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
Answer ALL the questions. Each carries TWO marks. (10 ´ 2 = 20 Marks)
 Distinguish between weighted and unweighted Index numbers.
 What do you mean by splicing of Index numbers?
 How do you eliminate the effect of trend from time series and measure seasonal variations?
 Distinguish between seasonal variations and cyclical fluctuations.
 Given the data: r_{xy} =0.6 r_{xz }= 0.4, find the value of r_{yz }so that R_{yz }, the coefficient of multiple correlation of x on y and z, is unity.
 Explain briefly the significance of the study of multiple correlation in statistical analysis.
 Define Vital statistics. What is the importance of these statistics?
 What are crude and standardised death rates? Why is comparison on the basis of standardised death rates more reliable?
 Write a short rote on DeFacto and DeJure enumeration.
 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
Answer any FIVE questions. Each carries eight marks. (5 ´ 8 = 40 Marks)
 An enquiry into the budget of the middle class families in a certain city in
India gave the following information.
Expenses on  Food  Fuel  Clothing  Rent  Misc. 
40%  10%  18%  20%  12%  
Prices (2001) (in Rs.)

2250  600  1000  1500  700 
Price (2003)  2500  900  1100  1600  800 
What changes in cost of living figures of 2003 as compared with that
of 2001 are seen?
 Obtain the trend of bank clearance by the method of moving averages by
assuming a 5 yearly cycle:
Year  1991  92  93  94  95  96 
Bank clearance
(in crores) 
53  79  76  66  69  94 
Year  1997  98  99  2000  01  02 
Bank clearance
(in crores 
105  87  79  104  97  92 
Also, draw original and trend lines on the graph and compare them.
 Production of a certain commodity is given below:
Year  1999  2000  2001  2002  2003 
Production (in lakh tons)  7  9  10  7  5 
Fit a parabolic curve of second degree to the production.
Estimate the production for 2004.
 The following means, standard deviations and correlations are found for
X_{1}= seed hay crop in kgs. per acre, X_{2} = spring rainfall in inches,
X_{3} = Accumulated temperature above 42°F.
r_{12 }= 0.8
r_{13} = – 0.4
r_{23} = – 0.56
Number of years of data = 25
Find the regression equation for hay crop on spring rainfall
and accumulated temperature.
 a) It is possible to get: r_{12 }= 0.06, r_{23 }= 0.8 and r_{13} = 5 from a set of
experimental data? (3)
 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 s^{th}
order is (5)
 a) Given the age returns for the two ages x = 9 years and x +1 = 10 years with
a few lifetable values as l_{9 }= 75,824, l_{10 }= 75,362, d_{10} = 418 and
T_{10} = 49,53,195. Give the complete lifetable for the ages of persons. (5)
 b) In what way, does the construction of an abridged lifetable differ
from a complete lifetable? (3)
 What are the current research developments and landmarks in
agricultural statistics?
 Explain in detail the different methods of measuring National Income.
SECTION – C
Answer any TWO questions. Each carries twenty marks. (2 ´ 20 = 40 Marks)
 a) Using the following data, construct Fisher’s Ideal Index number
and show how it satisfies Time Reversal and Factor Reversal tests:
Commodity 
Base year  Current year  
Price  Quantity  Price  Quantity  
A  6  50  10  56 
B  2  100  2  120 
C  4  60  6  60 
D  10  30  12  24 
E  8  40  12  36 
(12)
 What are Index numbers? How are they constructed? Discuss the
applications of Index numbers. (8)
 Calculate the seasonal variation indices by the method of link relatives for
the following figures.
Year  Quarterly cement production in 1000 tons  
Q_{1}  Q_{2}  Q_{3}  Q_{4}  
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 
 For the following set of data:
 Calculate the multiple correlation coefficientand the partial correlation coefficient .
 Test the significance of both population multiple correlation coefficient and partial population correlation coefficient at 5% level of significance.
Y  10  17  18  26  35  8 
X_{1}  8  21  14  17  36  9 
X_{2}  4  9  11  20  13  28 
(10+10)
 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  Males  Females  Male births  Females births  Survival rate 
15 19  6145  5687  65  60  0.91 
20 – 24  5214  5324  144  132  0.90 
25 – 29  4655  4720  135  127  0.84 
30 – 34  3910  3933  82  81  0.87 
35 – 39  3600  2670  62  56  0.85 
40 – 44  3290  3015  12  15  0.83 
45 – 49  2793  2601  3  3  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)