University Of Pune Question Paper
B. B. M. (I.B.) ( Semester - II ) Examination - 2013
BUSINESS STATISTICS
(New 2008 Pattern)
Time : 3 Hours] [Max. Marks : 80
Instructions :
(1) All questions are compulsory.
(2) Figures to the right indicate full marks.
(3) Use of calculator is allowed.
(4) Graph paper will be supplied on demand.
Q.1) Attempt each of the following : [05 each]
(a) Describe Systematic Sampling Procedure.
(b) Write merits and demerits of Arithmetic Mean.
(c) Mr. Sharma has taken insurance policy having following details :
Sum Assured : Rs. 80,000
Type : Endowment
Term : 25 years
Mode : Half Yearly
Date of Commencement : 07-09-1995
Due Date of last premium paid : 07-09-2010
Accrued Bonus Rs. 800 per thousand S.A.
Surrender Value Factor 25%
Find the Surrender Value as on 03-10-2010.
[4374]-205 1 P.T.O.
Seat
No.
(d) Find the Initial Basic Feasible Solution of following Transportation
Problem by using North - West Corner Method :
Factory Distribution Centres Monthly
Production
W X Y Z (in quintal)
A 10 8 5 4 7000
B 7 9 15 8 8000
C 6 10 14 8 10000
Demand 6000 6000 8000 5000
Q.2) (A) (a) The minimum weight of a special purpose brick is 5 kg
and it contains two basic ingredients B1
and B2
. B1
costs
Rs. 5 per kg and B2
costs Rs. 8 per kg. Strength
considerations dictate that the brick should contain minimum
of 4 kg of B1
and a minimum of 2 kg of B2
. Since the
demand for the product is likely to be relative to the price
of brick. Formulate the above Linear Programming Problem. [06]
(b) The mean hourly wage of 100 labours working in a factory,
running two shifts of 60 and 40 workers respectively is
Rs. 38. The mean hourly wage of 60 labours working in
the morning shift is Rs. 40. Find the mean hourly wage
of 40 labours working in the evening shift. [04]
OR
(A) Lives of two models of refrigerators in a survey are as follows :
Life (No. of Years) 0-2 2-4 4-6 6-8 8-10 10-12
Number of Model A 5 16 13 7 5 4
Refrigerators
Model B 2 7 12 19 9 1
(a) What is the average life of each model of these refrigerators.
(b) Which model has greater uniformity ? Justify. [10]
[4374]-205 2 Contd.
(B) What is Scatter Diagram ? Describe differed types of Correlation
using Scatter Diagram. [05]
Q.3) (A) The Production Manager of a Company maintains that flow time
in days(y) depends on number of operations (X) to be performed.
The following data gives necessary information :
X 2 23 4 4 5 6 6 77
Y 8 13 14 11 20 10 22 26 22 25
(a) Compute Correlation Coefficient between X and Y and
interprete it.
(b) Estimate Flowtime (Y) when number of operations performed
are 10. [10]
OR
(A) (a) Solve the following Transportation Problem by Vogel’s
Approximation Method to obtain Initial Basic Feasible
Solution :
To D E F Supply
From
A 6 4 1 50
B 3 8 7 40
C 4 4 2 60
Demand 20 95 35 150 [06]
(b) The data below gives the yearly profits (in thousand of
Rs.) of two companies A and B :
Year Profits (in ’000 Rs.)
Company ‘A’ Company ‘B’
1994-95 120 90
1995-96 135 95
1996-97 140 108
1997-98 160 120
1998-99 175 130
Represent the data by Means of Multiple Bar Diagram. [04]
[4374]-205 3 P.T.O.
(B) What do you mean by Classification ? Describe Inclustive and
Exclusive Methods of Classification. [05]
Q.4) (A) (a) Define Regression Coefficient of X on Y and Y on X and
state any three properties of Regression Coefficients. [05]
(b) Compute Range, Coefficient of Range, Quartile Deviation
and Coefficient of Quartile Deviation for the following
data :
54, 51, 58, 59, 52, 52, 51, 57, 55, 58, 56 [05]
OR
(A) (a) Following data relates to the number of defective items
found in 20 boxes, each containing 5 items. Prepare a
frequency distribution of number of defective items : [05]
4, 2, 3, 5, 4, 1, 3, 5, 4, 0,
1, 1, 0, 2, 3, 2, 1, 2, 1, 3
(b) Obtain Initial Basic Feasible Solution by using Matrix Minima
Method for the following Transportation Problem : [05]
Depot B1 B2 B3 B4 Stock
Unit
A1 2 3 5 18
A2 7 3 4 6 10
A3 4 1 7 2 20
Requirement 6 8 9 15 38
(B) Describe Scope of Statistics in Economics. [05]
Q.5) (A) (a) Calculate Mode for the following data : [04]
Wages 0-10 10-20 20-30 30-40 40-50
No. of
Employees 22 38 46 35 20
[4374]-205 4 Contd.
(b) An incomplete frequency distribution is given below :
Class
Interval 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency 12 30 – 65 – 25 18
Calculate missing frequencies if Median of the data is 46
and total frequency is 229. [06]
OR
(A) (a) Solve the following Linear Programming Problem by
Graphical Method :
max. z = 48x + 40y
subject to : 2x + y ≤ 90
x + 2y ≤ 80
x + y ≤ 50
x ≥ 0, y ≥ 0 [06]
(b) For a bivariate data, the mean value of X is 20 and the
mean value of Y is 45. The regression coefficient of Y on
X is 4 and that of X on Y is 1
/
9
. Find :
(i) Correlation Coefficient between X and Y.
(ii) The Standard Deviation of X if Standard Deviation
of Y is 12.
(iii) Coefficient of Variation of X. [04]
(B) Explain Absolute and Relative Measures of Dispersion. [
B. B. M. (I.B.) ( Semester - II ) Examination - 2013
BUSINESS STATISTICS
(New 2008 Pattern)
Time : 3 Hours] [Max. Marks : 80
Instructions :
(1) All questions are compulsory.
(2) Figures to the right indicate full marks.
(3) Use of calculator is allowed.
(4) Graph paper will be supplied on demand.
Q.1) Attempt each of the following : [05 each]
(a) Describe Systematic Sampling Procedure.
(b) Write merits and demerits of Arithmetic Mean.
(c) Mr. Sharma has taken insurance policy having following details :
Sum Assured : Rs. 80,000
Type : Endowment
Term : 25 years
Mode : Half Yearly
Date of Commencement : 07-09-1995
Due Date of last premium paid : 07-09-2010
Accrued Bonus Rs. 800 per thousand S.A.
Surrender Value Factor 25%
Find the Surrender Value as on 03-10-2010.
[4374]-205 1 P.T.O.
Seat
No.
(d) Find the Initial Basic Feasible Solution of following Transportation
Problem by using North - West Corner Method :
Factory Distribution Centres Monthly
Production
W X Y Z (in quintal)
A 10 8 5 4 7000
B 7 9 15 8 8000
C 6 10 14 8 10000
Demand 6000 6000 8000 5000
Q.2) (A) (a) The minimum weight of a special purpose brick is 5 kg
and it contains two basic ingredients B1
and B2
. B1
costs
Rs. 5 per kg and B2
costs Rs. 8 per kg. Strength
considerations dictate that the brick should contain minimum
of 4 kg of B1
and a minimum of 2 kg of B2
. Since the
demand for the product is likely to be relative to the price
of brick. Formulate the above Linear Programming Problem. [06]
(b) The mean hourly wage of 100 labours working in a factory,
running two shifts of 60 and 40 workers respectively is
Rs. 38. The mean hourly wage of 60 labours working in
the morning shift is Rs. 40. Find the mean hourly wage
of 40 labours working in the evening shift. [04]
OR
(A) Lives of two models of refrigerators in a survey are as follows :
Life (No. of Years) 0-2 2-4 4-6 6-8 8-10 10-12
Number of Model A 5 16 13 7 5 4
Refrigerators
Model B 2 7 12 19 9 1
(a) What is the average life of each model of these refrigerators.
(b) Which model has greater uniformity ? Justify. [10]
[4374]-205 2 Contd.
(B) What is Scatter Diagram ? Describe differed types of Correlation
using Scatter Diagram. [05]
Q.3) (A) The Production Manager of a Company maintains that flow time
in days(y) depends on number of operations (X) to be performed.
The following data gives necessary information :
X 2 23 4 4 5 6 6 77
Y 8 13 14 11 20 10 22 26 22 25
(a) Compute Correlation Coefficient between X and Y and
interprete it.
(b) Estimate Flowtime (Y) when number of operations performed
are 10. [10]
OR
(A) (a) Solve the following Transportation Problem by Vogel’s
Approximation Method to obtain Initial Basic Feasible
Solution :
To D E F Supply
From
A 6 4 1 50
B 3 8 7 40
C 4 4 2 60
Demand 20 95 35 150 [06]
(b) The data below gives the yearly profits (in thousand of
Rs.) of two companies A and B :
Year Profits (in ’000 Rs.)
Company ‘A’ Company ‘B’
1994-95 120 90
1995-96 135 95
1996-97 140 108
1997-98 160 120
1998-99 175 130
Represent the data by Means of Multiple Bar Diagram. [04]
[4374]-205 3 P.T.O.
(B) What do you mean by Classification ? Describe Inclustive and
Exclusive Methods of Classification. [05]
Q.4) (A) (a) Define Regression Coefficient of X on Y and Y on X and
state any three properties of Regression Coefficients. [05]
(b) Compute Range, Coefficient of Range, Quartile Deviation
and Coefficient of Quartile Deviation for the following
data :
54, 51, 58, 59, 52, 52, 51, 57, 55, 58, 56 [05]
OR
(A) (a) Following data relates to the number of defective items
found in 20 boxes, each containing 5 items. Prepare a
frequency distribution of number of defective items : [05]
4, 2, 3, 5, 4, 1, 3, 5, 4, 0,
1, 1, 0, 2, 3, 2, 1, 2, 1, 3
(b) Obtain Initial Basic Feasible Solution by using Matrix Minima
Method for the following Transportation Problem : [05]
Depot B1 B2 B3 B4 Stock
Unit
A1 2 3 5 18
A2 7 3 4 6 10
A3 4 1 7 2 20
Requirement 6 8 9 15 38
(B) Describe Scope of Statistics in Economics. [05]
Q.5) (A) (a) Calculate Mode for the following data : [04]
Wages 0-10 10-20 20-30 30-40 40-50
No. of
Employees 22 38 46 35 20
[4374]-205 4 Contd.
(b) An incomplete frequency distribution is given below :
Class
Interval 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency 12 30 – 65 – 25 18
Calculate missing frequencies if Median of the data is 46
and total frequency is 229. [06]
OR
(A) (a) Solve the following Linear Programming Problem by
Graphical Method :
max. z = 48x + 40y
subject to : 2x + y ≤ 90
x + 2y ≤ 80
x + y ≤ 50
x ≥ 0, y ≥ 0 [06]
(b) For a bivariate data, the mean value of X is 20 and the
mean value of Y is 45. The regression coefficient of Y on
X is 4 and that of X on Y is 1
/
9
. Find :
(i) Correlation Coefficient between X and Y.
(ii) The Standard Deviation of X if Standard Deviation
of Y is 12.
(iii) Coefficient of Variation of X. [04]
(B) Explain Absolute and Relative Measures of Dispersion. [
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