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
(10  2 = 20 Marks)
Answer ALL questions
01. Give the definition of statistics according to Croxton and Cowden.
02. Comment on the following: “ Sample surreys are more advantageous than
census”.
03. Give an example for
(i) Quantitative continuous data
(ii) Discrete time series data
04. Prove that for any two real numbers ‘a’ &’b’ , A.M  G.M.
05. Mention any two limitations of geometric mean.
06. From the following results obtained from a group of observations, find the
standard deviation. (X5) = 8 ; (X5)2 = 40; N = 20.
07. 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.
08. 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 X and Y .
09. Write the normal equations for fitting a second degree parabola.
10. Find the remaining class frequencies, given (AB) = 400;
(A) = 800; N=2500; (B) = 1600.
SECTION  B
Answer any FIVE questions.
(5 8 = 40 Marks)
11. Explain any four methods of collecting primary data.
12. Draw a histogram and frequency polygon for the following data.
Variable
100110
110120
120130
130140
Frequency
11
28
36
49
Variable
140150
150160
160170
Frequency
33
20
8
Also determine the value of mode from the histogram.
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13. Calculate arithmetic mean, median and mode from the following
frequency distribution.
Variable
1013
1316
1619
1922
2225
Frequency
8
15
27
51
75
variable
2528
2831
3134
3437
3740
Frequency
54
36
18
9
7
14. 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
A
B
C
No. of workers
employed
50
60
90
Mean Wages
(in Rs.)
1113
1120
1115
Standard deviation
(in Rs.)
60
70
80
15. Calculate Bowley’s coefficient of skewness from the following data.
Variable frequency
010
1020
20 30
30 40
40 50
5060
60 70
70 80
12
16
26
38
22
15
7
4
16. 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
17. Explain the concept of regression with an example.
18. The sales of a company for the years 1990 to 1996 are given below:
Year
1990
Sales (in lakhs of rupees) 32
1991
47
1992
65
1993
88
1994
132
1995
190
1996
275
Fit an equation of the from Y = abX for the above data and estimate the
sales for the year 1997.
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SECTION  C
(2  20 = 40 Marks)
Answer any TWO questions.
19. a) Explain (i) Judgement sampling (ii) Quota sampling and
(iii) Systematic sampling methods with examples.
b) (i) Draw a blank table to show the distribution of personnel in a
manufacturing concern according to :
(a) Sex: Males and Females.
(b) Salary grade: Below Rs.5,000; Rs.5,000 Rs.10,000;
Rs.10,000 and above.
(c) Years: 1999 and 2000
(d) Age groups: Below 25, 25 and under 40, 40 and above
(ii) Draw a multiple bar diagram for the following data:
Year
1992
1993
1994
1995
Sales (in’000Rs.)
120
135
140
150
Gross Profit
40
45
55
60
Net profit
20
30
35
40
(10+5+5)
20. a)
(i) An incomplete distribution is given below
Variable
Frequency
010
10
1020
20
2030
f1
3040
40
4050
f2
5060
25
6070
15
Given the median value is 35 and the total frequency is 170, find
the missing frequencies f1 and f2.
(ii)
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
b) Explain any two measures of dispersion.
(7+7+6)
21. a) The scores of two batsman A and B is 10 innings during a certain season are:
A 32
B 19
28
31
47
48
63
53
71
67
39
90
10
10
60
62
96
40
14
80
Find which of the two batsmen is consistent in scoring.
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b) Calculate the first four central moments and coefficient of skewness from the
following distribution.
Variable
2530
3035
3540
4045
frequency
2
8
18
27
Variable
4550
5055
5560
6065
Frequency
25
16
7
2
(10+10)
22. a) From the following data obtain the two regression equations and calculate
the correlation coefficient.
X
Y
60
68
62
60
65
62
70
80
72
85
48
40
53
52
73
62
65
60
82
81
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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