17.04.2004
9.00 - 12.00
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034
B.Sc., DEGREE EXAMINATION - STATISTICS
FIRST SEMESTER – APRIL 2004
ST 1500/STA 500 - STATISTICAL METHODS
Max:100 marks
SECTION -A
(10  2 = 20 marks)
Answer ALL questions.
1.
2.
3.
4.
5.
6.
7.
8.
9.
Give an example for primary and secondary data.
What is meant by judgement sampling?
Mention the difference between histogram and bar diagram?
What are the characteristics of a good measure of central tendency?
For a frequency distribution, the mean and mode were found to be 15 and 24 respectively.
Find the median of the distribution.
Comment on the following: "The mean deviation of a frequency distribution about an
origin is minimum, when the origin is the mean".
Define: Skewness
Give an example for positive correlation.
Find the regression equation of y on x given the following information:
x 18;  x 14; y 100;  y  20; r  0.6
10. Check the consistency of the following data:
(A) = 400;
(AB) = 250; (B) = 550;
N = 1,200.
SECTION - B
(5  8 = 40 marks)
Answer any FIVE questions.
11. Explain the different types of classification with examples.
12. The following data relate to the monthly expenditure of two families A and B:
Items of expenditure Expenditure (in Rs.)
Family A Family B
Food
1600
1200
Clothing
800
600
Rent
600
500
Fuel
200
100
Miscellaneous
800
600
Represent the above data by a percentage bar diagram.
13. Calculate Q1, Q2, P3 and P20 from the following data:
Class Interval: 0-5 5-10 10-15 15-20 20-25
Frequency
: 7
18
25
30
20
1
14. Calculate mean deviation about median and its coefficient from the following data:
Class
0-10
10-20
20-30
30-40
Frequency
5
8
12
15
Class
40-50
50-60
60-70
70-80
Frequency
20
14
12
6
15. Explain the concepts of correlation and regression through an example.
16. Ten competitors in a beauty contest are ranked by 3 judges in the following order:
Judge 1:
1
6
5
10
3
2
4
9
7
8
Judge 2:
3
5
8
4
7
10
2
1
6
9
Judge 3:
6
4
9
8
1
2
3
10
5
7
Use the rank correlation coefficient to determine which pair of judges has the nearest
approach to common tastes in beauty.
17. Find Yule's coefficient of association between literacy and unemployment from the
following data:
Total Adults:
10,000
Literate:
1,290
Unemployed:
1,390
Literate unemployed:
820
Comments on the results.
18. Fit a straight line trend for the following time series.
Year
: 1990 1991 1992 1993 1994
Production
of steel
(in tonnes) :
60
72
75
65
80
Estimate the production for the year 1997.
1995
1996
85
95
SECTION - C
Answer any TWO questions
(2  20 = 40 marks)
19. i) Explain the various method of collecting primary data.
ii) Draw 'less than' and 'more than' Ogive curves for the following data:
Profit
Number of
Profit
Number of
(in lakh)
Companies
(in lakh) companies
10-20
6
60-70
16
20-30
8
70-80
8
30-40
12
80-90
5
40-50
18
90-100
2
50-60
25
Also find the value of the median.
(10+10)
2
20. i) Calculate mode ( by grouping method) from the following data:
Class interva l: 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
Frequency
:
5
9
13
21
20
15
8
3
ii) From the prices of shares of 2 firms X and Y given below, find out which is more stable
in value.
Firm X:
35
54
52
53
56
58
52
50
51
49
Firm Y:
108
107
105
105
106
107
104
103
104
101
(10+10)
21. i) Explain the concept of kurtosis.
ii) Calculate the first four central moments from the following frequency distribution.
x:
2
3
4
5
6
f:
1
3
7
3
1
iii) Calculate Karl pearson's coefficient of correlation, for the following data and interpret
its value.
X:
48
38
17
23
44
Y:
45
20
40
25
45
(5+7+8)
22. i) From the following data, obtain the regression equations of Y on X and X on Y.
Aptitude scores(X): 60 62
65
70
72
48
53
73
65
82
Productivity
Index(Y)
: 68 60
62
80
85
40
52
62
60
81
Also estimate the productivity index, when test score is 92 and the test score when
productivity index is 75.
ii) Explain any two methods of studying the association between attributes.
(15+5)
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