

CS  08 Numerical & Statistical Computing

Item 
Amount in Rs. 
Food 
200 
Room Rent 
1000 
Transport 
500 
Books/Stationary 
500 
Maintenance 
1000 
g) Explain the concepts of 'skewness' and kurtosis' along with their significance in the study distribution of mass of data.
h) A computer while calculating correlation coefficient between 20 pairs
of two variables x and y obtains the following results:
n = 20, å x = 100, å
y = 80, å x^{2 }= 520, å
y^{2 }= 360, å xy = 420
It was later discovered at the time of checking that he had copied down
two pairs as (6, 4) 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.
i) A jar contains five 50 paisa coins, four one rupee, three two rupee and four 5rupee coins. A sample is taken out at random without replacement. Find the probability that the sample contains two 50paisa coins, two onerupee and one 5rupee coins.
Q. 2. a) Write a FORTRAN function which reads a value x. If x ³
1, then reads the value again. If 0 < x < 1
then computes f(x) = 1 + x^{2}/2! + x^{4}/4! + .... +
x^{100}/100!
In order to terminate the function, value of x may be 0 or negative.
b) Write a program to convert any ndigit decimal number to equivalent hexadecimal number. For example hexadecimal equivalent to 43919 is AB8F.
Q. 3. a) A departmental store keeps records of various items in a format
Stock number 
Item description 
Quantity at hand 
Unit price 
where stock number is a 2 digit number. Item description is a 13 character
name of the item and its quantity at hand is a 4 digit number, which is
the number of items in hand/store. Unit price is the price of a single
item. Develop a program to prepare sequential access file consisting of
N records, each record refers to one item. The program should be such
that it makes the following checks:
i) The stock number should not be outside 1 to 99.
ii) The initial data are to be entered from the terminal (unit =1)
iii) The price of an item should not be negative, and
iv) The number of terms of a particular type should not be negative.
b) For the following frequency distribution, draw (lessthan type) frequency polygon:
Class 
Frequency 
Class 
Frequency 
14 
3 
1619 
7 
47 
5 
1922 
5 
710 
4 
2225 
14 
1013 
1 
2528 
1 
1316 
6 
2831 
4 
Q. 4 a) A five figure number is formed by the digits 0,1,2,3,4 (without repetition). Find the probability that the number formed is divisible by 4.
b) The avarage number of radioactive particles through a counter during one millisecond in a laboratory experiment is 3. What is the probability that five particles enter the counter in a given millisecond?
c) The probability of a college student being male is 1/3 and that of being female is 2/3. The probability that a male student completes the course is 3/4 and that a female student does it is 1/2. A student is slelected at random and is found to have completed the course. What is the probability that the student is a male?
Q. 5. a) Calculate any one of the correlation coefficients for the following data:
X 
Y 
15 
9 
10 
12 
5 
18 
12 
10 
17 
5 
18 
2 
The following table gives the average wholesome prices of four grains for the years 1996 to 2000. Compute the chain base index number:
Grain 
1996 
1997 
1998 
1999 
2000 
Wheat 
100 
120 
115 
125 
150 
Gram 
100 
95 
105 
115 
98 
Barley 
100 
110 
105 
95 
120 
Rice 
100 
115 
110 
120 
115 
Q.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.
(b) From the following table of values of x and y, obtain dy/dx for x = 1.2.
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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