1
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
B.Com.DEGREE EXAMINATION -COMMERCE
SECOND SEMESTER APRIL 2018
ST 2104 /BC 2104 BUSINESS STATISTICS
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 Arithmetic mean. State any two of its merits.
2. Define Range and its coefficient.
3. Define Kurtosis.
4. The first four central moments of distribution are 2.5, 0.7 and 18.75. Comment on the skewness and
kurtosis of the distribution.
5. Define Correlation.
6. What are Regression Equations?
7. What are the three components involved in a linear programming problem?
8. What is a Transportation problem?
9. What do you mean by a Two-person Zero-sum Game?
10. Define Mixed Strategy.
Section B
Answer any FIVE questions. 5 x 8 40
11. Explain the various measures of central tendency.
12. Calculate mode for the following distribution:
Class Interval
5-10
10-15
15-20
20-25
25-30
30-35
35-40
40-45
Frequency
3
6
10
20
15
5
4
2
13. Compute Quartile Deviation and its co-efficient from the following data:
Marks
10
20
30
40
50
60
No. of students
4
7
15
8
7
2
14. The Karl Pearson's co-efficient of skewness of a distribution is 0.32. The Standard deviation is 6.5 and
Mean is 29.6. Find Mode.
15. Calculate Karl Pearson's co-efficient of correlation from the following data:
Marks in Commerce
48
35
17
23
47
Marks in Statistics
45
20
40
25
45
16. Explain the various components of Time Series.
17. Obtain an initial basic feasible solution to the following transportation problem, using least cost method:
D1
D2
D3
D4
Supply
O1
1
2
3
4
6
O2
4
3
2
0
8
O3
0
2
2
1
10
Demand
4
6
8
6
24
Here, Oi and Dj denote the ith origin and jth destination respectively.
2
18. Use the property of dominance to find the optimal strategies for players A and B in the following game.
Also, obtain the value of game:
Player B
B1 B2 B3
A1 1 7 2
Player A A2 6 2 7
A35 1 6
Section C
Answer any TWO questions. 2 x 20 40
19. Calculate Standard Deviation from the following data: marks)
Marks
10
20
30
40
50
60
No. of Students
8
12
20
10
7
3
The following table shows the Age and Weight of 8 persons:
Age(X)
23
33
36
20
27
25
37
35
Weight(Y)
60
63
68
55
57
58
70
65
Obtain the regression equation of Y on X and find the expected weight of a person who is 45 years old.
(12 marks)
20. Calculate the seasonal indices by the ratio to moving average method, from the following data:
Year
1st quarter
2nd quarter
3rd quarter
4th quarter
2006
68
62
61
63
2007
65
58
66
61
2008
68
63
63
67
21. Explain the procedure to obtain an initial basic feasible solution of a transportation problem using
North-West Corner Rule. marks)
Obtain an initial basic feasible solution to the following transportation problem, using Vogel's
Approximation Method: (12 marks)
Warehouses
Stores
I
II
III
IV
Availability
A
5
1
3
3
34
B
3
3
5
4
15
C
6
4
4
3
12
D
4

4
2
19
Requirement
21
25
17
17
80
22. Solve the following LPP by graphical method: (10 marks)
Maximize z 3x 5y
Subject to the constraints: 3x 2y 18
x 4
y 6
and x y 0.
Solve the following 2x4 game graphically: (10 marks)
Player B
B1 B2 B3 B4
A1 2 1 0
Player A
A2 1 0 3 2