

CS  08 Numerical & Statistical Computing

Weight in Kilograms 
Number of students 

4550 
01 
5055 
05 
5560 
21 
6065 
43 
6570 
22 
7075 
06 
7580 
02 
Calculate the standard deviation of the above frequency distribution.
(h) Fit a straight line to the data given by the following table: (4)
Independent Variable 
Dependent 

2 
3 
4 
17 
6 
38 
7 
49 
9 
80 
11 
120 
(i) A jar contains 7 red balls, 5 green balls, 4 blue balls, and 3
white balls. A sample of size 7 balls is selected at random without replacement.
Find the probability that the sample contains 2 red balls, 2 green balls,
2 blue balls, and 1 white ball. (4)
2. (a) Write a FORTRAN function SUMM with one integer parameter N, that computes the sum of first N natural numbers and prints a suitable message. (6)
(b) Write a FORTRAN subroutine MMM that computes the mean, the minimum and the maximum of an array A of N real numbers, and prints out the values with suitable messages. (9)
3. (a) Write a FORTRAN program which finds and prints all fourdigit prime numbers. (7)
(b) For a frequency distribution of marks in History of 200 candidates, the mean and standard deviation (s.d.) were found to be 40 and 15 respectively. Later it was discovered that the score 43 was misread as 53 in distribution. Find the correct mean and standard deviation corresponding to the correct distribution. (8)
4. (a) In a bolt factory machines A, B and C manufacture respectively 30, 35 and 35 percent of the total. Out of their total outputs 3, 4 and 3 percent are defective. A bolt is drawn at random and is found to be defective. What is the probability that it is manufactured by (i) factory A (ii) factory B? (8)
(b)A jar contains five 50paisa coins, four onerupee coins, three tworupee and four 5rupee coins. A sample of size 6 (coins) is taken out at random without replacement. Find the probability that the sample contains two 50paisa coins, two onerupee coins, one tworupee coin and one 5rupee coin. (7)
5. (a) The following table gives the average wholesale prices of the four grains for the years 1997 to 2001. Compute chain base index number. (7)
Grain 
1997 
1998 
1999 
2000 
2001 

Wheat 
400 
440 
360 
480 
500 
Gram 
800 
880 
960 
1000 
1200 
Barley 
480 
520 
420 
560 
600 
Rice 
600 
640 
720 
680 
720 
(b) Calculate the correlation coefficient for the following data:
(8)
x 
8 
12 
15 
20 
24 
27 
32 
y 
30 
24 
36 
44 
56 
64 
72 
6. (a) Compute the approximate value of the integral
I =(1
+ x^{2}) dx
using Simpson's rule by taking interval size h as one. (7)
(b) A portion of a table of sines is given below:
Angle in Radians 
Sine 

0.25 
0.2474 
0.26 
0.2571 
0.27 
0.2667 
0.28 
0.2764 
0.29 
0.2860 
Find the derivative of this function at x = 0.27. (8)




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