

CS  08 Numerical & Statistical Computing

Height in inches 
Number of students 

5760 
02 
6063 
06 
6366 
20 
6669 
45 
6972 
21 
7275 
05 
7578 
01 
Calculate the variance of the above frequency distribution.
(h) Fit a straight line to the data given by the following table: (4)
Independent Variable 
Dependent 

1 
1 
3 
8 
4 
17 
6 
34 
7 
52 
9 
78 
(i) Four cards are drawn from a well shuffled pack of cards. What is the
probability that they are from exactly (any) three different suits? (4)
2. (a) Write a program in FORTRAN to find whether a given square matrix is symmetric. The program should read the matrix size, the elements of the matrix and also should print out an appropriate message. (9)
(b) Write a FORTRAN function FACT with one integer parameter N, that computes the factorial of N and prints suitable message. (6)
3. (a) The constant p can be approximated by (8)
p^{2}/6 = (1 + 1/2^{2}
+ 1/3^{2} + 1/4^{2} + .......)
Write FORTRAN program which sums the first 700 terms and then on the basis
of this summation, computes the aproximate value of p.
(b) The following table shows monthly living expenses for an MCA student of IGNOU: (7)
Item 
Amount in (Rs.) 

Food 
100 
Apartment 
900 
Transport 
200 
Entertainment 
300 
Maintenance 
400 
Miscellaneous 
400 
4. (a) In a bulb making factory, three machines A, B and C manufacture respectively 15, 35 and 50 percent of the total. Out of their total outputs 4, 5 and 3 percent are defective. A bulb is drawn from the produce at random and is found to be defective. What is the probability that it is manufactured by (i) factory A (ii) factory C? (8)
(b) A box contains ten 50rupee notes, fifteen 10rupee notes, eighteen 20rupee notes and twelve 100rupee notes. A sample of six notes is taken out at random without replacement. Find the probability that the sample contains one 50rupee note, two 10rupee notes, one 20rupee note and two 100rupee notes. (7)
5. (a) A computer while calculating the correlation coefficient between
25 pairs of two variables x and y, obtained the following constants: (8)
n = 25, å x = 125,
å x^{2 }= 650, å y
= 100, å y^{2 } = 460, å
xy = 508
A recheck showed that the computer has copied wrongly two pairs (6, 14) and (8, 6) of values of (x, y) instead of the correct values (8, 12) and (6, 8) respectively. Obtain the correct value of the correlation coefficient.
(b) The following table gives the average wholesale prices of the four fruits for the years 1996 to 2000. Compute chain base index number. (7)
Fruit 
1996 
1997 
1998 
1999 
2000 

Apple 
1600 
1760 
1440 
1920 
2000 
Orange 
3200 
3520 
3840 
4000 
4800 
Banana 
1920 
2080 
1680 
2240 
2400 
Grapes 
2400 
2560 
2880 
2720 
2880 
6. (a) Compute the approximate value of the integral
I =(1
+ x^{2} + x^{3}) dx
using Trapezoidal rule or Simpson's rule by taking interval size h
as 1. (7)
(b) From the following table of values of x and y, obtain dy/dx for x = 1.2. (8)
x 
y 

1.0 
2.7183 
1.2 
3.3201 
1.4 
4.0552 
1.6 
4.953 
1.8 
6.0496 
2.0 
7.3891 
2.2 
9.025 




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