Loyola College B.Com Nov 2008 Introduction To Statistics Question Paper PDF Download

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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

 

  1. 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.

  1. 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

 

 

 

 

  1. 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.

 

  1. 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

 

 

 

 

  1. 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.

  1. 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.

 

  1. 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

 

  1. (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.

  1. (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

 

  1. 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

 

 

 

 

 

  1. (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

 

 

 

  1. (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.

 

  1. (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

 

 

 

 

 

 

 

  1. (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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