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
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: rxy =0.6 rxz = 0.4, find the value of ryz so that Ryz , 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 De-Facto and De-Jure 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.
|Prices (2001) (in Rs.)
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:
Also, draw original and trend lines on the graph and compare them.
- Production of a certain commodity is given below:
|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
X1= seed hay crop in kgs. per acre, X2 = spring rainfall in inches,
X3 = Accumulated temperature above 42°F.
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.
- a) It is possible to get: r12 = 0.06, r23 = 0.8 and r13 = -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 sth
order is (5)
- 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)
- What are the current research developments and landmarks in
- 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:
|Base year||Current year|
- 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|
- 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.
- 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|
|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)