LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 B.Com DEGREE EXAMINATION – COMMERCE
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THIRD SEMESTER – NOV 2006
ST 3101 – BUSINESS STATISTICS
(Also equivalent to STA 101)
Date & Time : 08-11-2006/1.00-4.00 Dept. No. Max. : 100 Marks
SECTION-A (10 x 2 = 20)
Answer All the questions. Each question carries 2 marks.
- What are the different levels of measurements?
- Create your own example and draw histogram.
- Distinguish between symmetric and asymmetric distributions.
- When do you prefer median as compared to arithmetic mean?
- What do you understand by Kurtosis?
- Explain briefly any two properties of Regression coefficients.
- Write the normal equations for fitting Quadratic model.
- Give the meaning of “Splicing the index numbers”.
- Distinguish between slack and surplus variables.
- Define a Transportation problem.
SECTION-B (5 x 8 = 40)
Answer any 5 questions. Each question carries 8 marks.
- Draw ogive curve for the following data and locate D39 and P63.
Also, verify it using the formula.
| Electricity consumption per month | 0-100 100-500 500-1000 1000-1500 1500-2000
|
| No. of families | 26 148 296 185 70 |
- The wage distribution of employees working in two different IT
industries are given below:
| Particulars | IT-1 | IT-2 |
| No. of Employees | 800 | 550 |
| Average Salary per month (in Rs.) | 16,500 | 21,300 |
| Standard Deviation (in Rs.) | 1,900 | 2,600 |
- Calculate the combined mean and combined standard deviation.
- b) Which industry is consistent in wage distribution? (4+4)
- Calculate the Bowley’s coefficient of skewness for the following
data:
| Processing time (in min.) | 0- 5 5-10 10-15 15-20 20-25 |
| No. of Operators | 8 24 58 31 14 |
- Calculate the rank correlation coefficient for the following data:
Awarded Scores out of 20 |
|
| Judge-1 | 8 14 16 19 20 10 5 7 3 14 |
| Judge-2 | 6 10 18 20 20 14 4 6 4 13 |
- a) What is the purpose of constructing index numbers?
- b) Distinguish between weighted and unweighted index numbers.
- Calculate the cost of living index using the Family Budget method for the following data:
| Particulars | Food | Rent | Fuel &Elect. | Education | Medical | Misc. |
| Weights | 4 | 4 | 1 | 2 | 2 | 3 |
| Base year expenses (in Rs.) | 2500 | 3000 | 600 | 900 | 800 | 1700 |
| Current year (in Rs.) expenses | 3000 | 3250 | 700 | 950 | 700 | 2200 |
- Product A offers a profit of Rs.25/- per unit and Product B yields a profit of Rs. 40/- per unit. To manufacture the products—leather, wood and glue are required in the amount shown below:
RESOURCES REQUIRED FOR ONE UNIT |
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| Product | Leather(in kg.) | Woods (in sq.metres) | Glue(in litres) |
| A | 0.5 | 4 | 0.2 |
| B | 0.25 | 7 | 0.3 |
Available resources include 2,200 kg. of leather; 28,000 square metres of wood and 1,400 litres of glue. Formulate the problem as an LPP.
- What do you mean by unbounded solution in LPP? Does
unboundedness implies no solution to the Problem? Explain in
detail.
SECTION-C (2 x 20 = 40)
Answer any 2 questions. Each question carries 20 marks.
- a) What are the scope and limitations of Statistics? (4+4)
- b) Distinguish between sample surveys and Census. Explain the
merits and demerits of both. (12)
- Consider the following data:
| Year (X) | 2001 2002 2003 2004 2005 |
| Profit in lakhs (Y) | 12.3 16.8 21.5 26.4 30.2 |
- Fit a regression line of Y on X
- Estimate profit for 2006
- Obtain the standard error of the estimate
- Draw the original and trend lines on the graph. (10+2+4+4)
- a) Explain in detail the major components of Time series. (8)
- b) Calculate the seasonal indices for the following data using the
ratio to moving average method:
| Quarterly Cement Production ( in lakh tons) | ||||
| YEAR | I | II | III | IV |
| 2003 | 48.3 | 62.1 | 36.1 | 41.2 |
| 2004 | 69.7 | 79.4 | 29.4 | 56.9 |
| 2005 | 84.1 | 96.3 | 59.1 | 62.8 |
(12)
- a) Solve the following LPP by Simplex method:
Max. Z = 3 X + 2 Y
S.to
X + Y ≤ 4
X – Y ≤ 2
X, Y ≥ 0 (12)
- MCS Inc. is a Software company that has three projects with the departments of health, education and housing. Based on the background and experiences of the project leaders, they differ in terms of their performance at various projects. The performance score matrix is given below:
| Projects | |||
| Project leaders | Health | Education | Housing |
| P1 | 20 | 26 | 42 |
| P2 | 24 | 32 | 50 |
| P3 | 32 | 34 | 44 |
Help the management by determining the optimal assignment that
maximize the total performance score. (8)