LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Com., B.B.A. DEGREE EXAMINATION – COMMERCE & COR.SECR.

BA 05

THIRD SEMESTER – November 2008

ST 3105 / ST 3102 – INTRODUCTION TO STATISTICS

 

 

 

Date : 11-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION  A

     Answer ALL questions.                                                                                                   (10 x 2 = 20 marks)

 

1. What are the limitations of statistics
2. State the various methods of collecting primary data.
3. State any two methods of non-probability sampling.
4. Distinguish between classification and tabulation.
5. List the various methods of representing a frequency distribution graphically.
6. Define quartile deviation.
7. Positive and negative correlation.
8. Pearson’s coefficient of skewness is – 0.7 and the value of the  median and standard deviation are 12.8 and 6 respectively. Determine the value of the mean.
9. List the various components of a time series.
10. Find the regression equation of X on Y from the following data:

E x² = 164 ,  Ex = 24,  Ey = 44,  Ey ²= 574    and  Exy =306, N = 10

Find the value of X when Y = 6.

                                                                     SECTION B                                              (5 X 8  =  40 Marks)

       Answer any FIVE questions

 

11. Below is given the frequency distribution of marks in mathematics obtained by 100 students in a class

Marks	20 – 29	30 – 39	40 – 49	50 – 59	60 – 69	70 – 79	80 – 89	90 -100
No.of students	7	11	24	32	9	14	2	1

 

 

Draw the Ogives( “ less than “ and “ more than” type) for this distribution and use it to determine the

Median.

12. Compute the geometric mean from the data given below:

Marks	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
No.of students	8	12	18	8	6

 

 

 

 

13. The following are some particular of the distribution of weights of boys and girls in a clas.

Boys                 Girls

Number                        100                    50

Mean weight                   60 kg                45  kg

Variance                          9                        4

Find the standard deviation of the combined data.

 

14. Find the mean deviation about the mean for the following data:

Class Interval	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70
Frequency	8	12	10	8	3	2	7

 

 

 

 

15. The marks obtained by the students in statistics and accounts are as following

 

Statistics	60	62	68	76	72	42	35	78	30	90
Accounts	50	66	58	74	60	40	28	64	38	88

 

 

Compute the ranks for the two subjects and find the coefficient of correlation of ranks.

16.The following table gives age ( X )  in years of cars and annual maintenance cost Y (In hundred Rs.)

X	1	3	5	7	9
Y	15	18	21	23	22

 

 

 

Estimate the maintenance cost for a 4 – year old car after finding the regression equation.

17. 200 candidates appeared for a competitive examination and 60 of them succeeded. 35 received

special coaching and out of them 20 candidates succeeded. Prepare a 2×2 contingency table and

using  Yule’s coefficient, discuss whether special coaching is effective or not.

 

18. Explain briefly the various methods of determining trend in the analysis of time series. Explain the

Merits and  demerits of each method.

                                                                            

SECTION   C                                   (2 X 20  =  40 Marks)

             Answer any TWO questions

 

19. (a) The scores of two players A and B in 12 rounds are given below:

 

X	74	75	78	72	78	77	79	81	79	76	72	71
Y	87	84	80	88	89	85	86	82	82	79	86	80

 

 

 

Identify the better player and the more consistent player.

19. (b)  From the following data  compute Bowley’s coefficient of skewness.

 

Income(Rs.)	Below 200	200 -400	400 – 600	600 – 800	800 – 1000	1000 above
No.of pearsons	25	40	85	75	16	16

 

20. Calculate Skewness and kurtosis for the following distribution

 

Class Interval	1 – 5	6 – 10	11 – 15	16 – 20	21 – 25	26 – 30	31 – 35
Frequency	3	4	68	30	10	6	2

 

 

 

 

 

21. (a) Calculate the correlation coefficient between X and Y from the following data:

 

X	61	72	73	63	84	80	66	76
Y	40	52	49	43	61	58	42	58

 

 

 

21. (b) In a laboratory experiment on correlation research study, the equation of the two regression

lines Were found to be 2x – y + 1 = 0 and 3x – 2y +7 = 0. Find the mean of X and Y. Also

worked the Values of the regression coefficient of correlation between the two variables  x and y.

 

22. (a ) Calculate seasonal indices by the ratio to moving average method from the following data.

Wheat Prices ( in rupees quintal )

Quarter /Year	1972	1973	1974	1975
I	75	86	90	100
II	60	65	72	78
III	54	63	66	72
IV	59	80	85	93

 

 

 

 

 

 

 

22. (b) Fit a straight line trend equation by the method of least square and estimate the trend values

 

Year	1961	1962	1963	1964	1965	1966	1967	1968
Value	80	90	92	83	94	99	92	104

 

 

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