*BA-1861/2ga-isor. Second Year B. C. A. (Sem. III) Examination. September/
October - 2009. Computer Oriented Numerical & Statistical Methods. Time : 3
Hours].
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A. (Sem. III) Examination September/October - 2009 Computer Oriented Numerical & Statistical Methods Second Year B. C.
Time
)r
: 3 Hours]
Instructions
[Total Marks
I
: 70
:
(1) eulicr 3 h*rilqtu{l fiota'i 6rtr,.rdl qQ ]tqQq c.tut 1r signs on your answer book.
Fillup strictly the details of
s. Y. B. C. A. Name of the Subject
:
\a-,\rnlr-lr(
Computer Oriented Numerical & Statistical Method lrSubjectCode No.
(2) (3) (4) (5) I
1il8il6il1
1-section No.
(
1,
2,.....),fl*liil
Attempt all questions. Figures to the right indicate full marks. Mention your options clearly. Question No. 1 is compulsory.
: (1) If Ld2 = 0 then value of correlation coefficient is
Do as directed
.
.
(2) (3)
What is the standard deviation of 5, The correlation coeffrcient is regression coeffi.cients.
(4) The roots of
' (5)
5, D,
10
b ano b.
mean of two
equation x" -9r+1=0 lies between
and
Construct forward difference table of the polynomial y = x2 when tc=I,3,5,7,9. A regression equation is given
by r+5y-10. If x=5 '(6) then find y. (7) If two variables have perfect positive correlation then .
(8) (9)
I
-_-
For use of Simpson's rule, interval is divided in how many subintervals ?
Write Newton's forward difference interpolation formula. (10) If the ranks of two variables are equal then correlation coeffi.cient r =
BA-186U
lContd...
(a) Find a real root of the equation 3 .
ft)
*3 -2*-b=0 upto decimal places using Newton Raphson method.
r and log,rox are
Certain corresponding values of (aoo,
2.477r), (ao+, 2.4829),
(aOz,
2.48i1), find log1oB01.
(805, 2.4848) and
OR
(a) Findarealrootof
theequation
*3-*-4=0
by
using false position method correct to three decimal places.
of a town goes as given below. Estimate the population for the year 1925
&)
T'he population
6
:
year (r) Population (thousand)
(a)
j
1
190
46
1
1911
L92l
1931
81
93
101
66
From the following table of values of
obtain x
189
1.0
#
1.6
1.4
2.7L83 3.3201 4.0552 4.9530
&)
and y
6
for r=1.6.
^ d, #
L.2
r
1.8
2
2.2
6.0496
7.3891
9.0250
Solve the following system of equations by Gauss-Seidal method (upto 5 iteration) : 83r+11y- 4z =95
using
6
7x + 52y +LBz = 104
3r+8y+292=7I OR 1
3 (a) (b)
Find the value
$ i#d. orl
using Trapezoidal
by taking h = 0.5, 0.25, 0.125 . Solve the following linear system by Gauss-elimination method
using
rule
6
6
:
3r1+6xt+rs=16 Zxr+ 4xr+ 3r, = 13 x\ +3x,2 +2xs
84,-18611
-
I
z
[Contd...
4
(a)
Define mean. Calculate mean and median for following data : 20-24 25-29 30-34
CIass
Frequency
(b)
3
6
35-39
40-44
45-49
6
2
2
2
D
the
From a group of 200 candidates, the mean and S.D. are 40 and 15 respectively. Later on it was found that the score misread as 34 instead of 43. Find the correct mean and correct S.D. OR
4
(a)
Define mean and median. Calculate mean and median for the following data : Income (Rs.) Number of persons
(b)
100
150
80
200
24
26
16
20
254 180 6
30
Given the following results, which of two group is better in individual observation :
6
Group-A Group-B
5
(a)
(b)
Lx
45
CD
Lx2
118
(.s132
n
20
30
Rank of 15 students in Mathematics and Statistics are given below. The figure indicate ranks : (L,2), (7,9), (2, 1), (9, 7), (L2, 15), (8, 8), (6, 5), (3, 3), (13, 13), (15, 14), (r4, 11), (10, 10), (11, 12), (4, 6), (5, 4). Find correlation coeffi.cient. Calculate correlation coeffi.cient : ,c
300
350
400
v 800 900 1000
5 (a)
450 1
100
500
550
600
650
700
1200
1300
1400
1500
1600
OR The following data are obtained
and
y. n = 30 , Lx =L20, Iy
=
for the variables
90,
=250, Lxy=356. Later on
r
6
Ir2 = 600,
it
was observed' that two pairs were wrongly taken as (8, 10) and (L2, 7) instead of (8, 12) and (10, 8). Find the correct value of correlation coeffrcient. Lyz
BA-186U
3
[Contd...
&)
Calculate correlation coefficient
6
:
Marks in Economics -+ 40-49 50-59 60-69 Marks in Account J
70-79
(a)
3
c
4
50-59
2
6
6
2
60-69
1
4
10
D
2
70-79
b
10
8
1
80-89
1
4
6
c
2
4
4
Obtain two regression lines and correlation coeffi.cient from the following data : )c
bc
66
o/ 67 68 69
v 67 68 64 68
(b)
90-99
40-49
90-99
6
80-89
72
70
7T
73
69
70
From the following data find two regression equations and estimate y when x=2g and r for I=4b : 3C
6
6
v
Mean 25 40 Variance 9 36
Correlation coeffrcient
is
0.gg-
6 (a) The equations of two l"l"rrr"" (b)
Iines are gy+BbO 5y=9x-22, 20x= then find (1) mean of r and y (Z) correlation coefficient between .r and y. The followittg information is obtained for two variables r and y. Find two regression equations. Also find correlation coeffrcient n = 2E , Lx IZd , =
Iy = 100, Ir2 = 650, Ly2 = 440 , Iry
BA-18611
4
\-
\ I
6
6
= 5gg.
[ 2000 I
