Loyola College B.Sc. Statistics Nov 2003 Statistical Methods Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI– 600  034

B.Sc. DEGREE EXAMINATION  –  STATISTICS

First SEMESTER  – NOVEMBER 2003

           ST 1500/ STA  500  STATISTICAL  METHODS

07.11.2003                                                                                        Max: 100 Marks

9.00 – 12.00

 

section A                    

Answer ALL questions                                                            (10 ´ 2 = 20 Marks)

  1. Give the definition of statistics according to Croxton and Cowden.
  2. Comment on the following: “ Sample surreys are more advantageous than census”.
  3. Give an example for

(i) Quantitative continuous data     (ii)  Discrete time series data

 

  1. Prove that for any two real numbers ‘a’ &’b’ , A.M £M.
  2. Mention any two limitations of geometric mean.
  3. From the following results obtained from a group of observations, find the standard deviation. S(X-5) = 8 ;  S(X-5)2 = 40;  N = 20.

 

  1. For a moderately skewed unimodal distribution, the A.M. is 200, the C.V.

is 8 and the  Karl Pearson’s coefficient of skewness is 0.3.  Find the mode

of the distribution.

 

  1. Given below are the lines of regression of two series X an Y.

5X-6Y + 90 = 0

         15X -8Y-130 = 0

Find the values of .

  1. Write the normal equations for fitting a second degree parabola.
  2. Find the remaining class frequencies, given (AB) = 400;

(A) = 800; N=2500; (B) = 1600.

                                                 SECTION – B

Answer any FIVE questions.                                                   (5 ´8 = 40 Marks)

  1. Explain any four methods of collecting primary data.
  2. Draw a histogram and frequency polygon for the following data.
Variable Frequency Variable Frequency
100-110 11 140-150 33
110-120 28 150-160 20
120-130 36 160-170 8
130-140 49

 

Also determine the value of mode from the histogram.

 

 

 

 

 

 

  1. Calculate arithmetic mean, median and mode from the following

frequency distribution.

 

Variable Frequency variable Frequency
10-13 8 25-28 54
13-16 15 28-31 36
16-19 27 31-34 18
19-22 51 34-37 9
22-25 75 37-40 7

 

  1. The number of workers employed, the mean wages (in Rs.) per month and standard deviation (in Rs.) in each section of a factory are given below. Calculate the mean wages and standard deviation of all the workers taken together.

 

Section No. of workers

employed

Mean Wages

(in Rs.)

Standard  deviation

(in Rs.)

A 50 1113 60
B 60 1120 70
C 90 1115 80

 

  1. Calculate Bowley’s coefficient of skewness from the following data.

 

Variable frequency
0-10 12
10-20 16
20 -30 26
30- 40 38
40 -50 22
50-60 15
60- 70 7
70 -80 4

 

  1. Calculate Karl Person’s coefficient of correlation from the following data.
X 44 46 46 48 52 54 54 56 60 60
Y 36 40 42 40 42 44 46 48 50 52

 

  1. Explain the concept of regression with an example.
  2. The sales of a company for the years 1990 to 1996 are given below:

 

Year 1990 1991 1992 1993 1994 1995 1996
Sales (in lakhs of  rupees) 32 47 65 88 132 190 275

 

Fit an equation of the from Y = abfor the above data and estimate the

sales for the year 1997.

 

 

 

 

 

SECTION C

Answer any TWO questions.                                                   (2 ´ 20 = 40 Marks)

 

  1. a) Explain (i) Judgement sampling (ii) Quota sampling and

(iii) Systematic sampling methods with examples.

 

  1. (i) Draw a blank table to show the distribution of personnel  in a

manufacturing concern according to :

  • Sex: Males and Females.
  • Salary grade: Below Rs.5,000; Rs.5,000 -10,000;

Rs.10,000 and above.

  • Years: 1999 and 2000
  • Age groups: Below 25, 25 and under 40, 40 and above

 

(ii) Draw a multiple bar diagram for the following data:

 

Year Sales (in’000Rs.) Gross Profit Net profit
1992 120 40 20
1993 135 45 30
1994 140 55 35
1995 150 60 40

(10+5+5)

 

  1. a) (i)  An incomplete distribution is given below

 

Variable 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 10 20 f1 40 f2 25 15

 

       Given the median value is 35 and the total frequency is 170, find

the missing frequencies f1 and f2.

  • Calculate the value of mode for the following data:
Marks 10 15 20 25 30 35 40
Frequency 8 12 36 35 28 18 9

 

  1. b) Explain any two measures of dispersion.                                       (7+7+6)
  2. a) The scores of two batsman A and B is 10 innings during a certain season are:

 

 A 32 28 47 63 71 39 10 60 96 14
 B 19 31 48 53 67 90 10 62 40 80

 

Find which of the two batsmen is consistent in scoring.

 

 

 

 

 

 

 

 

 

 

 

  1. Calculate the first four central moments and coefficient of skewness from the

following distribution.

 

Variable frequency Variable Frequency
25-30 2 45-50 25
30-35 8 50-55 16
35-40 18 55-60 7
40-45 27 60-65 2

(10+10)

  1. a) From the following data obtain the two regression equations and calculate

the correlation coefficient.

 

X 60 62 65 70 72 48 53 73 65 82
Y 68 60 62 80 85 40 52 62 60 81

 

  1. b) (i)   Explain the concept of Kurtosis.

(ii)   In a co-educational institution, out of 200 students 150 were boys.

They took an examination and it was found that 120 passed, 10 girls

had failed. Is there any association between gender and success in the

examination?                                                                 (10+5+5)

 

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