LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
|
B.COM. DEGREE EXAMINATION – COMMERCE
SECOND SEMESTER – April 2009
ST 2102 / 2101 / 3104 / 3101 – BUSINESS STATISTICS
Date & Time: 25/04/2009 / 1:00 – 4:00 Dept. No. Max. : 100 Marks
SECTION – A
Answer ALL the questions. (10 x 2 = 20)
- Clarify the difference between exclusive and inclusive class interval.
- What are the advantages of diagrammatic representation of the data?
- For what type of values harmonic mean is suitable?
- How will you calculate median in case of ungrouped data?
- What is a scatter diagram?
- Define correlation.
- Define regression.
- What are the important properties of regression coefficient?
- Define index number.
- Define time series and write its components.
SECTION – B
Answer any FIVE questions. ( 5 x 8 = 40)
- Draw the histogram, frequency curve and frequency polygon for the following data.
| Weekly wages( in Rs.) | No. of workers |
| 10 – 15 | 7 |
| 15 – 20 | 19 |
| 20 – 25 | 27 |
| 25 – 30 | 15 |
| 30 – 35 | 12 |
| 35 – 40 | 12 |
| 40 – 45 | 10 |
| 45 – 50 | 8 |
- The average score of girls in class X examination in a school is 67 and that of boys is 63. The average score for the whole class is 64.5, find the percentage of girls and boys in the class.
- The following are the run scored by two batsman A and B in ten innings.
| A | 101 | 27 | 0 | 36 | 82 | 45 | 7 | 13 | 65 | 14 |
| B | 97 | 12 | 40 | 96 | 13 | 8 | 85 | 8 | 56 | 15 |
Who is more consistent?
- Calculate the Karl Pearson’s coefficient correlation between the marks in English and Hindi obtained by 10 students.
| Marks in English | 10 | 25 | 13 | 25 | 22 | 11 | 12 | 25 | 21 | 20 |
| Marks in Hindi | 12 | 22 | 16 | 15 | 18 | 18. | 17 | 23 | 24 | 17 |
- Construct a 4 – year centered moving average from the following data.
| Year | 1940 | 1950 | 1960 | 1970 | 1980 | 1990 | 2000 |
| Imported cotton consumption
(in India ‘000 bales) |
129 | 131 | 106 | 91 | 95 | 84 | 93 |
- Compute Laspeyre’s, Paasche’s, Fisher’s and Kelly’s Price index numbers for 2005 for the following data.
| Commodity | 2000 | 2005 | ||
| Price Rs. | Quantity | Price | Quantity | |
| A
B C |
15
20 4 |
15
5 10 |
22
27 7 |
12
4 5 |
- Explain the components of time series.
- Find the minimum value of
z = – x1 + x2
subject to the constraints
– x1 + 3 x2 ≤ 10
x1 + x2 ≤ 6
x1 – x2 ≤ 10
x1 , x2 ≥ 0.
SECTION –C
Answer any TWO questions. ( 2 x 20 =40)
- Find the median, lower quartile, 7th decile and 85th percentile of the frequency distribution given below.
| Marks in statistics | Below 10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | Above70 |
| No. of students | 8 | 12 | 20 | 32 | 30 | 28 | 12 | 4 |
20 a). Ten competitors in a beauty contest are ranked by three judges in the following orders:
| 1st Judge | 1 | 6 | 5 | 10 | 3 | 2 | 4 | 9 | 7 | 8 |
| 2nd Judge | 3 | 5 | 8 | 4 | 7 | 10 | 2 | 1 | 6 | 9 |
| 3rd Judge | 6 | 4 | 9 | 8 | 1 | 2 | 3 | 10 | 5 | 7 |
Use the correlation coefficient to determine which pair of judges has the nearest approach to common
taste in beauty.
b). From the following data, obtain two regression equations:
| Sales | 91 | 97 | 108 | 121 | 67 | 124 | 51 | 73 | 111 | 57 |
| Purchases | 71 | 75 | 69 | 97 | 70 | 91 | 39 | 61 | 80 | 47 |
21). Find the seasonal variations by Ratio Trend method from the data given below.
| Year | 1st Quarter | 2nd Quarter | 3rd Quarter | 4th Quarter |
| 1987 | 34 | 54 | 38 | 38 |
| 1988 | 36 | 60 | 52 | 48 |
| 1989 | 40 | 58 | 56 | 52 |
| 1990 | 52 | 76 | 64 | 58 |
| 1991 | 70 | 90 | 88 | 84 |
22). 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 |