LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
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FIFTH SEMESTER – NOV 2006
ST 5502 – APPLIED STATISTICS
(Also equivalent to STA 507)
Date & Time : 30-10-2006/9.00-12.00 Dept. No. Max. : 100 Marks
PART – A
Answer ALL questions. (10 x 2 = 20 marks )
- Explain the two causes for seasonal variations in a time series.
- Describe the two models commonly used for the decomposition of a time series into its components.
- What are the steps involved in the construction of Chain Indices ?
- If L ( p ) and P ( q ) represent respectively Laspayres’ index number for prices and Paasche’s index number for quantities, then show that
L ( p ) / L ( q ) = P ( p ) / P ( q )
- Show that the Cost of Living Index Number obtained by Aggregate Expenditure Method and Method of Weighted Relatives is the same.
- Discuss a suitable method to determine the population at anytime `t’ after the census or between two censuses.
- Explain the Merits and Demerits of Standardized Death Rates.
- Describe multiple correlation with an example.
- Write a note on world agricultural census.
- Briefly explain labour statistics.
PART – B
Answer any Five questions. (5 x 8 = 40 marks )
- Explain the cyclical component of a time series. What are business cycles?
- Discuss the method of three selected points for fitting modified exponential curve.
- A company estimates its sales for a particular year to be . 24,00,000. The seasonal indices for sales are as follows :
—————————————————————————————
Month Seasonal Month Seasonal
Index Index
—————————————————————————————-
January 75 July 102
February 80 August 104
March 98 September 100
April 128 October 102
May 137 November 82
June 119 December 73
—————————————————————————————-
Using this information, calculate estimates of monthly sales of the company. ( Assume that there is no trend. )
- An enquiry into the budgets of middle class families in a city gave the following information:
Expenses on Food Rent Clothing Fuel Others
30% 15% 20% 10% 25%
Prices ( in Rs. ) in 1982 100 20 70 20 40
Prices ( in Rs. ) in 1983 90 20 60 15 35
Compute the price index number using :
( i ) Weighted A.M. of price relatives,
( ii ) Weighted G.M. of price relatives.
- An enquiry into the budgets of the middle class families of a certain city revealed that on an average the percentage expenses on the different groups were Food 45, Rent 15, Clothing 12, Fuel 8 and Miscellaneous 20. The group index numbers for the current year as compared with a fixed base period were respectively 410, 150, 343, 248 and 285. Calculate the consumer price index number for the current year. Mr. X was getting Rs.240 in the base period and Rs. 430 in the current year. State how much he ought to have received as extra allowance to maintain his former standard of living.
- Discuss the uses of Vital Statistics.
- Mention the assumptions used in the construction of the life tables.
- Discuss in detail about mining and quarrying statistics.
PART – C
Answer any TWO questions. ( 2 x 20 = 40 marks )
- You are given the population figures of India as follows :
Census Year ( X ) : 1911 1921 1931 1941 1951 1961 1971
Population ( in Crores): 25.0 25.1 27.9 31.9 36. 1 43.9 54.7
Fit an exponential trend Y = abx to the above data by the method of least squares and find the trend values. Estimate the population in 1981.
- ( a ) Describe in detail the problems involved in the construction of
index numbers. (14 marks)
( b ) On a certain date the Ministry of Labour retail price index was 204.6. Percentage increases in price over some basic period were : Rent 65 , Clothing 220, Fuel and Light 110, Miscellaneous 125. What was the percentage increase in the food group ? Given that the weights of the different items in the group were as follows :
Food 60 , Rent 16 , Clothing 12, Fuel and Light 8 , Miscellaneous 4.
( 6 marks)
21 ( a ). Find the standardized death rate by Direct and Indirect
methods for the data given below:
————————————————————————————–
Standard Population Population A
Age —————————————————————————
Population Specific Population Specific
in `000 Death Rate in `000 Death Rate
————————————————————————————–
0-5 8 50 12 48
5-10 10 15 13 14
10-15 27 10 15 9
>50 5 60 10 59
————————————————————————————-
( 10 marks )
( b ). Explain the concepts with examples:
( i ) Stationary Population
( ii ) Stable Population. (10 marks )
- ( a ) Find the multiple linear regression equation of X1 on X 2 and
X 3 from the data relating to three variables given below:
X1 : 4 6 7 9 13 15
X2 : 15 12 8 6 4 3
X3 : 30 24 20 14 10 4 ( 10 marks )
( b ) Discuss any two methods of national income estimation.
( 10 marks ).