LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2006

                                                        ST 5502 – APPLIED STATISTICS

(Also equivalent to STA 507)

 

 

Date & Time : 25-04-2006/1.00-4.00 P.M.   Dept. No.                                                       Max. : 100 Marks

 

 

PART – A

 

Answer  ALL  questions.  Each  carries TWO  marks.     (10 x 2 =  20 marks)

 

1. Define Time series and give an example.
2. Distinguish between a Linear Trend and a Non-Linear Trend in a Time series.
3. Explain multiplicative model for the decomposition of a time series.
4. What are the merits and limitations of the method of Semi-Averages?
5. Write the steps in the construction of Chain Indices.
6. State the four test criteria for choosing a good Index Number.
7. Explain cost of Living Index Number.
8. Under what situations Base Shifting of Index Numbers is necessary?
9. What are Rates and Ratios of Vital Events?
10. How will you determine the population at any time “t” after the census or between two censuses using births, deaths and migration statistics?

 

 

PART – B

Answer  any FIVE  questions.  Each  carries EIGHT marks.     (5 x 8 =  40 marks)

 

11. Show that for the following series of fixed base index numbers, the chain indices are same as fixed base index numbers.

 

Year :          1972   1973  1974  1975  1976  1977  1978  1979  1980  1981  1982

Index No.:    100    120    122    116    120    120    137    136    149    136    137

 

12. From the following data on clothing prices, show that the arithmetic mean of relatives (unweighted) does not meet the time reversal test :

 

Price (in Rs.)

Item

 

• 1983

 

A                       5.00               6.00

B                      1.00               1.50

C                      8.00               8.00

 

 

13. Mention the uses of cost of Living Index Number.
14. Explain the method of fitting a straight line by the principle of least squares.

 

15. A study of demand (d_i ) for the past 12 years (i = 1,2,…,12) has indicated the following :

 

d _i    = 100; i = 1,2,…,5

 

=   20; i = 6

 

=  100; i = 7,8,…,12

Compute a 5-year moving average.

16. Explain the various steps involved in the method of simple averages for measuring seasonal variations. State the merits and demerits of this method.
17. Distinguish between a stationary population and stable population. Under what situation a stable population will become a stationary population?
18. Write a short note on Central Statistical Organisation and a National Sample Survey Organisation.

 

PART – C

Answer any TWO questions.   Each carries TWENTY  marks.    (2 x 20 = 40 marks)

 

19 (a). Explain the various problems that are involved in the construction of an

index number of prices. (14)

19 (b). Given below are two price index series. Slice them on the base 1974=100.

By what percent did the price of steel rise between 1970 and 1975? (6)

 

 

 

Year                  Old price index for Steel                 New price index for Steel

Base (1965 = 100)                             Base (1974 = 100)

 

• 5                          –
• 7 –
• 2 –
• 8 99.8
• 1                   100.0
• –                                                         3

 

 

 

20 (a)   Explain the method of three selected points for fitting the Logistic Curve to the            given data. (10)

 

20 (b)   The data below gives the average quartertly prices of a commodity for five years.
Calculate the seasonal variation indices by the method of link relatives. (10)

 

 

Year

1979     1980     1981    1982    1983

 

Quarter

 

 

I               30           35       31        31         34

II               26           28       29        31         38

III               22          22        28        25         26

IV              31          36        32        35         33

 

 

 

21(a).   An enquiry into the budget 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, Light 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. (10)

 

21(b).   A price index number series was started with 192 as base. By 1976 it rose by

25%.  The link relative for 1977 was 95. In this year a new series was started.

This new series rose by 15 points in the next year. But during the following four

years the rise was not rapid. During 1982 the price level was only 5% higher

than 1980 and in 1980 these were 8% higher than 1978. Splice the two series

and calculate the index numbers for the various years by shifting the base to

1978. (10)

 

22(a).  Find the multiple linear regression equation of  X₁   on X₂   and  X₃   from the data relating to three variables given below: (10)

 

 

 

X₁        4        6        7      9      13         1

 

X₂       15     12       8       6        4        3

 

 

          X₃       30     24     20      14     10        4

 

 

22(b).  Explain any one method of national income estimation. (5)

 

22(c).  The simple correlation coefficients between temperature (X₁ ),

corn yield (X₂ )  and rainfall (X₃ ) are r₁₂  =  0.59, r₁₃ =  0.46  and r₂₃ =  0.77.

Calculate partial correlation coefficient   r_{12 . 3}   and  multiple correlation

coefficient  R_{1 . 23 .}  (5)

 

 

 

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