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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
B.Com.DEGREE EXAMINATION -COMMERCE
SECOND SEMESTER APRIL 2018
17/16UST2AL01- BUSINESS STATISTICS II
Date: 28-04-2018 Dept. No. Max. 100 Marks
Time: 01:00-04:00
SECTION A
Answer all the questions. (10 X 2 20)
1. Define statistics.
2. What are the various measures of central tendency?
3. Write any two properties of correlation coefficient.
4. The lines of regression of a bivariate distribution are as follows: 5X 145 14Y -208 -8X.
Find the means of X and Y.
5. What are the various components of a time series?
6. State the principles of least squares.
7. State the methods of determining the Initial Basic Feasible Solution(IBFS) for a transportation
Problem.
8. Write two limitations of graphical method in solving LPP?
9. Define a two-person zero sum game.
10. Find the value of the
SECTION- B
Answer any five questions. X 8 40)
11. Calculate Mean, Median and Mode for the following data:
Wages 0-10 10-20 20-30 30-40 40-50 50-60 60-70
No. of Workers 20 45 85 70 55 35 30
12. From the following series, find out Karl Pearson's Coefficient of Skewness:
Measurement 11 12 13 14 15
Frequency 3 9 6 4 3
13. Calculate Karl Pearson's coefficient of correlation between sales and expenses:
Sales 2 4 5 6 8 10
Expenses 8 12 10 8 7 5
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14. Obtain the Rank Correlation coefficient for the following data
X 68 64 75 50 64 80 75 40 55 64
Y 62 58 68 45 81 60 68 48 50 70
15. Fit a straight line for the given data and estimate sales for the year 2017
Year 2009 2010 2011 2012 2013
Sales(000s) 35 56 79 80 40
16. Find the trend of the following time series by the method of 4 yearly moving average and also
find short term fluctuations.
Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Value 53 79 76 66 69 94 105 87 79 104 97 92 101 105
17. Determine the optimum solution for the given LPP problem by Graphical method
Maximize: Z 100x1 40x2
Subject to: 5x1+2x2 1000
3x1+2x2 900
x1+2x2 500
and x1, x2
18. Solve the following Game graphically:
Player K
Player L
I II III IV
1 18 4 6 4
2 6 2 13 7
3 11 5 17 3
4 7 6 12 2
SECTION- C
Answer any two questions. X 20 40)
19. Scores obtained by 2 teams are given below:
Team A 15 10 7 5 3 2
Team B 20 10 5 4 2 1
Which is a more consistent team?
ii) Define Skewness, Kurtosis and Moments.
20. Data on Advertisement Expense and Sales are given below
Advertisement 22 23 23 24 26 27 27 28 30 30
Sales 18 20 21 20 21 22 23 24 25 26
Construct a Regression line of Y on X.
ii) Construct a Regression line of X on Y.
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iii) Find Correlation Coefficient.
iv) Estimate Sales when Advertisement expense equals 25
21. Calculate seasonal indices by the ratio to moving average method, from the following data:
Quarter
Wheat prices (in rupees per quintal)
Year→
2011
2012
2013
2014
I
75
86
90
100
II
60
65
72
78
III
54
63
66
72
IV
59
80
85
93
22. Determine Initial Basic Feasible Solution (IBFS) for the following transportation problem
by the method of
North west corner rule
Least Cost method
Vogels Approximation Method
Destination
Origin
D1
D2
D3
D4
Supply
O1
1
2
1
4
30
O2
3
3
2
1
50
O3
4
2
5
9
20
Demand
20
40
30
10