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7 3 5 *
M E -3 7 3 5
S eco n d Y ear B. C. A. (Sem . I ll) E xam in ation
O ctob er/N ovem b er - 2013
301 : S ta tis tic a l M ethods
Time : 3 Hours] [Total M ar
In str u c tio n s :
01
(1)
Pminkiuft Hi w i
F iilu p strictly the d etails o f
Name of the Examination :
Second Year B. C. A. (Sem. 3)
s ig n s on yo u r a n sw e r book.
K
- I
Name of the Subject:
301 : Statistical Methods
^ -Subject Code No. :j 3 |j 5 ^ -Section No. (1,2.....) I N I
(2) All questions are c o m p u ls o ry .
(3) Figures to th e r ig h t indicate fu
(4) M ention your options clea
1 Do as directed : 14
(i) Define M ean.
(ii) Compute m edian for th e following d a ta :
4, 6, 5, 8, 12. 7, 10, 5, 15, 9, 10, 11.
(iii) . If two variable are perfect ly correlated and one regression
co-efficient is 0.5. F ind another regression co-efficient.
(iv) Show th a t correlation efficient is geometric m ean between
two regression co-efficient.
(v) W halris the sta n d a rd deviation of 5, 5, 5, 5 and 5.
(vi) If two variables have perfect positive correlation th en
(vii) If the sum of ra n k difference of 7 p airs are 74 th e n find
-efficient of correlation.
If m ean of the d a ta is 275 an d th e total frequency is
th en Find 'EFiXi.
X < 2
ra n k correlation coefficient if HLd = 0, P = _ _ ____ ■
If X - M = 3 and Z = 2 th en find m ean an d m edian.
xi) If two regression lines are X + 37 - 7 = 0 and 2 X + 5F = 12,
then X and f are _______ an d ______ ,
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(xii) If «(« - l ) = 90 an d ^ d 2 = 82.5 find ra n k correlation
coefficient.
(xiii) W hat is regression line ? Give the m ethod of th e ir
estim ation.
(xiv) Find bXy from the following
Sx = 19A,Sy =2.7,r = 0.S.
2 A ttem pt any tw o :
(a) The hu m an resource m anager a t a city hospital began
a study of the overtim e hours of th e registered n u rs
Twenty Five n u rses w ere selected a t random in d
following overtim e hours during a m onth were recorded
13 13 12 15 7 15
10 9 13 12 5 9
6 9 12
C alculate the arithm etic m ean of ov irs d uring
the m onth.
(b) F ind the m issing frequencies in ring frequency
distribution.
The arithm etic m ean of given da is 11.09 :
Class Frequency Class^ Frequency
93-9.1 2 11.3-11.7 14
9.8-10.2 11.8-12.2 6
5
10.3-10.7 F3 12.3-12.7 l~3
10.8-11.2 F4 12.8-13.2 1
Total Frequency = 60
(c) The fol awing are th e profit figures earned by 50
comp? in thff country :
Profit (in Rs. lakh) No. of Companies
• |p i« « T e s s 4
20 or less 10
30 or less 30
) 40 or less 40
~ 50 or less 47
60 or less 50
Calculate the median
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A ttem pt any tw o : 14
(a) The distribution of age a t the m arriage of grooms w ith
brides of age group 15.39 is displayed here :
Age groups (years) : 15-19 19-23 23-27 27-31 31-35 35-39
No. of grooms : 8 59 47 23 6 4
C alculate m ean deviation.
(b) M onthly wages of employee in a factory are distribute
as given below :
Wages (Rs.): 300-400 400-500 500-600 600-700 700-800 800-900
§
4 0Q0)ll00
VO
po
o
No. of employee: 15 22 18 14 9 7 5 ^ 4
Calculate variance of given distributi
(c) Find th e sta n d a rd deviation from the
Item : 6 7 8 9 10 11 12
Frequency : 3 6 9 13 8 5 4 (
A ttem pt any tw o : 14
(a) The following table gives in d i strial production
and num bers of registered une ed people, (in lakh)
C alculate the value of the co ation coefficient.
Year : 1991 1992 1993 1994 1995 1996 1997 1998
Index of 100 102 ( 104 ) 107 105 112 103 99
Production :
- - ^
No. of 12 13 - 11 12 12 19 26
unemployed :
-
(b) lowing table gives th e frequency, according to the
ts, obtained by 67 stu d en ts in an intelligence test,
ce th e degree of relationship betw een age and
Age in years Total
18 19 20 21
200-250 4 4 2 1 11
250-300 3 5 4 2 14
300-350 2 6 8 5 21
350-400 r 4 6 10 21
Total 10 19 20 18 67
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(c) Ten com petitors in a b eau ty contest are ran k e d by th ree
judges in th e following order :
Judge -1 1 6 5 10 3 2 4 9 7 8
Judge - 2 3 5 8 4 7 10 2 1 6 9
Judge - 3 6 4 9 8 1 2 3 10 5 7
Use th e ra n k correlation coefficient to determ ine which
p a ir of judges h a s th e n e arest approach to common
taste s in beauty.
A ttem pt any tw o :
(a) The following d a ta relate to th e scores o
salesm an of a com pany in an intelligence
weekly sales, (in Rs. 1000's)
Salesman : A B C D E F 1
0 H
Test Scores : 50 60 50 60 80 50 ■ 4 70
Weekly Sales : 30 60 40 50 60 1,50 70 50 60
(i) O b tain th e reg re ssit of sales on
intelligence te s t score lesm an.
(ii) If th e intelligence a salesm an is 65,
w hat would be his e? weekly sales,
(b) You are given the follo\ lation about advertising
expenditure and sales i
Advertisement (X) Sales (Y)
JR ^ in lakh Rs. in lakh
Arithmetic Mean 10 90
Standard deviation 12
nV 3
C orrelation coefficient = 0.8
O btain two regression equation.
In a p artially distroyed laboratory record of an analysis
essiori data, the following resu lts only are legible :
of X = 9
ession equations : 8 X -1 0 F + 66 = 0 and 4 0 X -187 = 214-
(i) The m ean value of X an d Y.
(ii) Coefficient of correlation betw een X a n d Y.
(iii) S a ta n d a rd deviation of Y.
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