LOYOLA COLLEGE (AUTONOMOUS), CHENNAI– 600 034

B.Sc. DEGREE EXAMINATION  –  STATISTICS

Fifth  SEMESTER  – NOVEMBER 2003

ST 5502/STA 507 APPLIED STATISTICS

07.11.2003                                                                                        Max: 100 Marks

1.00 – 4.00

 

SECTION –A                                                         

Answer ALL the questions.  Each carries TWO marks.                   (10 ´ 2 = 20 Marks)

1. Distinguish between weighted and unweighted Index numbers.
2. What do you mean by splicing of Index numbers?
3. How do you eliminate the effect of trend from time series and measure seasonal variations?
4. Distinguish between seasonal variations and cyclical fluctuations.
5. Given the data: r_xy =0.6 r_xz = 0.4, find the value of r_yz so that R_yz , the coefficient of multiple correlation of x on y and z, is unity.

 

6. Explain briefly the significance of the study of multiple correlation in statistical analysis.

 

7. Define Vital statistics. What is the importance of these statistics?
8. What are crude and standardised death rates? Why is comparison on the basis of standardised death rates more reliable?

 

9. Write a short rote on De-Facto and De-Jure enumeration.
10. Give that the complete expectation of life at ages 35 and 36 for a particular group are respectively 21.39 and 20.91 years and that the number living at age 35 is 41,176, find the number that attains the age 36.

 

SECTION – B

Answer any FIVE questions.  Each carries eight marks.                (5 ´ 8 = 40 Marks)

 

11. An enquiry into the budget of the middle class families in a certain city in

India gave the following information.

 

Expenses on	Food	Fuel	Clothing	Rent	Misc.
	40%	10%	18%	20%	12%
Prices (2001) (in Rs.)	2250	600	1000	1500	700
Price (2003)	2500	900	1100	1600	800

 

What changes in cost of living figures of 2003 as compared with that

of 2001 are seen?

 

 

 

 

 

 

12. Obtain the trend of bank clearance by the method of moving averages by

assuming a 5 -yearly cycle:

 

Year	1991	92	93	94	95	96
Bank clearance (in crores)	53	79	76	66	69	94
Year	1997	98	99	2000	01	02
Bank clearance (in crores	105	87	79	104	97	92

 

Also, draw original and trend lines on the graph and compare them.

 

13. Production of a certain commodity is given below:

 

Year	1999	2000	2001	2002	2003
Production (in lakh tons)	7	9	10	7	5

 

Fit a parabolic curve of second degree to the production.

Estimate the production for 2004.

 

14. The following means, standard deviations and correlations are found for

X₁= seed hay crop in kgs. per acre, X₂ = spring rainfall in inches,

X₃ = Accumulated temperature above 42°F.

 

r₁₂  = 0.8

r₁₃  = – 0.4

r₂₃   = – 0.56

 

Number of years of data = 25

Find the regression equation for hay crop on spring rainfall

and accumulated temperature.

 

15. a) It is possible to get: r₁₂ = 0.06, r₂₃ = 0.8 and r₁₃ =  -5 from a set of

experimental data?                                                                                     (3)

1. If all the correlation coefficients of zero order on a set of p variates are

equal to  then show that every partial correlation coefficient of the s^th

order is                                                                                             (5)

 

16. a) Given the age returns for the two ages x = 9 years and x +1 = 10 years with

a few life-table values as l₉ = 75,824, l₁₀ = 75,362, d₁₀ = 418 and

T₁₀ = 49,53,195. Give the complete life-table for the ages of persons.       (5)

1. b) In what way, does the construction   of an abridged life-table differ

from a complete life-table?                                                                          (3)

 

 

 

 

 

 

17. What are the current research developments and landmarks in

agricultural statistics?

 

18. Explain in detail the different methods of measuring National Income.

 

 

SECTION – C         

Answer any TWO questions.  Each carries twenty marks.      (2 ´ 20 = 40 Marks)

 

19. a) Using the following data, construct Fisher’s Ideal Index number

and show how it satisfies  Time Reversal and Factor Reversal tests:

 

Commodity	Base year		Current year
	Price	Quantity	Price	Quantity
A	6	50	10	56
B	2	100	2	120
C	4	60	6	60
D	10	30	12	24
E	8	40	12	36

(12)

1. What are Index numbers? How are they constructed? Discuss the

applications of Index numbers.                                                                 (8)

 

20. Calculate the seasonal variation indices by the method of link relatives for

the following figures.

 

Year	Quarterly cement  production in 1000 tons
	Q1	Q2	Q3	Q4
1998	45	54	72	60
1999	48	56	63	56
2000	49	63	70	65
2001	52	65	75	73.5
2002	63	70	84	66

21. For the following set of data:
22. Calculate the multiple correlation coefficientand the partial correlation coefficient .
23. Test the significance of both population multiple correlation coefficient and partial population correlation coefficient at 5% level of significance.

 

Y	10	17	18	26	35	8
X1	8	21	14	17	36	9
X2	4	9	11	20	13	28

 

(10+10)

 

 

 

 

 

 

 

 

22. The population and its distribution by sex and number of births in a

town in 2001 and survival rates are given in the table below.

 

Age group	Males	Females	Male births	Females births	Survival rate
15  -19	6145	5687	65	60	0.91
20 – 24	5214	5324	144	132	0.90
25 – 29	4655	4720	135	127	0.84
30 – 34	3910	3933	82	81	0.87
35 – 39	3600	2670	62	56	0.85
40 – 44	3290	3015	12	15	0.83
45 – 49	2793	2601	3	3	0.82

 

 

From the above data, calculate

 

1. i) Crude Birth Rate
2. ii) General fertility  rate

iii)   Age specific fertility  rate

1. iv) Total fertility rate
2. v) Gross reproduction rate and
3. vi) Net reproduction rate; assuming no mortality.           (2 +2 + 4 + 2 + 5 +5)

 

 

Go To Main page

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)

 

1. What is the purpose of constructing index numbers?
2. How do you select base period while constructing index numbers?
3. Distinguish between seasonal variations and cyclical fluctuations.
4. What do you understand by the term moving average? How is it used in measuring trend?
5. Given the following values:

r₂₃ = 0.4,  r₁₃ = 0.61,   r₁₂  = 0.7

Find the partial correlation coefficient r_12.3.

6. Define multiple correlation and give an example.
7. Distinguish between crude and specific death rates.
8. Describe the significance and importance of a life table.
9. What are De-Jure and De-Facto enumeration in population census?
10. Write a brief note on National Institute of Agricultural Marketing.

 

SECTION – B

Answer any FIVE questions                                                                        (5 ´ 8 = 40 marks)

 

11. 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

12. 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

13. Fit a curve of the type Y = ab^X to the following data and estimate for 2004.

Year:                     1999         2000           2001        2002            2003

Population:            132            142            157          170              191

(in 1000 tons)

14. Describe one method each of i) eliminating the effect of trend from a time series and ii) measuring the seasonal variations.
15. 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.

 

 

16. 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

17. Write an elaborate note on population census.
18. 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)

 

19. a) By giving suitable examples, explain
20. Splicing of index numbers
21. Deflating of prices and income          (4+4)
22. 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)

20. 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

 

21. 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)

1. b) For the problem in (a), test the significance of the population multiple correlation at 5%

level of significance.                                                                                                      (8)

 

22. a) Define vital statistics. What is the importance of these statistics?                              (5)
23. b) Distinguish between Age specific fertility rate and General fertility rate. (5)
24. 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)

 

 

Go To Main page

             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)

 

 

 

Go To Main page

                          LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AB 15

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 )

 

1. Explain the two causes for seasonal variations in a time series.
2. Describe the two models commonly used for the decomposition of a time series into its components.
3. What are the steps involved in the construction of Chain Indices ?
4. 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 )

 

5. Show that the Cost of Living Index Number obtained by Aggregate Expenditure Method and Method of Weighted Relatives is the same.
6. Discuss a suitable method to determine the population at anytime `t’ after the census or between two censuses.
7. Explain the Merits and Demerits of Standardized Death Rates.
8. Describe multiple correlation with an example.
9. Write a note on world agricultural census.
10. Briefly explain labour statistics.

PART – B

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

 

11. Explain the cyclical component of a time series. What are business cycles?

 

12. Discuss the method of three selected points for fitting modified exponential curve.
13. 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. )

 

14. 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.

 

15. 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.
16. Discuss the uses of Vital Statistics.

 

17. Mention the assumptions used in the construction of the life tables.

 

18. Discuss in detail about mining and quarrying statistics.

                                                    PART – C

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

 

19. 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 = ab^x   to the above data by the method of least squares and find the trend values. Estimate the population in 1981.

 

20. ( 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 )

 

22. ( a ) Find the multiple linear regression equation of X₁ on X ₂  and

X ₃   from the data relating to three variables given below:

 

X_{1   :}           4          6          7         9        13         15

X_{2    :}        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 ).

 

Go To Main page

 

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc.

AC 18

DEGREE EXAMINATION –STATISTICS

FIFTH SEMESTER – APRIL 2007

ST 5502 – APPLIED 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)

 

11. Briefly explain the Trend Component in a Time Series.
12. Describe Fitting of Straight Line and Exponential Curve by Least  Square
13. 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.

 

14. 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

 

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

 

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

 

17. Given the following table for l_x ,  the number of rabbits living atage x ,

complete the life table for rabbits.

 

x …        0         1        2         3        4         5           6

l_{x . . .}       100     90      80       75      60       30         0

 

18. Discuss in detail about livestock and poultry statistics.

 

PART – C

 

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

 

19. 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

 

20. (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 )

 

22. (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)

 

Go To Main page

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

NO 26

FIFTH SEMESTER – APRIL 2008

ST 5502 – APPLIED STATISTICS

 

 

 

Date : 03/05/2008                Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A      ( 10 x 2 = 20 Marks)

Answer ALL questions.

 

1. What is an index number? What are its uses?
2. What is meant by splicing an index number?
3. Define a Time series and give examples.
4. Describe semi-average method of measuring trend.
5. Define crude and specific death rates.
6. Define Pearle’s Vital index in the measurement of population growth.
7. Define partial correlation coefficient.
8. Give a formula for multiple correlation coefficient R_1.23.
9. What is meant by Economic Census?
10. Write a note on live stock statistics.

 

 

SECTION – B     (5 x 8 = 40 Marks)

Answer any FIVE questions.

 

1. Discuss the steps involved in the construction of cost of living index number.
2. The prices of six commodities in the years 2001 and 2005 are given below.  Compute the price index based on price relatives using the arithmetic mean.

 

 

	Commodity
Year	A	B	C	D	E	F
2001	90	120	40	100	170	240
2005	110	140	60	150	180	260

 

1. What are the components of time series? Explain them.
2. Compute the linear trend by the method of least squares given the following data.  Estimate the trend for the year 2009.

 

Year	2002	2003	2004	2005	2006	2007
Sales(Lakhs)	75	83	109	129	134	148

 

1. Describe the components of a Life Table.
2. Explain the Gross and Net Reproduction Rates.
3. Discuss the functions of National  Sample Survey Organisation.
4. Given the values of  r₁₂=0.8, r₁₃=0.6 and r₂₃=-0.7, compute the values of r_23.1 and r_13.2.

 

 

 

 

 

SECTION-C     (2 x 20 = 40 Marks)

Answer any TWO questions.

 

19. (a). What are the properties to be satisfied by a good index number?  Explain them in detail.

(b). The index numbers for the years from 1992 to 2002 are given below.  Compute the chain base index numbers.

 

Year	1992	1993	1994	1995	1996	1997	1998	1999	2000	2001	2002
Index	100	120	122	116	120	120	137	136	149	156	137

 

1. (a). Discuss various methods of measuring Seasonal indices in Time series.

(b). The following table gives the prices of a spare part of a car for the period of five years.  Using the method of Link relatives, compute the Seasonal indices.

 

Quarter/Year	1990	2000	2001	2002	2003
I	30	35	31	31	34
II	26	28	29	31	36
III	22	22	28	25	26
IV	31	36	32	35	33

 

21. (a). Compute the General Fertility Rate, Specific Fertility Rate, Total Fertility Rate and the Gross Reproduction Rate from the following table.

 

 

Age group of Child bearing females	15-19	20-24	25-29	30-34	35-39	40-44	45-49
Number of women(‘000)	16.0	16.4	15.8	15.2	14.8	15.0	14.5
Total births	260	2244	1894	1320	916	280	145

 

 

(b). In the usual notation, derive the multiple regression equation of X₁ on X₂ and X₃.

 

1. (a). Write short notes on shifting and deflating index number.

(b). Discuss the methods of National Income estimation.

(c). Given the age returns for the two ages x=9 years and x+1=10 years with l₉=75,824, l₁₀=75,362, d₁₀=418 and T₁₀=49,53,195, complete the entries of the life table for the two ages.

 

 

Go To Main page

 

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – STATISTICS

BA 12

FIFTH SEMESTER – November 2008

ST 5502 – APPLIED STATISTICS

 

 

 

Date : 07-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

SECTION – A      ( 10 x 2 = 20 Marks)

Answer ALL questions.

 

1. Define an index number.  Mention its uses.
2. Discuss the concept of deflating an index number.
3. Define a Time series and give examples.
4. List down different methods of measuring trend.
5. Define total and specific fertility rates.
6. Specify Pearle’s Vital index in the measurement of population growth.
7. Define multiple correlation coefficient.
8. Write down the formula for partial correlation coefficient r_12.3.
9. What is meant by financial statistics?
10. Write a note on live stock statistics.

 

SECTION – B     (5 x 8 = 40 Marks)

Answer any FIVE questions.

 

1. What are the steps to be followed in the construction of consumer price index number?
2. The following table gives the quantities and prices of five commodities for two periods.  Compute the quantity and the price indices using Fisher’s formula.

 

Commodity	Base Year		Current Year
	Quantity	Price	Quantity	Price
A	6	5	8	6
B	8	3	10	2
C	12	2	10	4
D	2	8	2	7
E	5	9	6	9

1. What are the components of a time series? Explain them.
2. The following data gives the yearly sales of a product.  Compute the linear trend by the method of least squares.  Estimate the trend for the year 2008.

 

Year	2001	2002	2003	2004	2005
Sales(Lakhs)	26	30	38	50	56

 

1. What are the components of a Life Table.  Explain them.
2. Explain the Gross and Net Reproduction Rates.
3. Discuss the functions of Central Statistical Organisation (CSO).
4. Given the values of  r₁₂=0.8, r₁₃=0.7 and r₂₃=0.9, compute the values of R_1.23 and _2.31.

 

 

 

 

SECTION-C     (2 x 20 = 40 Marks)

Answer any TWO questions.

 

19. (a). Discuss the unit test, time reversal test, factor reversal test and the circular test associated with index numbers.

(b). Construct the wholesale price index number for the years 2007 and 2008 given the following data.

 

Commodity	Wholesale price in rupees per quintal
	2006	2007	2008
I	140	160	190
II	120	130	140
III	100	105	108
IV	75	80	90
V	250	270	300
VI	400	420	450

 

1. (a). Discuss various methods of measuring Seasonal indices in Time series.

(b). The following table gives the cost of an item for the period of five years.  Using the method of Link relatives, compute the Seasonal indices.

 

Quarter	Year
	2001	2002	2003	2004	2005
I	60	62	65	70	72
II	65	68	70	75	80
III	62	65	64	68	70
IV	69	68	62	67	78

 

21. (a). Compute the crude and standardized death Rates of the two populations X and Y regarding X as the standard population.

 

Age group	Under 10	10-20	20-40	40-60	Above 60
Population  in X	20000	12000	50000	30000	10000
Deaths in X	600	240	1250	1050	500
Population in Y	12000	30000	62000	15000	3000
Deaths in Y	372	660	1612	325	180

 

 

(b). Derive the multiple regression equation of X₁ on X₂ and X₃ in the usual notation.

 

1. Write short notes on the following

• Partial and mulitiple correlations.

(ii)  Discuss the methods of National Income estimation.

(iii) Economic census and labour statistics.

 

 

Go To Main Page

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

   B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – NOVEMBER 2010

ST 5506/ST 5502 – APPLIED STATISTICS

 

 

 

Date : 03-11-10                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

PART – A

Answer ALL the questions                                                                                            (10×2=20 Marks)

1. List out the different tests in index numbers.
2. Explain the deflating procedure of index numbers.
3. Define Time Series.
4. State the mathematical models applied in time series analysis.
5. What is meant by Specific Death Rates?
6. Define Life Table.
7. What do you mean by partial correlation and partial regression?
8. List out any three properties of multiple correlation co-efficient.
9. Write some functions of Central Statistical Organization.
10. State the merits of De Facto and De Jure methods.

 

PART – B

Answer any FIVE questions                                                                                     (5×8=40 Marks)

 

1. What is the difference between the Weighted and Unweighted Indices? Also explain the construction of index number by Unweighted Indices.
2. Describe cost of living index and also state its uses.
3. Explain the procedure of finding trend values using the method of least squares.
4. Describe the method of Ratio-to-Moving average to calculate seasonal indices.
5. Explain the various methods available for the measurement of population growth
6. In a tri-variate distribution:

σ₁ = 2; σ₂ = σ₃ = 3; r₁₂ = 0.7; r₂₃ = r₃₁ = 0.5.

Find: i) r_23.1     ii) R_1.23      iii) b_12.3      iv) b_13.2       v) σ_1.23

1. Write a note on National Sample Survey Organization.
2. Describe the national income and social accounting.

 

 

 

PART – C                             

Answer any TWO questions                                                                                         (2×20=40 Marks)

 

1. a) Explain Fisher’s index number. Why it’s called as an ideal index numbers?

1. b) Prove that the Factor Reversal Test and Time Reversal Test are satisfied

by Fisher’s Index.

Year	Article I		Article II		Article III		Article IV
	Price	Qty	Price	Qty	Price	Qty	Price	Qty
1982	5.00	5	7.75	6	9.63	4	12.50	9
1983	6.50	4	8.80	10	7.75	6	12.75	9

 

1. a) Describe the procedure of cyclic variation and irregular variation.

1. b) Calculate the seasonal indices by the method of link relatives

Quarter\ Year	1979	1980	1981	1982	1983
I	30	35	31	31	34
II	26	28	29	31	36
III	22	22	28	25	26
IV	31	36	32	35	33

 

 

 

 

 

1. a) Describe the methods of obtaining vital statistics. Also write its uses?

1. b) From the data, calculate the gross reproduction rate and Net

reproduction rate. [ratio Male:Female = 52:48]

Age Group	No of children born to 1000 women passing through the age group	Mortality rate
16-20	150	120
21-25	1500	180
26-30	2000	150
31-35	800	200
36-40	500	220
41-45	200	230
46-50	100	250

 

1. Explain the following:

1. a) Agricultural Statistics
2. b) Financial Statistics
3. c) Components of Time Series.

 

 

Go To Main Page

 

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2011

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,

 

 

 

Go To Main page

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,

 

Go To Main page

 

 

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – APRIL 2012

ST 5506/ST 5502 – APPLIED STATISTICS

 

 

 

Date : 30-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

PART – A

 

Answer ALL the questions:                                                                                           (10 x2 = 20)

 

1. What are index numbers?
2. State Time Reversal Test.
3. What are the components of a time series?
4. Define Multiplicative Time Series model
5. Define Crude Birth Rate.
6. Distinguish between gross reproduction rate and net reproduction rate.
7. Give the meaning of multiple correlation coefficient.
8. Write down the expression for .
9. Mention the role of NSSO.
10. Mention the use of Statistics in livestock and poultry industry.

 

PART – B

Answer any FIVE Questions:                                                                                        (5 X 8 = 40)

 

1. Explain the concept of Splicing and Deflating of index numbers.
2. Explain the steps involved in the construction of index numbers?
3. Explain the method of moving averages in estimation of trend.
4. Explain ratio to trend method of estimating seasonal variation.
5. Describe in detail various rates associated with fertility.
6. Explain how vital statistics is obtained in India.
7. Prove the relation .
8. Describe the functions of CSO.

PART – C

Answer any TWO Questions:                                                                                        (2 x 20 =40)

 

1. (a) Define : Fisher’s Index number. Show that it is an Ideal Index number.

(b) Write a descriptive note on Consumer Price Index number.

 

1. (a) Find the trend component in the following data with the help of 3 yearly moving averages.

Year:            1978  1979  1980 1981 1982 1983 1984 1985 1986 1987 1988 1989

Production:    19      22      25     27     29     30     32      34     37     41    44     45

(in tonnes)

(b) Explain the method of Link Relatives.

1. (a) Write a short note on Season Variation.

(b) The population size of a country are given below:

Year :              1960    1970    1980    1990    2000    2010

Population :      22       27       36         48        59       72

(in crores)

Fit an exponential trend and estimate the population for the year 2014.

1. Write short notes on the following:

(a) Chain Index Numbers

(b) Measurement of Mortality

(c)  National Income Statistics

(d) Partial Correlation.

 

 

Go To Main page

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

FIFTH SEMESTER – NOVEMBER 2012

ST 5506/ST 5502 – APPLIED STATISTICS

 

 

 

Date : 06/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

PART – A

Answer ALL the questions:                                                                                 (10X2=20 Marks)

 

1. Mention any two uses of index numbers.
2. Define Laspeyre’s and Paasche’s index numbers.
3. Explain the concept of business cycle.
4. Mention the different types of time series models for the component combinations.
5. State any two uses of vital statistics.
6. Define total fertility rate.
7. Define partial correlation coefficient.
8. Given r₁₂ = 0.77, r₁₃= 0.72, r₂₃= 0.52, find R₂₃
9. What is forest statistics?
10. Define national income.

 

PART – B

 

Answer any FIVE questions                                                                                (5X8=40 Marks)

11. Explain the tests to be satisfied by a good index number. Show that Fisher’s Index number is an Ideal Index number.
12. What is meant by (a) splicing (b) deflating and (c) base shifting of index numbers?
13. Explain link relative method to measure seasonal fluctuations.
14. Explain fitting of a second degree parabola by the method of least squares.
15. What is life table? Briefly outline the uses of life table.
16. Define gross and net reproduction rates. Discuss the steps for estimating the net reproduction rate.
17. Discuss the methods of national income estimation.
18. Write short notes on (i) De Facto method (ii) De Jure method.

P.T.O]

PART – C

Answer any TWO questions:                                                                              (2X20=40 Marks)

1. (a) Discuss the problems and precautions in the construction of an index number.

(b) What are the uses of consumer price index number? Calculate the CPI using the following data:

Items	Index Number	Weight
Food	352	48
Fuel	220	10
Clothing	230	8
Rent	160	12
Miscellaneous	190	15

 

20. (a) Briefly explain the components of time series.

(b) Explain Ratio to Moving Average method for determining seasonal index.

 

21. (a) Explain the various mortality rates used in vital statistics and discuss their relative merits.

(b) Estimate the standardized death rates for the two countries from the data given below:

Age group (in years)	Death Rate per 1000		Standardised Population (in lakhs)
	Country A	Country B
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 and above	120.00	110.00	10

 

22. (a) Write short notes on (i) Central Statistical Organisation

(ii) National Sample Survey Organisation

(b) Define (i) Partial Regression (ii) Multiple Correlation (iii) Multiple Regression

 

Go To Main page