LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
|
FIRST SEMESTER – NOV 2006
ST 1500 – STATISTICAL METHODS
(Also equivalent to STA 500)
Date & Time : 01-11-2006/1.00-4.00 Dept. No. Max. : 100 Marks
SECTION A
Answer ALL questions. (10 x 2 =20 marks)
- Define Statistics.
- Distinguish between primary and secondary data.
- What are the advantages of diagrammatic and graphic presentation of data?
- What are the desirable properties of a good average?
- What purpose does a measure of dispersion serve?
- Interpret r when r = 1, -1, 0, where r is the correlation coefficient.
- What is the purpose of regression analysis?
- Define kurtosis.
- How would you distinguish between association and correlation?
- Check for consistency: (A) = 100, (B) = 150, (AB) = 60, N = 500.
SECTION B
Answer any FIVE questions. (5 x 8 =40 marks)
- Explain the various methods that are used in the collection of primary data, pointing out their merits and demerits.
- Represent the above frequency distribution by means of a histogram and superimpose the corresponding frequency polygon. Experience (in months).
| Experience | 0-2 | 2-4 | 4-6 | 6-8 | 8-10 | 10-12 | 12-14 | 14-16 |
| No. of Workers | 5 | 6 | 15 | 10 | 5 | 4 | 2 | 2 |
- (i) Calculate the Geometric Mean for the following values:
85, 70, 15, 75, 500, 8, 45, 250, 40, 36.
(ii) An aero plane covers four sides of a square at speeds of 10000, 2000, 3000 and 4000 Kms. per hour respectively. What is the average speed of the plane in the flight around the square?
- Calculate Quartile deviation and coefficient of Quartile deviation from the following data:
| Wages (in Rs.) | Less than 35 | 35-37 | 38-40 | 41-43 | Over 43 |
| No. of wage earners | 14 | 62 | 99 | 18 | 7 |
- Find Bowley’s coefficient of skewness for the following frequency distribution.
| X | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 7 | 10 | 16 | 25 | 18 | 11 | 8 |
- Fit a straight line to the following data.
| X | 6 | 2 | 10 | 4 | 8 |
| Y | 9 | 11 | 5 | 8 | 7 |
- The ranking of two students in two subjects A and B are as follows:
| A | 6 | 5 | 3 | 10 | 2 | 4 | 9 | 7 | 8 | 1 |
| B | 3 | 8 | 4 | 9 | 1 | 6 | 10 | 7 | 5 | 2 |
Calculate rank correlation coefficient.
- 300 people of German and French nationalities were interviewed for finding their preference
of music of their language. The following facts were gathered out of 100 German nationals,
60 liked music of their own language, whereas 70 French nationals out of 200 liked German
music. Out of 100 French nationals, 55 liked music of their own language and 35 German
nationals out of 200 Germans liked French music. Using coefficient of association, state
whether Germans prefer their own music in comparison with Frenchmen.
SECTION C
Answer any TWO questions. (2 x 20 =40 marks)
- (i) Define sampling and explain the different methods of sampling.
(ii) Draw an ogive for the following distribution and calculate the median wage.
| Wages | 1000-1100 | 1100-1200 | 1200-1300 | 1300-1400 | 1400-1500 | 1500-1600 |
| Workers | 6 | 10 | 22 | 16 | 14 | 12 |
- (i) Following are the records of two players regarding their performance in cricket matches.
Which player has scored more on an average? Which player is more consistent ?
| Player A | 48 | 52 | 55 | 60 | 65 | 45 | 63 | 70 |
| Player B | 33 | 35 | 80 | 70 | 100 | 15 | 41 | 25 |
(ii) You are given the following data about height of boys and girls in a certain college. You are required to find out the combined mean and standard deviation of heights of boys and girls taken together.
| Number | Average height | Variance | |
| Boys | 72 | 68” | 9” |
| Girls | 38 | 91” | 4” |
- (i) Find the coefficient of correlation with the help of Karl Pearson’s method.
| 10 | 20 | 30 | 40 | 50 | |
| 5 | 2 | 4 | 1 | 4 | 1 |
| 10 | 8 | 2 | 5 | 1 | – |
| 15 | – | 3 | 2 | 1 | – |
| 20 | – | 1 | 3 | 2 | 4 |
| 25 | – | – | 4 | 2 | – |
Marks in Mathematics
Marks in
Statistics
(ii) In a group of 800 students, the number of married is 320. But of 240 students who failed, 96 belonged to the married group. Find out whether the attributes marriage and failure are independent.
- The following table gives the aptitude test scores (X) and productivity indices (Y) of 10 workers selected at random:
| X | 60 | 62 | 65 | 70 | 72 | 48 | 53 | 73 | 65 | 82 |
| Y | 68 | 60 | 62 | 80 | 85 | 40 | 52 | 62 | 60 | 81 |
- Find the two regression equations.
- Estimate the productivity index of a worker whose test score is 92.
- Estimate the test score of a worker whose productivity index is 75.
- Using the two regression equations find the correlation coefficient.
Latest Govt Job & Exam Updates: