# Loyola College B.Sc. Statistics April 2007 Applied Statistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc.

 AC 18

DEGREE EXAMINATION –STATISTICS

FIFTH SEMESTER – APRIL 2007

ST 5502APPLIED STATISTICS

Date & Time: 30/04/2007 / 1:00 – 4:00          Dept. No.                                                     Max. : 100 Marks

SECTION– A

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

1. Define a Time Series and give two examples.
2. What are the merits and drawbacks of Graphic method of studying Trend ?
3. Describe the Simple Aggregate Method of calculating Price Index Number and write the drawbacks of this method.
4. State the mathematical tests which are used for measuring formula error in the construction of index numbers.
5. What is meant by Base shifting of Index Numbers?
6. Explain Census Method of obtaining Vital Statistics. What is the main drawback of this method?
7. Explain Crude Death Rate used in measuring mortality.
8. Describe partial correlation with an example.
9. Write a note on economic census.
10. Briefly explain financial statistics.

SECTION –B

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

1. Briefly explain the Trend Component in a Time Series.
2. Describe Fitting of Straight Line and Exponential Curve by Least  Square
3. The Seasonal indices of the sale of readymade garments of a particular type in a certain store are

given below :

Quarter                                    Seasonal Index

Jan. – March                                       98

Apr – June                                          89

July – Sep.                                          82

Oct. – Dec.                                        130

If the total sales in the first quarter of the year be worth Rs. 10,000, determine how much worth

of garments of this type should be kept in  stock by the store to meet the demand in each of the

remaining quarters.

1. Given the data :

——————————————————————

Commodity             p0                q0            p1        q1

——————————————————————

A                   1               10             2             5

B                   1                 5             x             2

——————————————————————

where p and q respectively stand for price and quantity and the subscripts stand for time period.

Find  x , if the ratio between Laspeyre’s  (L)  and Paasche’s  (P) index numbers is L : P : : 28 : 27

1. Discuss the uses of cost of living index number.

1. What is the purpose of standardizing death rates? Describe the direct method of standardization.

1. Given the following table for lx ,  the number of rabbits living atage x ,

complete the life table for rabbits.

x …        0         1        2         3        4         5           6

lx . . .       100     90      80       75      60       30         0

1. Discuss in detail about livestock and poultry statistics.

PART – C

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

1. Given the three selected points U1 , U2, and U3 corresponding to t1 = 2, t2 = 30 and t3  = 58 as follows:

t1   = 2,    U1 = 55.8

t2   = 30,  U2 = 138.6

t3   = 58,  U3 = 251.8

Fit the Logistic curve by the method of selected points. Also obtain the

trend values  for   t  =  5, 18, 25, 35, 46, 50, 54, 60, 66, 70

1. (a) A price index number series was started with 1972 as base. By 1976 it rose by 25%. The index number for 1977 was 118.75. 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 marks)

• You are given the inventory position of a company for six years. Find out the index number of physical volume of inventory . Comment upon the nature of the inventory position.

Year                  1977        1978        1979       1980        1981        1982

Inventory

(in ‘000 Rs)      425.6        447.8     472.4        492.6      524.7       540.8

Wholesale

Price Index

(1971=100)       108.2        121.5     158.0        173.9      162.6     181.5            (10 marks)

21 ( a ) Describe the Registration Method of obtaining Vital Statistics.

Discuss the shortcomings of this method.              ( 12 marks )

( b )  Estimate the standardized death rates for the following two  countries :

Age Group               Death Rate per 1000                    Standardized

( in years )               Country A      Country B           Population ( in lakhs)

——————————————————————————————–

0  –  4                   20.00                 5.00                         100

5  –  14                   1.00                 0.50                         200

15  –  24                   1.40                 1.00                         190

25  –  34                   2.00                 1.00                         180

35  –  44                   3.30                 2.00                         120

45  –  54                   7.00                 5.00                         100

55  –  64                 15.00               12.00                           70

65  –  74                 40.00               35.00                           30

75 & above          120.00             110.00                           10                               (8 marks )

1. (a)  On the basis of observations made on 39 cotton plants ,  the total

correlation of yield of cotton ( X1  ), number of seed vessels ( X2 ) and

height ( X3  ) are found to be :

r12  =  0.8 ,   r13  =  0.65  and  r23  =  0.7

Compute the partial correlation between yield of cotton and the number

of seed vessels eliminating the effect of height.                                                    (5 marks)

• The following are the zero-order correlation coefficients :

r12   =  0.98 ,  r13  =  0.44  and  r23  =  0.54

Calculate multiple correlation coefficient treating first variable as dependent variable , second and third variables as independent variables.                                                                   (5 marks)

( c ) Describe the main functions of National Sample Survey Organisation.  (10 marks)

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