LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034
B.Sc., DEGREE EXAMINATION – STATISTICS
FIFTH SEMESTER – APRIL 2004
ST 5502/STA 507 – APPLIED STATISTICS
12.04.2004 Max:100 marks
1.00 – 4.00
SECTION – A
Answer ALL questions (10 ´ 2 = 20 marks)
- What is the purpose of constructing index numbers?
- How do you select base period while constructing index numbers?
- Distinguish between seasonal variations and cyclical fluctuations.
- What do you understand by the term moving average? How is it used in measuring trend?
- Given the following values:
r23 = 0.4, r13 = 0.61, r12 = 0.7
Find the partial correlation coefficient r12.3.
- Define multiple correlation and give an example.
- Distinguish between crude and specific death rates.
- Describe the significance and importance of a life table.
- What are De-Jure and De-Facto enumeration in population census?
- Write a brief note on National Institute of Agricultural Marketing.
SECTION – B
Answer any FIVE questions (5 ´ 8 = 40 marks)
- Calculate price index using Fisher’s ideal formula from the following data:
| 2002 | 2003 | |||
| Commodity | Price | Quantity | Price | Quantity |
| A | 10 | 50 | 12 | 60 |
| B | 8 | 30 | 9 | 32 |
| C | 5 | 35 | 7 | 40 |
- A textile worker in Chennai earns Rs.3500 per month. The cost of living index for a particular month is given as 136. Using the following data, find out the amounts he spent on house rent and clothing:
| Group: | Food | Clothing | House rent | Fuel and lighting | Misc. |
| Expenditure: | 1400 | – | – | 560 | 630 |
| Group index: | 180 | 150 | 100 | 110 | 80 |
- Fit a curve of the type Y = abX to the following data and estimate for 2004.
Year: 1999 2000 2001 2002 2003
Population: 132 142 157 170 191
(in 1000 tons)
- Describe one method each of i) eliminating the effect of trend from a time series and ii) measuring the seasonal variations.
- In a trivariate distribution, it was found:
r12 = 0.7 s1 = 3
r23 = 0.4 s2 = 4
r31 = 0.61 s3 = 5
Find the regression equation of X1 on X2 and X3, when the variables are measured from their means.
- Compute gross reproduction rate and net reproduction rate from the data given below:
| Age-group | Female Population | Female births | Survival rate |
| 15-19 | 13,000 | 300 | 0.9 |
| 20-24 | 9,000 | 630 | 0.89 |
| 25-29 | 8,000 | 480 | 0.88 |
| 30-34 | 7,000 | 280 | 0.87 |
| 35-39 | 6,000 | 150 | 0.85 |
| 40-44 | 5,000 | 35 | 0.83 |
- Write an elaborate note on population census.
- Explain in detail the developments in Fisheries and point out the welfare programmes available for Traditional Fishermen.
SECTION – C
Answer any TWO questions (2 ´ 20 = 40 marks)
- a) By giving suitable examples, explain
- Splicing of index numbers
- Deflating of prices and income (4+4)
- b) Show that Fisher’s formula satisfies both time reversal and factor reversal tests using
the following data:
| Base year | Current year | |||
| Commodity | Price | Quantity | Price | Quantity |
| A | 4 | 3 | 6 | 2 |
| B | 5 | 4 | 6 | 4 |
| C | 7 | 2 | 6 | 2 |
| D | 2 | 3 | 1 | 5 |
(6+6)
- Compute seasonal indices by the ratio to moving average method from the following data:
| Year | |||||
| Current production in 1000 tons | Quarter | 2000 | 2001 | 2002 | 2003 |
| I | 75 | 86 | 90 | 100 | |
| II | 60 | 65 | 72 | 78 | |
| III | 54 | 63 | 66 | 72 | |
| IV | 59 | 80 | 85 | 93 | |
- a) Calculate the multiple correlation coefficient of X1 on X2 and X3 from the following
data:
| X1: | 5 | 3 | 2 | 4 | 3 | 1 | 8 |
| X2: | 2 | 4 | 2 | 2 | 3 | 2 | 4 |
| X3: | 21 | 21 | 15 | 17 | 20 | 13 | 22 |
(12)
- b) For the problem in (a), test the significance of the population multiple correlation at 5%
level of significance. (8)
- a) Define vital statistics. What is the importance of these statistics? (5)
- b) Distinguish between Age specific fertility rate and General fertility rate. (5)
- c) Given the age returns for the two ages x = 9 years and x+1 = 10 years with a few life – tale values as = 75,824, = 75,362, d10 = 418 and T10 = 49,53,195. Give the complete life-table for two ages of persons. (10)
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