LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – COMMERCE
THIRD SEMESTER – NOVEMBER 2012
ST 3104/3101 – BUSINESS STATISTICS
Date : 07/11/2012 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION – A
Answer All the Questions: ( 10 x 2 =20)
- Define the term Statistics
- How are statistics being mis-used? Give anyone mis-interpretation of statistics.
- Define Weighted Arithmetic Mean.
- Why is median called a positional average?
- State the properties of Pearson’s correlation coefficient.
- What is meant by regression analysis?
- What is the scatter diagram?
- What are the uses of index numbers?
- Define trend and seasonal variation.
- State the components of time series.
SECTION – B
Answer any five questions: ( 5 x 8 =40 )
- Explain the scope and limitation of statistics.
- Draw a histogram and frequency polygon for the following data:
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| Frequency | 4 | 6 | 7 | 14 | 16 | 14 | 8 |
- Find coefficient of correlation between the costs and sales for the following data:
| Cost | 39 | 65 | 62 | 90 | 82 | 75 | 25 | 98 | 36 | 78 |
| Sales | 47 | 53 | 58 | 86 | 62 | 68 | 60 | 91 | 51 | 84 |
- An analysis of the weekly wages paid to workers in two firms, A and B belonging
to the same industry give the following results.
| Firm A | Firm B | |
| No. of wage earners | 586 | 648 |
| Avg. Weekly wage | Rs. 52.5 | Rs. 47.5 |
| Variance of the distribution of wage | 100 | 121 |
Find the average weekly wage and the standard deviation of the wage of all the workers in two firms, A and B taken together.
- Find the coefficient of skewness from the following data:
| Value | 6 | 12 | 18 | 24 | 30 | 36 | 42 |
| Frequency | 4 | 7 | 9 | 18 | 15 | 10 | 5 |
- Analyse the following frequency distribution by the method of moments, find β2 and interpret your results.
| X | 2 | 3 | 4 | 5 | 6 |
| F | 1 | 3 | 7 | 3 | 1 |
- Calculate Laspeyre’s, Paashe’s, and Fisher’s index numbers for the data given below
| Commodity | Base year | Current year | ||
| Price | Expenditure | Price | Expenditure | |
| A | 5 | 50 | 6 | 72 |
| B | 7 | 84 | 10 | 80 |
| C | 10 | 80 | 12 | 96 |
| D | 4 | 20 | 5 | 30 |
| E | 8 | 56 | 8 | 64 |
- Solve (using graphical method)
Max Z = 3X1 + 4 X2
Subject to the constraints 4X1 + 2X2 80
2X1 + 5X2 180
and X1, X2 0.
SECTION –C
Answer any TWO questions. ( 2 x 20 =40)
- a) From the following data, calculate mean and mode (7)
| Maks | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 |
| No. of students | 10 | 20 | 30 | 50 | 40 | 30 |
- b) From the marks given below obtained by two students taking the same course,
find out who is more consistent. (13)
| A | 58 | 59 | 66 | 65 | 66 | 52 | 75 | 31 | 46 | 48 |
| B | 56 | 87 | 89 | 46 | 93 | 65 | 44 | 54 | 78 | 68 |
- The following table represents aptitude test scores and productivity indices of 10 workers selected at random.
| Aptitude test scores | 60 | 62 | 65 | 70 | 72 | 48 | 53 | 73 | 65 | 82 |
| Productivity indices | 68 | 60 | 62 | 80 | 85 | 40 | 52 | 62 | 60 | 81 |
Calculate two regression equations and estimate the productivity index of a worker
whose test score is 92.
- From the following data, calculate seasonal indices by Ratio to trend method.
| Year | QUARTERLY SALES (Rs. Lakhs) | |||
| I | II | III | IV | |
| A | 8 | 16 | 24 | 32 |
| B | 48 | 36 | 24 | 12 |
| C | 48 | 16 | 32 | 64 |
| D | 72 | 108 | 144 | 36 |
| E | 56 | 28 | 84 | 112 |
- Obtain an initial basic feasible solution to the following transportation problem by
(i) North-west corner rule
(ii) Least cost method
(iii) Vogel’s approximation methods.
| Destination | |||||
| origin | D | E | F | G | Availability |
| A | 11 | 13 | 17 | 14 | 250 |
| B | 16 | 18 | 14 | 10 | 300 |
| C | 21 | 24 | 13 | 10 | 400 |
| Requirement | 200 | 225 | 275 | 250 | |
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