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University of Madras (UoM)

University of Madras (UoM)

Syllabus

Test Papers

Permission for writing BE/BTech/BArch/ME Exams

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Statistical and Numerical Methods
OCTOBER 2003
U/IC 14675/NCM

Time: Three hours
Maximum: 100 marks

Use of Statistical Table is permitted.

PART A - (5 x 8 = 40 marks)

Answer any FIVE questions.
All questions carry equal marks.

1. Calculate mean and median of the following series. 

	Wages	No. of	Wages	No. of
		    workers		    workers

	100-105	200	130-135	410


	105-110	210	135-140	320


	110-115	230	140-145	280


	115-120	320	145-150	210


	120-125	350	150-155	160


	1257130	520	155-160	90
2. Given the following data, which series is more variable? 
	Variable	Series A	Series B
	15	10	18
	25	18	22
	35	32	40
	45	40	32
	55	22	18
	65	18	10


3. A number is chosen at random from 1 to 40. What is the probability that the chosen number is either a multiple of 2 or 3 or 5?

4. The scores made by candidates on a test are normally distributed with mean 500 and standard deviation 100. What percentages of the candidates receive scores :

(a) exceeding 700
(b) less than 400

W between 400 and 600.

5. What is systematic random sampling? How does it differ from purposive sampling? Explain the advantages of purposive sampling.

6. Find the rank correlation coefficient between X and Y from the data given below:

X: 42 36 38 42 35 27 43 42 38
Y 65 32 40 65 42 52 48 52 40

7. Find the value of y(1. 1) using the following data:

X 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Y 2.7 4.2 5.8 7.2 10.6 12.8 16.2

8. Evaluate the value of I= 1 dx using f

Trapezoidal rule with h = 0.25.

PART B - (3 x 20 = 60 marks)
Answer any THREE questions.
All questions carry equal marks.

9. Calculate P, and 02 (measures of skewness and kurtosis) of the following frequency distribution:

X 2 3 4 5 6
f 1 3 7 2 1

10. Fit a Poisson distribution to the following data:
Deaths : 0 1 2 3 4 5 6
Frequency: 120 90 60 50 40 30 20

11. Random samples from two countries gave the following data: 
	Country A	Country B
Mean heights	67.42	67.25
Standard deviation	2.58	2.50
No. of samples	1000	1200
(a) Is the difference between the means significant?

(b) Is the difference between the standard deviation significant?

12. Find the two regression lines from the following:

X: 56 55 58 58 57 56 60 54 59 57
Y: 68 67 67 70 65 68 70 66 68 66

13. Find the Lagrange's Interpolation formula fitting the following data:

X: 0 1 2 3 4 f: 1 2 5 16 41
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