06.11.2003
9.00 - 12.00
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034
B.com. DEGREE EXAMINATION - COMMERCE
THIRD SEMESTER – NOVEMBER 2003
ST – 3101/STA101 – BUSINESS STATISTICS
Max:100 marks
SECTION-A
Answer ALL questions.
(10x2=20 marks)
1.
2.
3.
4.
5.
Define statistic and state any two misuses.
Mention any four one-dimensional diagrams.
State a merit and a demerit of median.
Provide any two properties of Arithmetic mean.
For a moderately asymmetric distribution, find median when mean and mode are
respectively 48 and 60.
6. Depict ‘skewness’ and ‘kurtosis’ with the help of diagrams.
7. If the regression coefficient of Y on X an X on Y are respectively 0.58 and0.65, Calculate
the coefficient of correlation.
8. From the following index number of prices, shift the base from 1987 to 1993 and recast
the index numbers.
Year: 1987 1988 1989 1990 1991 1992 1993 1994
Index: 100
110
120
200
400
410
400
380
9. Construct 5-yearly moving average:
Year: 1988 1989 1990 1991 1992 1993 1994 1995
No. of: 332 317
357
392
402
405
410
417
students
10. Express an mxn transportation problem as a Linear programming Problem (L.P.P).
SECTION-B
Answer any FIVE questions.
(5x8=40 marks)
11. For the following data on heights of 150 students, construct Histogram and locate the
mode from it:
Height (In cm): 120-130 130-140 140-150 150-160 160-170 170-180
No. of students: 18
30
40
33
17
12
12. Find Geometric mean and Harmonic mean of the following frequency distribution:
C.I: 0-4
4-8
8-12 12-16 16-20
F:
6
10
16
10
8
13. Compute rank correlation coefficient between Debenture price and share price of a
company given the following data:
Debentures
Price:
79
81
83
85
87
87
89
92
Share
Price:
67
65
66
64
64
64
63
62
1
14. The first four moments of a distribution about the value 3 are 2, 20, 40, 50. Find the first
four central moments, 1 and 2 .
15. Fit the equation Y = a + bX to the following data:
Year(x) : 1990 1991 1992 1993 1994 1995 1996
Sales(y): 32
47
65
88
132
190
275
Estimate sales for 1997.
16. Explain the four components of a time series.
17. a) Find Fisher’s Price index number given the following data:
Item
Price (1985) Price (1986) Quantity (1985)
Quantity (1986)
A
1
5
40
30
B
1
2
20
25
C
8
20
50
60
D
2
5
10
8
E
2
6
15
10
(b) Verify that Time Reversal Test is satisfied by Fisher’s index.
18. Solve Graphically:
Minimize
Z = 20x1+ 40x2
subject to the constraints:
36x1 + 6x2  108
3x1 + 12x2  36
20x1 + 10x2  100
x1, x2  0
(4+4)
SECTION-C
Answer any TWO questions.
(2x20=40 marks)
19. a) From the data given below, find which series is more consistent:
X
Series A
Series B
FA
FB
10-20
20
13
20-30
18
22
30-40
32
40
40-50
40
32
50-60
22
18
60-70
18
10
b) Calculate Bowley’s coefficient of skewness for the following frequency distribution:
X: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
f: 10
25
20
15
10
35
25
10
(12+8)
2
20. a) The following data relates to the intelligence test scores and the weekly sales of 9
salesmen.
Intelligence
Test Score (X):
70 40
80
50
80
60
50 60 50
Weekly sales
(Y):
60 50
70
30
60
50
40 60 30
Obtain the regression line of Y on X and estimate Y when X = 65.
(12+8)
b) Explain the problems involved in the construction of index numbers.
21. Find the seasonal indices by Ratio to Trend method:
Year
I
II
III
IV
1993
1994
1995
1996
1997
30
34
40
54
80
40
52
58
76
92
36
50
54
68
86
34
44
48
62
82
22. a) Solve the following Transportation problem:
Destination
Source
1
2
3
4
Availability
1
21
16
25
13
11
2
17
18
14
23
13
3
32
27
18
41
19
Requirement: 6
10
12
15
43
b) These are 4 jobs A, B, C,D and these are to be performed on 4 machine centres I, II,
III,IV. One job is to be allocated to a machine centre, though each machine is capable of
doing any job, at different costs given by the matrix below:
I
A 15
B 23
C 31

D  21
II
III IV
14 12 16 
22 25 24
34 32 33

32 44 53
Find the allocation of jobs to the machine centres so that the total cost of processing
is minimum.
(10+10)
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