LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2011

ST 5506/ST 5502 – APPLIED STATISTICS

 

 

 

Date : 19-04-2011              Dept. No.                                                  Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A

Answer ALL questions                                                                                                  ( 10 x 2 = 20 Marks)

 

1. State any two uses of index numbers.
2. What are price and quantity index numbers?
3. Define additive and multiplicative models in time series.
4. Indicate the importance of time series in business.
5. Explain the meaning of vital statistics.
6. Define crude death rate.
7. Distinguish between partial and multiple correlation coefficients.
8. Show that 1 – R²₂₃ = (1 – r²₁₂)(1 – r²_13.2)
9. Explain De Facto method of collecting census data
10. Define national income.

SECTION  – B

Answer any FIVE questions.                                                                                     (5 X 8 = 40 Marks)

 

11. Explain ‘deflating of index numbers’ with suitable example. What is the need for deflating index numbers?
12. Given the chain base index numbers, find the fixed base index numbers:

Year                       :    2000    2001    2002    2003     2004    2005

Chain index        :     105        75        71        105       95          90

13. Explain the method of moving averages in measuring trend.
14. A firm estimates its sales for a particular year to be Rs. 24,00,000. Given the seasonal indices, calculate the estimates of monthly sales of the firm assuming no trend.

Month                  :  jan  feb  mar  apr  may   jun   july   aug   sep  oct   nov   dec

Seasonal index  :   75   80   98    128  137   119  102  104  100   102     82     73

15. Define reproduction rates. In what way do total fertility rate, gross reproduction rate and net reproduction rate differ from one another as measures of reproduction?
16. Find the standardized death rate for the data given below:

Age                  Standard population                              Population A

Population    Specific               Population          Specific

(in ’000)       death rate           (in ’000)                death rate

0 – 5                       8                  50                            12                            48

5 – 15                    10                15                            13                            14

15 – 50                  27                10                            15                             9

50 and above      5                  60                            10                          59

17. In a trivariate distribution, Find b₃
18. Write a detailed note on NSSO.

SECTION – C

Answer any TWO questions.                                                                                       (2 X 20 = 40 Marks)

 

19. a) Explain the problems involved in the construction of index numbers.
20. b) Calculate the price and quantity index numbers for 2005 with 2002 as base year using Fisher’s formula. Also verify whether it satisfies the factor reversal test and time reversal test.

Year           Item I                   Item II                   Item III                 Item IV

Price   qty            Price    qty           Price   qty           Price   qty

2002       5.00     5              7.75       6             9.63     4              12.5       9

2005      6.50    7               8.80      10           7.75     6              12.75     9

20. a) Explain seasonal variation in a time series. Also explain the link relative method of computing the indices of seasonal variation.
21. b) The population figures of a country are given below:

Year              :    1911     1921     1931     1941     1951      1961      1971

Population  :     25         25.1      27.9      31.9      36.1      43.9        54.7

(in crores)

Fit an exponential trend y = ab^x and estimate the population in 2011.

21. a) Explain the method of fitting a logistic curve by the method of three selected points.
22. b) Complete the following life table:

x   :       0        1         2          3           4          5           6

  :    100     90       80         75        60        30          0

22. a) Explain in detail ‘livestock’ and ‘agricultural statistics’.
23. b) State the properties of multiple correlation coefficient. Also prove that,

 

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