Test Papers / Previous Question Papers of IGNOU CS08 Numerical and Statistical Computing June 2005

ADCA / MCA (II Yr)
Term-End Examination

June, 2005

CS08 : Numerical and Statistical Computing

Time: 3 hours
Maximum Marks: 75

1. (a) Write a FORTRAN 90 statement fo each of the following: (3)
(i) R = X²Y³ + √(X+Y)Z
(ii) F = 1/4 π ε_o Q₁Q₂/r²
(iii) Z = √R²+(ωL - 1/ωC)²

(b) Which of the following are correct representations of real constants ? Give reasons for your answers. (4)
2225; 0.137; 2E-7; 101.2E+2

(c) Write a program in FORTRAN which reads a, b, and c (the lengths in met€rs of the sides of a triangle), computes the area of the triangle and then determines the number of one-litre tins of paint required to paint this area with one coat of paint (assuming that one litre of paint can cover 10 m² area). Note that the area of a triangle is given by √s(s-a)(s-b)(s-c) where s = 0.5 x (a + b + c). (4)

K = 0
DO 10   J = 1, 3
DO 10   N = J + 1, 4
10   K = K + J * N
PRINT *, K

PROGRAM   VYAS
  IMPLICIT   NONE
REAL    a,b,P,Q,R
INTEGER   X,Y,Z
a = 2.5
b = 4.0
P = a + b
X = a + b
Q = a * b
Y = a * b 
R = P/Q
Z = X/Y
PRINT *, P,Q,R
PRINT *, X,Y,Z
STOP
END

(e) Write a program in FORTRAN to calculate and print the ratio of surface area to volume of sphere with radii ranging from 1 unit to 20 units, in steps of 1 unit. (3)

(f) Give a situation, with justification, in which the median is the best measure of central tendency for a given set of data points. (3)

(g) Fit a straight line to the data given by the following table : (4)

(h) Calculate the mean and standard deviation for the following :(5)

2. (a) What values will be printed by the following program ?
PROGRAM EG2
I = 2
J = 4
x = 22.5
Y = -10.0
Z = 0.25
P = Z+X*Y
Q = P+2.0*Y**I
R = -Y*8.0/REAL (J)
X = Q+R
Y = X*2.0 - Z
Z = Z * R
J = INT(3.0*Z/REAL (I)
I = I + 6
PRINT *, I,J,X,Y,Z
PRINT *, P,Q,R
STOP
END

(b) Write a FORTRAN program to find the two roots of the quadratic equation AX² + BX + C = 0. Read the values of A, B, and C as 15.25, 30.12512 and 0.675 E-01, respectively. (4)

(c) Each of the following arithmetic statements contains at least one error. Point out the errors and correct the statements : (3)
(i) V = X/Y - 37,375.15
(ii) Z = 7.52 E+(2*I)
(iii) MAX/N = P

(d) After analysing the wage pallen of the workers of three firms A, B and C, the following results were obtained :

Find which of these have the larger variation. (4)

3. (a) The sum of the squares of the first n natural numbers is given by
S = n(n+1)(2n+1)/6
Write a FORTRAN program that will find S for n = 10[10] 250, i.e., n = 10, 20, 30,. . . ,250. (4)

(b) Write a FORTRAN program to read 50 numbers a₁, a₂, a₃, . . . , a₅₀ and print them in the order a₅₀, a₄₉, a₄₈,.., a₁.(4)

(c)Calculate the mean, median, and mode of the following data relating to weight of 120 articles : (5)

(d) A speak the truth in 70% cases and B speaks the truth in 80% cases. What is the probability that they will say the same thing while describing a single event ? (2)

4. (a) A factory manufacturing televisions has four units A, B, C and D. The units A, B, C, D manufacture 15%, 20%, 30%, and 35% of the total output, respectively. It was found that out of their output 1%, 2%, 2% and 3% are defective, A television is chosen at random from the total output, and found to be detective. What is the probability that it came from unit D ? (3)

(b) In a partially destroyed laboratory record, only the lines of regression of y on x, and x on y are available as
4x - 5y + 33 = 0 and 20x - 9y = 107
respectively. Calculate xBar, YBar and the co-efficient of correlation between x and y. (5)

(c) Write a program using FORTRAN 77 to check the consistency of the following system of equations:
2x - 5 = 3y + 7z
6x + y + 2z = 3
x - 5y = 20
Further, list the modifications required, if any, for effective program execution. If the program were written using FORTRAN 90 instead. (7)

5. (a) Calculate the Cost of Living Index Number from the following data : (5)

(b) Given below is a series of weekly demand for out-patient Care at an ambulatory centre. Also shown are forecasts of demand calculated by two forecasting methods that are under consideration.

(i) Compute the MAD for each forecast model.
(ii) Indicate which model you think is better-and why. (6)

(c) The Mother Dairy Ice Cream Shoppe has recorded the demand for a particular flavour during the past 6 weeks, as shown below :

(i) Calculate a 3-week moving average for the data to forecast demand for the next week.
Caculate a weighted average forecast for the data, using a weight of 0.6 for the most recent data and weights of 0.3 and 0.1 for successively older data. (4)