Dharmsinh Desai University 2007 M.C.A Computer Aplications Computer Oriented numerical & Statistical Methods - Question Paper
Dharmsinh Desai University
MCA Sem - III
3S< JL
DHARMSINH DESAI UNIVERSITY, NADIAD.
M. C. A. SEM. Ill , EXAMINATION
. COMPUTER ORIENTED NUMERICAL & STATISTICAL METHODS DATE fyi fX O"7 TIME .fOlOO fo / / i>
DAY : -p,og MAX- MARKS : 60
SECTION I
1 Do as directed. [10]
A. Indicate whether the following statements are True or False :
(i) Statistics cannot be misused.
(ii) There is difference between survey and an experiment.
(iii) In a symmetrical distribution, the coefficient of skewness is 1.
(iv) The standard deviation of binomial distribution is npq.
Tick the correct answer.
(i) Classification is the process of arranging data in
(a) different columns (b) different rows (c) different rows and columns
(d) grouping of related facts in different classes.
(ii) Diagrams and graphs are tool of
(a) collection of data (b) presentation (c) analysis (d) summarization
C. What do you mean by Secondary data? Discuss methods of collecting primary data.
D. What is measure of central tendency? Define various measures of central tendency.
E. What is Chai-Square test? Describe the uses of it.
2. Attempt any TWO. [ 10]
(a) A survey was conducted to know about the average number of the first information reports lodged per day in a district.
For this purpose 60 districts were selected. The following gives the number of FIR lodged in the police stations of each district on a day.
|
46 |
38 |
39 |
45 |
48 |
50 |
28 |
29 |
31 |
55 |
6 |
10 |
|
58 |
56 |
0 |
25 |
32 |
35 |
35 |
9 |
35 |
36 |
38 |
35 |
|
33 |
46 |
28 |
31 |
35 |
52 |
78 |
17 |
60 |
50 |
35 |
38 |
|
30 |
10 |
48 |
5 |
19 |
25 |
35 |
40 |
46 |
42 |
45 |
25 |
|
60 |
41 |
68 |
48 |
35 |
30 |
31 |
21 |
23 |
23 |
50 |
72 |
Generate frequency distribution taking the first mid value is 5.
Calculate an average FIR per day using (i) Direct Method & (ii) Short-cut method Draw (i) Histogram and (ii) Cumulative Frequency Curve
(b) Define Binomial distribution. Obtain mean, variance and moment generating function of it.
(c) For the following data find Mean, Median, Mode and Coefficients of Quartile Deviation and variation.
Class: 54-56 56-58 53-60 60-62 62-64 64-66 66-68 68-70 70-72
Frequency: 37 76 132 115 72 50 15 2 1
3. Attempt any TWO. [10]
(a) Calculate Karlpearsons coefficient of skewness for the following data.
Classes Frequency
300 - 400 5
400-500 10 500 - 600 10 600-700 3
700-800 2
(b) Taking an appropriate example, define the following terms.
(i) An event as subset (ii) Equally likely events (iii) Mutually exclusive events
(iv) Exhaustive events (v) Dependent & Independent events
(c) A group of seven*week-old chickens reared on a high protein diet weigh 12, 15, 11, 16,14,14 and 16 ounces,
a second group of five chickens similarly treated except that they receive a low protein diet weighted 8, 10, 14, 10 and 13 ounces. Test whether there is sufficient evidence that additional protein has increased the weight of the chickens.
4. Answer the following questions: [10]
a. Explain any two methods of determining trend in a time series.
b. Explain Forward difference & backward difference in brief.
c. Which method is better to find a root of an algebraic equation? Why?
d. Derive the formula of Simpsons 1/3 rule.
e. Discuss utilities of time series analysis.
5. ' Attempt any TWO. [10]
(a) Find a root for the given function using Newton - Raphson method.
f(x) = x" 2x 5
(b) Solve the given differential equation y = x2 + y2, with initial condition y(0) = 1 . Find y(0.2) and y(0.4) using
Runge Kutta fourth order formula.
(c) Given the table values
x 150 152 154 156
y=f(x) : 12.247 12.329 12.410 12.490
Find y(l 55) using Lagranges interpolation formula.
6. Attempt any TWO. [10]
(a) Two random samples were drawn from two normal populations and their values are
A: 66 67 75 76 82 84 88 90 92
B : 64 66 74 78 82 85 87 92 93 95 97 Test whether the two populations have the same variance at the 5% level of significance.
(b) From the following table, find thl area bounded by the curve and the x-axis from x - 7.47 to x = 7.52, using
Trapezoidal rule and Simpsons 1/3 rule.
x 7.47 7.48 7.49 7.50 7.51 ' 7.52
f(x) 1.93 1.95 1.98 2.01 2.03 2.06
(c) What is an interpolation & extrapolation? Obtain Newtons Backward Interpolation Formula.
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| Earning: Approval pending. |
