LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIRST SEMESTER – APRIL 2011

ST 1502/ST 1500 – STATISTICAL METHODS

 

 

 

Date : 19-04-2011              Dept. No.                                          Max. : 100 Marks

Time : 9:00 – 12:00

 

PART – A

Answer ALL questions                                                                                           10×2=20

1. Write any two limitation of statistics.
2. What is classification?
3. Mention Various measures of central tendency.
4. Define Skewness.
5. Write the normal equations to fit a parabola by the principles of least squares.
6. Explain curve fitting.
7. Define correlation.
8. State any two properties of regression coefficients.
9. Find the missing frequencies from the following data, (A)=400,  (AB)=250, (B)=500,  N=1200.
10. Explain Yule’s coefficient of association.

 

PART – B

Answer any FIVE questions.                                                                                 5×8=40

11. Explain the various types of classification of data.
12. Distinguish between primary data and secondary data.
13. Find Arithmetic mean and mode for the following data:

Profit per shop:         0-10      10-20      20-30      30-40      40-50           50-60

No. of shops   :           12         18            27            20          17               6

14. Define Kurtosis. Also explain various measures of Kurtosis.
15. Fit a straight line trend for the following data:

Year:             1994         1995           1996               1997               1998               1999

Production      7             9                12                 15                  18                  23

16. What is a scatter diagram? How does it help us in studying the correlation between two variables with respect to their nature of relationship?
17. The following table gives the age of cars of certain make and annual maintenance costs. Obtain the regression equation for costs related to age:

Age of cars in years:            2          4          6          8

Maintenance cost

in Rs. Hundreds:                10          20        25        30

 

18. Find out the coefficient of association from the following data:

Passed                       Failed             Total

Married                         90                                 65                 155

Unmarried                   260                             110               370

 

PART – C

Answer any TWO questions                                                                                  2×20=40

 

19. a) What do you understand by Tabulation? What are the different parts of a table?

Explain.                                                                                                                               (2+8)

 

1. b) Draw a histogram and frequency polygon to represent the following data.

 

Weekly wages:         10-15              15-20              20-25              25-30              30-35              35-40

No. of workers;           7                      19                   27                    15                     12                    8                                                                                                                                                                     (7+3)

20. a) Calculate mean deviation from mean for the following data:

Class interval:     2-4      4-6      6-8      8-10

No. of person:     3         4          2          1                                                                        (3+5)

 

1. b) Calculate Bowley’s coefficient of Skewness from the following data:

 

Marks:            1-10    10-20    20-30     30-40     40-50         50-60     60-70    70-80

No. of

persons:          10         25         20          15           10            35           25         10           (12)

 

21. a) Write the procedure to fit a second degree parabola using method of least squares.

(6)

1. b) Fit a second degree parabola to the following.

 

Year ;      1978           1979               1980               1981               1982               1983

 

Price:       100            107                  128                140                 181                  192        (14)

 

22. a) Show that the coefficient of correlation lies between -1 and +1.       (10)

 

1. b) The following results were obtained in a survey:

Boys               Girls

No. of candidates appeared at an examination             800                200

Married                                                                                   150                   50

Married and successful                                                       70                   20

Unmarried and successful                                                 550                 110

Find the association between marital status and the success at the examination both for boys and girls.                                                                                                                                                       (10)

 

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