LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – COMMERCE
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THIRD SEMESTER – November 2008
ST 3104/ST 3101/ST 2101 – BUSINESS STATISTICS
Date : 11-11-08 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION A
Answer ALL questions. (10 x 2 =20 marks)
- Define statistics.
- Differentiate between primary and secondary data.
- What is the mode of 110, 120, 130, 120, 110, 140, 130, 120, 140.
- If the mode and mean of a moderately asymmetrical distribution are 80 and 68, what is the median?
- If Q1 = 30 and Q3 = 50, what is the coefficient of quartile deviation?
- Define skewness.
- Define correlation.
- Find the mean value of X and Y, from the following regression equations:
4 X – 5 Y + 33 = 0, 20 X – 9 Y – 107 = 0.
- What are the uses of index numbers?
- Define time series data.
SECTION B
Answer any FIVE questions. (5 x 8 =40 marks)
- Explain the scope and limitations of statistics.
- Draw a histogram and frequency polygon for the following data:
| Length of leaves(cms.) | 6-7 | 7-8 | 8-9 | 9-10 | 10-11 | 11-12 | 12-13 |
| No. of leaves | 5 | 12 | 25 | 48 | 32 | 6 | 1 |
- Calculate Karl Pearsons’ coefficient of skewness:
| X | 6 | 12 | 18 | 24 | 30 | 36 | 42 |
| f | 4 | 7 | 9 | 18 | 15 | 10 | 5 |
| E1 | E2 | E3 | |
| No. of employees | 20 | 25 | 40 |
| Avg. daily salaries | 305 | 300 | 340 |
| Standard deviation | 50 | 40 | 45 |
- A company has 3 establishments E1, E2, E3 in 3 cities. Analysis of the daily salaries (Rs.) paid
to the employees is given below:
Find the average and standard deviation of the monthly salaries of all the 85 employees.
- Analyze the following frequency distribution by the method of moments, find β 2 and interpret the result.
| X | 2 | 3 | 4 | 5 | 6 |
| f | 1 | 3 | 7 | 3 | 1 |
- From the following data, calculate coefficient of rank correlation.
| X | 33 | 56 | 50 | 65 | 44 | 38 | 44 | 50 | 15 | 26 |
| Y | 50 | 35 | 70 | 25 | 35 | 58 | 75 | 60 | 55 | 26 |
- Calculate fixed base and chain base index numbers for the following data.
| Average wholesale prices (Rs.) | |||||
| Commodities | 2003 | 2004 | 2005 | 2006 | 2007 |
| A | 2 | 3 | 5 | 7 | 8 |
| B | 8 | 10 | 12 | 4 | 18 |
| C | 4 | 5 | 7 | 9 | 12 |
- Solve the following Linear Programming Problem: Max z = 22 x + 18 y subject to the constraints, 360 x + 240 y ≤ 5760, x + y ≤ 20, x, y ≥ 0.
SECTION C
Answer any TWO questions. (2 x 20 =40 marks)
- From the prices of shares of company X and Y given below, state which share prices are more stable in value, using coefficient of variation.
| X | 35 | 54 | 52 | 53 | 56 | 58 | 52 | 50 | 51 | 49 |
| Y | 108 | 107 | 105 | 105 | 106 | 107 | 104 | 103 | 104 | 101 |
- From the following data of sales and purchases (Rs. crores), obtain the two regression equations, and find the estimated sales when the purchase is Rs. 100 Crores.
| Sales | 91 | 97 | 108 | 121 | 67 | 124 | 51 | 73 | 111 | 57 |
| Purchases | 71 | 75 | 69 | 97 | 70 | 91 | 39 | 61 | 80 | 47 |
- Calculate seasonal variations given the average quarterly price of a commodity for 5 years by ratio to trend method.
| Year | I Quarter | II Quarter | III Quarter | IV Quarter |
| 2001 | 28 | 22 | 22 | 28 |
| 2002 | 35 | 28 | 25 | 36 |
| 2003 | 33 | 34 | 30 | 35 |
| 2004 | 31 | 31 | 27 | 35 |
| 2005 | 37 | 36 | 31 | 36 |
- There are three sources A, B, C which store a given product. These sources supply these products to four dealers D, E, F, G. The cost (Rs.) of transporting the products from various sources to various dealers, the capacities of the sources and the demands of the dealers are given below.
| D | E | F | G | Supply | |
| A | 3 | 7 | 6 | 4 | 5 |
| B | 2 | 4 | 3 | 2 | 2 |
| C | 4 | 3 | 8 | 5 | 3 |
| Demand | 3 | 3 | 2 | 2 |
Find out the initial solution for transporting the products by using (i) North-West Corner Rule, (ii) Least Cost method and (iii) Vogel’s Approximation Method. Compare the costs and write down the best initial solution.
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