accounting Notes (15) financial management (18) Financial statements analysis (14) funds flow statement (3) guwahati university (289) guwahati university syllabus (52) Hire Purchase (5) Human Resource Management (11) icwai (38) icwai notes (39) ignou solved assignments (83) ignou solved question papers (121) income from house property (5) income from salary (4) Income Under the head Salaries (11) information technology (10) Installment Purchase (4) issue of shares (4) kkhsou (13) M.com (62) Management Accounting Notes (31) MCQ (11) paper I (1) paper II (9) paper III (1) principle of business mangement (16) Principles of Marketing Notes (16) royalty accounts (3) sale of goods act (8) semester I (151) Semester II (154) semester III (81) semester IV (149) semester V (111) semester VI (91) slet (13) Slet Ne (10) Small Business Management (7) solved assignments (22) UGC - NET: Commerce (08) (14) UGC - NET: Commerce (08) Paper II (3) UGC - NET: Commerce (08) Paper III (14) ugcnet solved question papers (23) Variance Analysis Notes (1)