LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

AB 36

P.G. DEGREE EXAMINATION – COMMON PAPER

THIRD SEMESTER – November 2008

MT 3925 – MATHEMATICAL SOCIAL SCIENCES

Date : 12-11-08 Dept. No. Max. : 100 Marks

Time : 9:00 – 12:00

Answer ALL Questions.

(a) Define a research problem.

(or)

What are the essential characteristics of sampling? (5 marks)

Explain briefly all the sources of hypothesis.

(or)

Explain the utilities of Social Science research. Explain the difficulties in social science research.

(15 marks)

(a) (i) Give an example of a graph which has a cut vertex but does not have a bridge.

(ii) Find G₁ + G₂ and G₁ x G₂ if G₁ = and G₂ =

(2 + 3 marks)

(or)

(b) Define (i) closed walk, (ii) trial, and (iii) path. Give examples. (5 marks)

(ii) Find adjacency matrix and incidence matrix for the following graph.

(iii) In the following graph, find x – y walk, x – y trial, x – y path and length of the x – y walk, trial and path.

(2 + 7 + 6 marks)

(or)

(d) (i) Define directed graph, indegree and outdegree of a directed graph. Give an example.

(ii) Prove that, in a graph G every x – y walk contains an x – y path.

(iii)If G contains no odd degree vertices then prove that G contains no bridges.

(2 + 7 + 6 marks)

III. (a) Calculate the mean for the following distribution.

Cost of production: 2 – 6 6 – 10 10 – 14 14 – 18 18 – 22 22 – 26 26 – 30 30 – 34

No. of Holdings : 1 9 21 47 52 36 19 3

(or)

(b) Certain crosses of pea gave 5321 yellow and 1804 green seeds. The expectation is 25 percent of green seeds on a Mendelian hypothesis. Can the divergence from the expected value have arisen from the fluctuation of simple sampling only? (5 marks)

Series A 192 288 236 229 184 260 348 291 330 243

Series B 83 87 93 109 124 126 126 101 102 108

(or)

(d) Find the mean, median and mode for the following data.

Marks 0 – 4 4 – 8 8 – 12 12 – 16 16 – 20 20 – 24 24 – 28

No. of students 10 12 18 7 5 3 2

(15 marks)

(a) Write L-formula, P-formula, L-P formula, M.E formula, Walsch Price index formula for the

construction of index numbers.

(or)

(b) Construct quantity index numbers taking 1967 as the base:

Commodity Average Price Production

1967 1968 1969 1970

A 1.00 62 65 66 90

B 1.50 138 120 110 80

C 0.25 500 540 580 800

D 2.25 10 10 10 10

(5 marks)

(or)

(d) Prepare price and quantity index numbers for 1972 with 1961 as base year from the following data by using (i) Laspeyre’s, (ii) Paasche’s, (iii) Marshall-Edgeworth, and (iv) Fisher’s method.

Article I Article II Article III Article IV

Year Price Quantity Price Quantity Price Quantity Price Quantity

1961 5.00 5 7.75 6 9.63 4 12.50 9

1972 6.50 7 8.80 10 7.75 6 12.75 9

(15 marks)

(a) Explain briefly scaling individual test items in terms of difficulty.

(or)

(b) The fifth grade norms for a reading examination are mean = 60, s.d = 10, and for an arithmetic examination mean = 26, s.d = 4. Ram scores 55 on the reading test and 24 on the arithmetic test. Compute his -scores. In which test is he better? (5 marks)

(c) (i) Five problems are solved by 15%, 34%, 50%, 62% and 80% respectively of a large unselected group. If the zero point of ability in this test is taken to be at – 3, what is the –value of each problem as measured from this point?

(ii) A test is administered on 400 pupils. It gives mean 60 and standard deviation 12. Complete the following table of equivalent raw scores.

Raw Score : 84 78 72 66 60 54 48 42 36

– score : __ __ 1 __ 0 __ __ __ __

Standard score: __ __ __ __ __ __ 40 __ __

(10 + 5 marks)

(or)

(d) (i) Given three test items 1, 2 and 3 are passed by 50%, 40% and 30% respectively of a large group, on the assumption of normality of the distribution, what percentage of this group must pass test item 4 in order for this to be as much more difficult than 3, as 2 is more difficult than 1?

(ii) Write short notes on Intelligence Quotient. (10 + 5 marks)

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