Veer Narmad South Gujarat University 2011-3rd Sem B.C.A Computer Application SB-1441 Computer oriented numerical & Statistical Methods Second Year ( ) - Question Paper

SB-1441

Second Year B. C. A. (Sem. - III) Examination March / April - 2011 Computer Oriented Numerical & Statistical Methods

SB-1441

[Total Marks : 70

Instructions

(1)

6silq<3i Puunkiufl [qaim SuwiA u* qsq d-onql. Fillup strictly the details of signs on your answer book.

Name ofthe Examination :

S. Y. B. C. A. (SEM. - 3)

Name ofthe Subject:

COMPUTER ORIENTED NUMERICAL & STATISTICAL METHODS

-Subject Code No.

1 4 4 1 Section No. (1,2,.....

NIL

(2)    Attempt all questions.

(3)    Figures to the right indicate full marks.

(4)    Mention your options clearly.

1 Do as directed :    10

(1)    What is meant by absolute error ?

(2)    Show that iterative method applied to the equation

^x=(⁵~^x)^lA

(3)    Find Mode for the following data :

1, 2, 3, 3, 4, 4, 4

(4)    If covariance between two variables X and Y is 20.25 and Standard deviation of X and Y are 6 and 4.5 respectively, calculate correlation coefficient between X and Y.

(5)    The method of fitting of regression line are _

and_.

(6)    Write the general formula for trapezoidal rule.

(7)    If y₀=l, y_x=5, y₂ = 19, _y₃=55 find y(x).

(8)    Find variance for the following data :

4, 6, 10, 12, 18

SB-1441]    1    [Contd...

(9)    For the iteration method to find an approximate root it is necessary that |(|)'(x)|>l, is it true or false ?

(10)    For use of Simpson's and rule interval is divided in to how many subintervals.

2 (a) Find an approximate root correct to 3 decimal places 6 for the equation _x3_4_x_9 ₌ q using Bisection method.

(b) By divided difference formula find / (8) and /(l 5). 6

X	4	5	7	10	11	13
Y	48	100	294	900	1210	2028

OR

2 (a) Find approximate root correct upto 3 decimal space 6 for the equation /(x) = x³ -3x² -3 = 0 using iteration method.

Estimate the population for the year 1925 :

Year (x)	1891	1901	1911	1921	1931
Population (Thousand)	46	66	81	93	101

3 (a) Find the value of J, 2^x using Trapezoidal rule 6

0-L + X

by taking h = 0-5, 0-25, 0 125.

(b) Solve the following linear system by Gauss-elimination 6 method.

5x-2_y + z = 4 7x + y-5z = 8

3x + 7_y + 4z = 10 (By 5 iteration)

OR

3 (a) Solve the following system of equation by Gauss-Seidal 6 method :

1 Ox + 2y + z = 9 2x + 20y-2z = -44 -2x + 3y + l0z = 22

dy    d2y (b) From the following table obtain and at    6 (IX    CtX

X 1-4 1-6 1-8 2-0 2-2 y 4-0552 4-9530 6-0496 7-3891 9-0250

4 (a) Define mean. Calculate mean and median for the    6

following :

Class:	20-24	25-29	30-34	35-39	40-44	45-49
Frequency:	3	5	2	6	2	2

(b) The time taken by 12 runners in a race were 73, 82, 6 75, 68, 70, 90, 80, 71, 78, 65, 70, 66 seconds.

Find the standard deviation and co-efficient of variation.

OR

4 (a) Define mode. Calculate mean and median for the    6

following data :

Class	3-5	5-10	10-20	20-50	50-80	80-100
Frequency	8	12	40	70	15	5

(b) The median of a frequency distribution of marks of 6 400 students is 38.5. Find the missing frequencies :

Marks	11-20	21-30	31-40	41-50	51-60	61-70	71-80
No. of Students	42	38	a	54	b	36	32

5 (a) Calculate rank correlation co-efficient :    6

X	48	33	40	9	16	16	65	24	16	57
y	13	13	24	6	15	4	20	9	6	19

(b) Find correlation co-efficient using following data :    6

r| = 13, Xx = 117, Xx² =1313, ly = 260, I,/=6580,

Zxy = 2827

OR

X	300	350	400	450	500	550	600	650	700
y	800	900	1000	1100	1200	1300	1400	1500	1600

(b) Calcualte correlation coefficient :    6

Marks in Economics - 40-49 50-59 60-69 70-79 80-89 90-99 Marks in Accounts i 90-99 - - - 2 4 4 80-89 - - 1 4 6 5 70-79 - - 5 10 8 1 60-69 1 4 9 5 2 - 50-59 3 6 6 2 - - 40-49 2 5 4 - - -

6 (a) Find both regression equations using following data : 6

X	4	5	6	7	1	2	3
y	6	5	6	5	2	4	7

(b) The following information is obtained for two variables 6 X and Y. Find two regression equations and also find correlation coefficient.

r| = 25, Zx = 125, Zy = 100, Zx¹ =650, Zy² = 440, Zxy = 508

OR

6 (a) The regression equation of two variables are    6

5 y = 9x- 22 20x = 9>> + 350

Find means of x and y also value of r.

(b) Find the most likely production corresponding to a 6 rainfall of 40 inches from the following data :

Rainfall (in inches) Production (in quintals) Average 35 50 Standard deviation 5 8

coefficient of correlation r = 0.8.

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