LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034
B.com. DEGREE EXAMINATION – COMMERCE
THIRD SEMESTER – NOVEMBER 2003
ST – 3101/STA101 – BUSINESS STATISTICS
06.11.2003 Max:100 marks
9.00 – 12.00
SECTION-A
Answer ALL questions. (10×2=20 marks)
- 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.
- Depict ‘skewness’ and ‘kurtosis’ with the help of diagrams.
- If the regression coefficient of Y on X an X on Y are respectively 0.58 and0.65, Calculate the coefficient of correlation.
- 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
- 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
- Express an mxn transportation problem as a Linear programming Problem (L.P.P).
SECTION-B
Answer any FIVE questions. (5×8=40 marks)
- 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
- 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
- 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
- The first four moments of a distribution about the value 3 are 2, 20, 40, 50. Find the first four central moments, b1 and b2 .
- 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.
- Explain the four components of a time series.
- 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. (4+4)
- Solve Graphically:
Minimize Z = 20x1+ 40x2
subject to the constraints: 36x1 + 6x2 ³ 108
3x1 + 12x2 ³ 36
20x1 + 10x2 ³ 100
x1, x2 ³ 0
SECTION-C
Answer any TWO questions. (2×20=40 marks)
- 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
- 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)
- 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.
- Find the seasonal indices by Ratio to Trend method:
Year I II III IV
1993 30 40 36 34
1994 34 52 50 44
1995 40 58 54 48
1996 54 76 68 62
1997 80 92 86 82
- 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 II III IV
Find the allocation of jobs to the machine centres so that the total cost of processing
is minimum. (10+10)
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