LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

YB 01

FIRST SEMESTER – April 2009

ST 1502/ST 1500 – STATISTICAL METHODS

 

 

 

Date & Time: 20/04/2009 / 1:00 – 4:00  Dept. No.                                                      Max. : 100 Marks

 

 

PART – A

Answer ALL questions:                                                                                   10 x 2 = 20     

1. States any two applications of statistics.
2. Distinguish between primary and secondary data.
3. What are the characteristics of a good measure of central tendency?
4. Find the coefficient of variation from the following data.

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5. State the principle of least squares.
6. Write the normal equations for fitting the curve .
7. The ranks of two attributes in a sample are given below. Find the correlation between them.
8. If and are the regression coefficients of y on x and x on y respectively, show that.
9. Check whether A and B are independent given the data:

N=10,000,       (A)=4500,        (B)=6000,        (AB)=3150

10. Distinguish between correlation and regression.

PART – B

Answer any FIVE questions:                                                               5 x 8 = 40

 

11. Explain classification and tabulation of data.
12. Draw less than and more than ogives from following data:

Profits: (Rs. Lakhs	10-20	20-30	30-40	40-50	50-60
No. of Companies:	6	8	12	18	25
Profits: (Rs. Lakhs)	60-70	70-80	80-90	90-100
No. of companies:	16	8	5	2

13. Calculate the mean, median and hence mode from the following data:

Mid pt:	15	25	35	45	55	65	75	85
Frequency:	5	9	13	21	20	15	8	3

14. For a moderately skewed data, the arithmetic mean is 200, the coefficient of variation is 8 and Karl Pearson’s coefficient of skewness is 0.3. Find the mode and median.
15. Fit a straight line trend for the following data:

Year:	1980	1981	1982	1983	1984	1985	1986
Y:	83	60	54	21	22	13	23

16. Show that the coeffient of correlation lies between -1 and +1.
17. In a group of 800 students, the number of married students is 320. But of 240 students who failed, 96 belonged to the married group. Find out whether the attributes of marriage and failure are independent.
18. Given the following data, find the two regression equations:

PART – C

Answer any TWO questions:                                                               2 x 20 = 40

19. a) Explain the scope and limitations of statistics.
20. b) The following table gives the frequency, according to groups of marks obtained by 67 students in an intelligence test. Calculate the degree of relationship between age and intelligence test.

	Age in years
Test marks	18	19	20	21	Total
200-250	4	4	2	1	11
250-300	3	5	4	2	14
300-350	2	6	8	5	21
350-400	1	4	6	10	21
	10	19	20	18	67

20. a) Define measure of dispersion. Prove that the standard deviation is independent of change of origin but not scale.
21. b) Find the coefficient of quartile deviation from the following data.

Wages:	0-10	10-20	20-30	30-40	40-50
No.of Workers:	22	38	46	35	20

21. Calculate the first four moments about the mean and also the values of and from the following data:

Marks:	0-10	10-20	20-30	30-40	40-50	50-60	60-70
No. of Students:	8	12	20	30	15	10	5

22. a) Fit the curve using the principle of least squares.
23. b) From the following data, calculate the remaining frequencies and hence test whether A and B are

independent.

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