LOYOLA COLLEGE (AUTONOMOUS), CHENNAI– 600 034
B.Sc. DEGREE EXAMINATION  STATISTICS
FIFTH SEMESTER  NOVEMBER 2003
ST 5502/STA 507 APPLIED STATISTICS
07.11.2003
Max: 100 Marks
1.00  4.00
SECTION A
(10  2 = 20 Marks)
Answer ALL the questions. Each carries TWO marks.
01. Distinguish between weighted and unweighted Index numbers.
02. What do you mean by splicing of Index numbers?
03. How do you eliminate the effect of trend from time series and measure seasonal
variations?
04. Distinguish between seasonal variations and cyclical fluctuations.
05. Given the data: rxy =0.6 rxz = 0.4, find the value of ryz so that Rx.yz , the coefficient
of multiple correlation of x on y and z, is unity.
06. Explain briefly the significance of the study of multiple correlation in statistical
analysis.
07. Define Vital statistics. What is the importance of these statistics?
08. What are crude and standardised death rates? Why is comparison on the basis of
standardised death rates more reliable?
09. Write a short rote on DeFacto and DeJure enumeration.
10. Give that the complete expectation of life at ages 35 and 36 for a particular group
are respectively 21.39 and 20.91 years and that the number living at age 35 is
41,176, find the number that attains the age 36.
SECTION  B
(5  8 = 40 Marks)
Answer any FIVE questions. Each carries EIGHT marks.
11. An enquiry into the budget of the middle class families in a certain city in
India gave the following information.
Expenses on
Prices (2001)
(in Rs.)
Price (2003)
Food Fuel
40% 10%
2250 600
Clothing
18%
1000
Rent
20%
1500
Misc.
12%
700
2500
1100
1600
800
900
What changes in cost of living figures of 2003 as compared with that
of 2001 are seen?
1
12. Obtain the trend of bank clearance by the method of moving averages by
assuming a 5 yearly cycle:
Year
Bank clearance
(in crores)
Year
Bank clearance
(in crores
1991
53
92
79
93
76
94
66
95
69
96
94
1997
105
98
87
99
79
2000
104
01
97
02
92
Also, draw original and trend lines on the graph and compare them.
13. Production of a certain commodity is given below:
Year
1999 2000
Production (in lakh tons) 7
9
2001
10
2002
7
2003
5
Fit a parabolic curve of second degree to the production.
Estimate the production for 2004.
14. The following means, standard deviations and correlations are found for
X1= seed hay crop in kgs. per acre, X2 = spring rainfall in inches,
X3 = Accumulated temperature above 42F.
X 1  28.02
X 2  4.91
X 3  594
ˆ 1  4.42
ˆ 2  1.10
ˆ 3  8.5
r12 = 0.8
r13 =  0.4
r23 =  0.56
Number of years of data = 25
Find the regression equation for hay crop on spring rainfall
and accumulated temperature.
15. a) It is possible to get: r12 = 0.06, r23 = 0.8 and r13 = 0.5 from a set of
experimental data?
(3)
b) If all the correlation coefficients of zero order on a set of p variates are
equal to  then show that every partial correlation coefficient of the sth
order is

1  s
(5)
16. a) Given the age returns for the two ages x = 9 years and x +1 = 10 years with
a few lifetable values as l9 = 75,824, l10 = 75,362, d10 = 418 and
T10 = 49,53,195. Give the complete lifetable for the ages of persons.
(5)
b) In what way, does the construction of an abridged lifetable differ
from a complete lifetable?
(3)
2
17. What are the current research developments and landmarks in
agricultural statistics?
18. Explain in detail the different methods of measuring National Income.
SECTION  C
Answer any TWO questions. Each carries TWENTY marks.
(2  20 = 40 Marks)
19. a) Using the following data, construct Fisher’s Ideal Index number
and show how it satisfies Time Reversal and Factor Reversal tests:
Commodity
A
B
C
D
E
Base year
Price Quantity
6
50
2
100
4
60
10
30
8
40
Current year
Price
Quantity
10
56
2
120
6
60
12
24
12
36
(12)
b) What are Index numbers? How are they constructed? Discuss the
applications of Index numbers.
(8)
20. Calculate the seasonal variation indices by the method of link relatives for
the following figures.
Year
Quarterly cement production in 1000 tons
Q1
Q2
Q3
Q4
1998
45
54
72
60
1999
48
56
63
56
2000
49
63
70
65
2001
52
65
75
73.5
2002
63
70
84
66
21. For the following set of data:
a) Calculate the multiple correlation coefficient RY . X1 X 2 and the partial correlation
coefficient rYX 1 .X 2 .
b) Test the significance of both population multiple correlation coefficient and
partial population correlation coefficient at 5% level of significance.
Y
X1
X2
10
8
4
17
21
9
18
14
11
26
17
20
35
36
13
8
9
28
(10+10)
3
22. The population and its distribution by sex and number of births in a
town in 2001 and survival rates are given in the table below.
Age group
15 19
20  24
25  29
30  34
35  39
40  44
45  49
Males
6145
5214
4655
3910
3600
3290
2793
Females
5687
5324
4720
3933
2670
3015
2601
Male births
65
144
135
82
62
12
3
Females births
60
132
127
81
56
15
3
Survival rate
0.91
0.90
0.84
0.87
0.85
0.83
0.82
From the above data, calculate
i) Crude Birth Rate
ii) General fertility rate
iii) Age specific fertility rate
iv) Total fertility rate
v) Gross reproduction rate and
vi) Net reproduction rate; assuming no mortality.
(2 +2 + 4 + 2 + 5 +5)
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