LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034
B.Sc., DEGREE EXAMINATION – STATISTICS
FIRST SEMESTER – APRIL 2004
ST 1500/STA 500 – STATISTICAL METHODS
17.04.2004 Max:100 marks
9.00 – 12.00
SECTION -A
Answer ALL questions. (10 ´ 2 = 20 marks)
- Give an example for primary and secondary data.
- What is meant by judgement sampling?
- Mention the difference between histogram and bar diagram?
- What are the characteristics of a good measure of central tendency?
- For a frequency distribution, the mean and mode were found to be 15 and 24 respectively. Find the median of the distribution.
- Comment on the following: “The mean deviation of a frequency distribution about an origin is minimum, when the origin is the mean”.
- Define: Skewness
- Give an example for positive correlation.
- Find the regression equation of y on x given the following information:
- Check the consistency of the following data:
- = 400; (AB) = 250; (B) = 550; N = 1,200.
SECTION – B
Answer any FIVE questions. (5 ´ 8 = 40 marks)
- Explain the different types of classification with examples.
- The following data relate to the monthly expenditure of two families A and B:
| Items of expenditure | Expenditure (in Rs.) | |
| Family A | Family B | |
| Food | 1600 | 1200 |
| Clothing | 800 | 600 |
| Rent | 600 | 500 |
| Fuel | 200 | 100 |
| Miscellaneous | 800 | 600 |
Represent the above data by a percentage bar diagram.
- Calculate Q1, Q2, P3 and P20 from the following data:
Class Interval: 0-5 5-10 10-15 15-20 20-25
Frequency : 7 18 25 30 20
- Calculate mean deviation about median and its coefficient from the following data:
| Class | Frequency | Class | Frequency |
| 0-10 | 5 | 40-50 | 20 |
| 10-20 | 8 | 50-60 | 14 |
| 20-30 | 12 | 60-70 | 12 |
| 30-40 | 15 | 70-80 | 6 |
- Explain the concepts of correlation and regression through an example.
- Ten competitors in a beauty contest are ranked by 3 judges in the following order:
Judge 1: 1 6 5 10 3 2 4 9 7 8
Judge 2: 3 5 8 4 7 10 2 1 6 9
Judge 3: 6 4 9 8 1 2 3 10 5 7
Use the rank correlation coefficient to determine which pair of judges has the nearest approach to common tastes in beauty.
- Find Yule’s coefficient of association between literacy and unemployment from the following data:
Total Adults: 10,000
Literate: 1,290
Unemployed: 1,390
Literate unemployed: 820
Comments on the results.
- Fit a straight line trend for the following time series.
Year : 1990 1991 1992 1993 1994 1995 1996
Production
of steel
(in tonnes) : 60 72 75 65 80 85 95
Estimate the production for the year 1997.
SECTION – C
Answer any TWO questions (2 ´ 20 = 40 marks)
- i) Explain the various method of collecting primary data.
- ii) Draw ‘less than’ and ‘more than’ Ogive curves for the following data:
| Profit
(in lakh) |
Number of Companies | Profit
(in lakh) |
Number of companies |
| 10-20 | 6 | 60-70 | 16 |
| 20-30 | 8 | 70-80 | 8 |
| 30-40 | 12 | 80-90 | 5 |
| 40-50 | 18 | 90-100 | 2 |
| 50-60 | 25 |
Also find the value of the median. (10+10)
- i) Calculate mode ( by grouping method) from the following data:
Class interva l: 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
Frequency : 5 9 13 21 20 15 8 3
- ii) From the prices of shares of 2 firms X and Y given below, find out which is more stable
in value.
Firm X: 35 54 52 53 56 58 52 50 51 49
Firm Y: 108 107 105 105 106 107 104 103 104 101
(10+10)
- i) Explain the concept of kurtosis.
- ii) Calculate the first four central moments from the following frequency distribution.
x: 2 3 4 5 6
f: 1 3 7 3 1
iii) Calculate Karl pearson’s coefficient of correlation, for the following data and interpret
its value.
X: 48 38 17 23 44
Y: 45 20 40 25 45 (5+7+8)
- i) From the following data, obtain the regression equations of Y on X and X on Y.
Aptitude scores(X): 60 62 65 70 72 48 53 73 65 82
Productivity
Index(Y) : 68 60 62 80 85 40 52 62 60 81
Also estimate the productivity index, when test score is 92 and the test score when productivity index is 75.
- ii) Explain any two methods of studying the association between attributes. (15+5)
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