Kerala University 2005 B.Sc Mathematics group 7 - Question Paper

Reg. No..............................................(Pages 2)    K5143

Name.....................................

FIRST YEAR B.Sc. DEGREE EXAMINATION, MARCH/APRIL 2005

Part IIIGroup (vii)Statistics (Main)

Paper IDESCRIPTIVE STATISTICS AND NUMERICAL METHODS Time : Three Hours    Maximum : 65 Marks

Not more than 13 marks will be awarded from each unit.

Unit I

1.    Distinguish between Arithmetic mean and Geometric mean. Specify the gelds in which Geometric mean can be more appropriately used.

(5 marks)

2.    Obtain the standard deviation of the first n' natural numbers.    (5 marks)

3.    Show that the root mean square deviation is least when it is measured from the mean.

(5 marks)

4.    Define skewness and kurtosis of a distribution. Give any one measure of skewness and kurtosis.

(5 marks)

5.    Define the following :

. (a) Sheppard's Correction.    - (b) Principle of least squares.

(c) Lorenz Curve.

(6 marks)

Unit II

6.    Distinguish between correlation and regression.    (5 marks)

7.    Prove that correlation coefficient is the geometric mean between the regression coefficients.

(5 marks)

8.    In a trivariate distribution Cj = 2, <r₂ = o₃ = 3, r₁₂ ⁼ 0.7, r₂₃ = r₃₁0.5. Find :

W *23.1.    Ri.fcj

(3) b₁₂₃.

9.    Show that 1~R ₂₃ = (1- r) (1- rf₃₂)    (6 marks)

10.    Explain the following :

(a) Correlation ratio.    (b) Intra class correlation.

(5 marks)

Unit III

11.    Define index number and point out the limitatipns.    (5 marks)

12.    What is meant by weighting in index numbers ? What are the various ways of assigning weights in the construction of index numbers ?

(5 marks) Turn over

2    K 5143

13.    Explain Time Reversal Test and Factor Reversal Test.    (5 marks)

14.    What are the steps involved in the construction of consumer price index numbers ? (5 marks)

15.    Explain the terms Deflating, splicing and base shifting.    (6 marks)

Unit IV

16.    Define :

(a) Time Series.    (b) Secular Trend.

(c) Irregular variations.

(6 marks)

17.    What do you mean by multiplicative and additive models of the composition of components of times series ?

18.    Explain the meaning and use of Moving averages.

19.    Explain the method of fitting :

(1) Straight Une trend.    (2) Quadratic trend to a time series.

20.    What are the advantages and disadvantages of the method of least squares ?

UnitV

21.    Prove that :

22.    Show that the n^th difference of a polynomial of n^th degree are constant, when the values of the independent variable are taken in arithmetic progression.

23.    Establish Lagrange's formula for interpolation.    (5 marks)

24.    Obtain Everette's Formula for numerical interpolation.    (5 marks)

25.    Derive Weddle's rule of numerical integration.    (5 marks)

Attachment: kerala-university-2005-b-sc-mathematics-39214-1.pdf

Earning:   Approval pending.