Pre University Board 2009 P.U.C. Commerce (SEBA) Statistics - Question Paper
[ Total No. of Printed Pages : 16
Code No. 31
Total No. of Questions : 42 ]
March, 2009
( Kannada and English Versions )
Time : 3 Hours 15 Minutes ] [ Max. Marks : 100
( Kannada Version )
: i) sraoX XejXrt>o Xe$art Xadoartod)o.
ii) d.qaaX n raXaed Xd d<aeA,oo.
<=i
iii) yao 00a 0n>R rOjjdaA eD,X@Q.
- A
I. X>A 0a dJ, 0 : 10 X 1 = 10
7 l <=i >
1. 0d do d&jrart> w-aert &3rt>o ae,Dd)X@ /d d/do d<aeA,odo ?
2. ,,aoXdaA ,aa,oXrt> O(o0 /d do ,oa,0oo >,do ?
d cp 6 co -d ci
3. dao 0 ,aa,oX O(o0 /d Xri>, >,oaArf ?
6 CO Ct
4. Uod dad}rt$naA /d)adda odo ,o$Fdo $.
5. odo Odd d}(o dddaA d/ = 7 doo d,0ra = 11 wA.
doe daXd) ,0oe ?
6. x 2 - - } >,oXoy, aoea Xae wdo a<ododeo ?
7. daedo, dazaa.
8. , do%j<o d/X do oa&onad /d)o ?
9. d <o,o X> sart, ,ador X>doXa>o,d ,oXd}rt>o doao,odart ,0,d deo ?
10. aoX rtora a<oorad) /d d}oo XodbSoodY ,a<oXdaA ?
- B
11. odo dortdd doX@>o dod ort,d dtio dod3&rX aar dtiod ddo3Xtio dd 26, 63, 65, 46, 24, 13 doJo 7 wAd. dort, d<do3Xtio dddo Xodoaoo.
ct
12. odo d,o dtioo 2002 d 10 d).rt> doJo 2008 d 35 d.rt>0.
_o co _o co
wrt - d ,>,oX dddo Xodoaoo.
6
13. &dd ,&).oXdo aX wdr ,>,oXdodo Xdtioorto J d ?
* ) c ) _D
14. X> A dX6rt>i yKetio ti/d &XX@ ,ooad ?
a) dooododdd qd d,tiooX dodra ddd XoJ
ny> ZJ s co
b) ,oA tio yod d d.ert dyrt>b.
n co i$ 6
15. odo de, >Jdratio< dd ,odJtio dod/rad 0-2725. dd doooa ,oddJtio dod/rado Xodoaoo.
ot
16. X dd Jd}tioo. X>A atiododoJ XdoAd.
ot
i I ( X - 100 ) 2
f ( X ) = c 2 ( 5 )
5y/2'n
dd d/d6 doJo d/X otiooR doo.
17. odo a do Jo 0ddo atio doeX.rt>o d3,z>,a.
_o oOk c 6 6
18. odo rtdd ,,3.w3ort> d3>Jd) 048 wAd. toJ, 20 d> ti/dX dotio , ,aon> oa Jd dedo Xodoaoo.
19. d/6n> ,d/Jtio doeX\tio dortd -doeXtio adrX dJo
JoJoXrto doo.
20. ,d>deeid dd aa ,d,.<d ttd dO>ddd ro>,z>,ab.
J * 6 co 6 _o i 6 6
21. od w<dt edd, A w&nsdd e-w" d/tXd X>notd :
|
B 1 |
B 2 |
B 3 |
B 4 | |
|
A 1 |
5 |
3 |
8 |
- 6 |
|
A 2 |
5 |
10 |
- 3 |
- 6 |
w&TOd B d de-w" d/tdd doO.
22. adot,ra X\ nodded ? drt> adot,ra dXdd ,Ob.
- C
III. X> Ad)rt> d/d)dd 0o&o drtrt toOb : 8 x 5 = 40
23. d A dd wd SfotA t n dXod adt dodra dddd XodaoO dt adrb :
_D
|
S!xbA rt3C)rt>3 |
a,cZ6 |
aarj | ||
|
A |
B |
A |
B | |
|
0 - 20 |
4,000 |
3,000 |
7-5 |
10 |
|
20 - 40 |
12,000 |
20,000 |
3-33 |
5 |
|
40 - 60 |
6,000 |
4,000 |
10 |
10 |
|
60 dt deOjOj |
8,000 |
3,000 |
8-75 |
20 |
|
24. X>n dtoSX d" oXd) add dOeXjdd rtdt ddod teOb : eJ _o _o | |||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||
|
nboj |
&& r d (ti.rttfQ ) |
&,)g r tfd (ti>.rt>&t) |
&d r id |
|
wDd |
120 |
160 |
600 |
|
40 |
60 |
320 | |
|
od do3o d>do _D |
80 |
100 |
800 |
|
odo |
20 |
40 |
500 |
|
a oo dDwDt, 4 _o 6*6 |
30 |
60 |
450 |
|
ot |
45 |
80 |
1,350 |
26. X>A d6,X@ d<o@ ddrrt> <d ,oD,Ort>o d<>eAft ddA drt>o oDft :
ot
|
r |
jlOw 6 |
|
1994 |
12 |
|
1995 |
25 |
|
1996 |
39 |
|
1997 |
54 |
|
1998 |
70 |
|
1999 |
87 |
|
2000 |
105 |
|
2001 |
100 |
|
2002 |
82 |
|
2003 |
65 |
27. odo ,D,O<d dd 10 dY 1 ddrto doo>rtod). 5 ddrtort> de dd\ 4 ,oda\3dDA 3od)d dodoSoO.
28. d do,ddoR 3/O,od 5DZD0y Cj/d)d Dd 00 do,dd) deddPOdDrtod ,d6J 1/500 wAdod. dodrtEo odo drad 10 do3 d$,DAd. dPeaDS*1 >3d}oo ddieAft 20,000 dPrart> ,ddS, odo deddPO3 d do,dd doadod dPrart> odo od dd dodoSoO.
29. doeX.n 490 rtodo d3,arrt> doJo 450 rao >da,arrt>i
6 e? cm 6 * -o rs 6 *
saKoafidad. rtodo d36arn> oXd d/d6 dJo d/X tioo X,dodaA 543 doJo 175 wAdoJd. rao da,arrt> oXn> d/d. dJo
V -o -o rs 6 * * 6 -c
d/X tioo X,ddaA 506 dJo 180 wAdoJ d. rtodo dJo rao
y o _o _o rs
d3,arrt> oXrt dJ ddad d.Ja,,d<de .aoodd doeS,.
* CO 0 6 6 oOl
30. d-dod3 dJo aXed yaodrtrt ti/d)de ,ood<,dodo odo JoroS Xodatioo ,doarX>o,Jod. ,dodrtioo JaZ d/dd)dX@e,@d 40 ood 50 dtie rtoo& 300 nodd, dSetio Jda,}rt >da,aartoJd. rtdad do Jaod) X>Ao3d :
|
ystfod |
&?,,&& ystfod Bdo& cJ CO | |
|
75 |
105 | |
|
< tido * CO |
25 |
95 |
de d/3tio dyd d>doda dJo aXed yaodrt> JoJdaAdtioe 0odo 3ed/ra,dde ?
31. Jde3 ddoo dJo oJd 5 &ort IQ doeXtiod, aedoaoJo dd Jao d) X>Ao3d :
|
&$s@rri>b |
I |
II |
III |
IV |
V |
|
rifitico IQ : |
110 |
120 |
123 |
132 |
125 |
|
od IQ : |
120 |
118 |
125 |
136 |
121 |
d.arrt> IQ Jdetio oJd aadd rtraaetiodad doad}
> *' co
32. nodd Xad - Xadd nod JJ,dd >da X>a 3/dtiod, a.
CO CO &5 y ct
&&nd- B
|
B i |
B 2 |
B 3 | ||
|
A i |
1 |
3 |
1 | |
|
&&nvd A |
A 2 |
0 |
- 4 |
- 3 |
|
A 3 |
1 |
5 |
- 1 |
33. d/0eX j d>ds XdJn> dd, noeaftd d 8,000 d>d dsd
&,3@ d, ddr adrdra dd) X>n XdoaAd :
|
T |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
adrdra d ti (da<-n >0) |
1,000 |
1,300 |
1,700 |
2,200 |
2,900 |
3,800 |
4,800 |
6,000 |
|
dsdsd (da<-n >0) |
4,000 |
2,000 |
1,200 |
600 |
500 |
400 |
400 |
400 |
(d/d yaX, &As doasftdd addadsXdanJd 0o2ds
6 y 6 -e
34. >$ aodsrtod woftd djJs Jbodbrt>s X>n doad:
1, 4, 3, 2, 5, 4, 6, 7, 2, 3, 2, 5, 7, 6, 4, 5, 2, 1, 3, 8
,X a<dsoJ,ra X,dss rtsdsft dd adsoJ,ra XodoasO.
-o y <A t V t
- D
IV. X> Ad)rt>0 d/d)dadd 0do drtrt Joft : 2 x 10 = 20 35. djds dsJb Sortd Jd} dsJo edoJ oZ.dss X>A
Z/ _o _o > i
|
( s&rri>&i) |
rtoti,d a,oZ6 |
a,oZ6 |
tfeo& & |
|
0 - 14 |
20,730 |
19,840 |
0 |
|
15 - 19 |
7,366 |
7,310 |
212 |
|
20 - 24 |
7,300 |
7,120 |
657 |
|
25 - 29 |
6,030 |
5,860 |
592 |
|
30 - 39 |
9,980 |
9,120 |
326 |
|
40 - 49 |
7,400 |
6,910 |
81 |
|
50 doJ deOj&Sj |
8,400 |
7,900 |
0 |
Xj dd, ,ad/6 d<doX dd dsJS aar d<dsft d<doXds ddrt>x XodsasO.
ot
36. /F-0,3F & ><3 0Q
|
00 e$X33 X>A > oao : c _0 | |||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||
|
37. ,X@d y3<z>F< ,oZ633 (,> oioo,) X>n | |||||||||||||||||||||||||||||
|
sST |
2001 |
2002 |
2003 |
2004 |
2005 |
2006 |
2007 |
|
(m>d 3j0Kri>Q ) |
80 |
90 |
92 |
83 |
94 |
99 |
92 |
a) oe ,oZ6rtn ,d>de(o oab.
b) 2008 d 03b.
CO ej <=i
c) rt>3 dOiOD.
|
38. d&Y X>A rtoa,>Arf : | ||||||||||||
|
oe oX@ PJd} 0Qb ><o ,oo&,sle 0Oy dOeS.b.
t <*A
- E
V. X>A (/>d)de 0- dLrt O :
39. X odo ,ad/6 d. - d/d6 64 do d} 144 wdd,
i) P ( X > 67 )
ii) P ( 60 < X < 66 ) rt>o ar0.
40. d&.raA ood 1000 &d />d X doao 400 rtaea ,e,oaO.
eJ e) ti co _o
d &,ra B ood 800 &d doao 400 rtaea ,e,oaO. rtaea
0 CO 0
,e,d addS d&.ra A do d&.ra B dd -dad d,sa.,do
co eo _oeJ _o 6 6
daoad<oe 0o o2doct doe dod) aeO,d<oe ?
41. 8 ,d>ort> XdrX Oe d : 8, 3, 12, 14, 7, 13, 9, 6
&n >o. d/X (doo 2 &n$Ao {a 0o d<doo dOeS,.
_D c oOl
42. na,dXOrt de ,aeddad odo d,p 400 (dooairt ,on5ado
3 oo&, esarto d. a.dXOod do odo <dooaiM 50 da.oJ d, do
_0 >J _D c
nOea,a . a.dXOod odo wde2X,, wde2 d doo ,anaX d 75
_o J u -f
da. wrtod. od ddrX, ,ort,d adrdra d d,> d(do 75% ddo,
_0 t J/ _0 0
wrto d.
_D
i) wprX ,0S na,
li *
Note : i) Statistical tables will be supplied on request.
ii) Scientific calculators may be used.
iii) All working steps should be clearly shown.
I. Answer the following questions : 10 x 1 = 10
1. Which measure should be used for comparing health conditions of two towns ?
2. Theoretically which best average is used in the construction of index numbers ?
3. Which weights are used in the construction of Paasches price index number ?
4. Mention any one of the factors causing seasonal variations.
5. For a Binomial distribution mean = 7 and variance =11.
Is the above statement correct ?
6. For the application of x 2 -distribution, what is the condition for expected cell frequency ?
7. Define Standard Error.
8. Which is the best estimator of the population mean ?
9. What is the principle adopted for replacement of equipment which deteriorate with age ?
10. SQC helps in detecting which type of variation ?
II. Answer any ten of the following questions : 10 x 2 = 20
11. The Quinquennial ASFRs for women of child bearing age of a community are 26, 63, 65, 46, 24, 13 & 7. Compute TFR.
12. If price of a commodity is Rs. 10 in 2002 and Rs. 35 in 2008, then compute the index number of price.
13. Why Fishers index number is called an Ideal ?
14. Which components of a time series are associated with the following sentences ?
a.) Fall in death rate due to advance in science.
b) An increase in employment during harvest season.
15. In a Poisson distribution the first probability term is 0-2725. Find the next probability term.
16. The distribution of a variable X is given by the law
1
e
Write down the values of mean and standard deviation.
17. Define one-tailed and two-tailed tests.
18. The proportion of vegetarians in a city is 0-48. Find the standard error of the proportion of vegetarians in a random sample of size 20.
19. Write down the t-test statistic and degrees of freedom in the case of test for equality of means.
20. In an LPP define optimal solution.
21. In a rectangular game pay-off matrix of Player A is
|
B1 |
B 2 |
B 3 |
B 4 | |
|
A 1 |
5 |
3 |
8 |
- 6 |
|
A 2 |
5 |
10 |
- 3 |
- 6 |
Write down the pay-off matrix of Player B.
22. What is a Control Chart ? Name the control chart for variables.
III. Answer any eight of the following questions : 8 x 5 = 40
|
23. Taking Town A as standard, find the STDRs & comment. | |||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||
|
24. For the following data verify whether Fishers index number satisfies | |||||||||||||||||||||||||||||
|
FRT : | |||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||
|
25. Construct a suitable consumer price index number for the folowing | |||||||||||||||||||||||||||||
|
data : | ||||||||||||||||||||||||||||
|
26. Estimate the trend values using the data given below by taking four yearly moving averages :
|
Year |
Values |
|
1994 |
12 |
|
1995 |
25 |
|
1996 |
39 |
|
1997 |
54 |
|
1998 |
70 |
|
1999 |
87 |
|
2000 |
105 |
|
2001 |
100 |
|
2002 |
82 |
|
2003 |
65 |
27. If on an average 1 ship in every 10 is sunk, find the chance that out of 5 ships expected at least 4 will arrive safely.
28. In a certain factory turning out optical lenses there is a small chance 1/500 for any one lens to be defective. The lens are supplied in packets of 10. Use Poisson distribution to calculate the approximate number of packets containing one defective lens in a consignment of 20,000 packets.
29. 490 male students and 450 female students appeared at an examination in commerce. The mean and S.D. in marks of male students are 54-3 and 17-5 respectively, whereas those of female students are 50-6 and 18-0. Is there a significant difference in marks of male and female students ?
30. A tobacco company claims that there is no relationship between smoking and lung ailments. To investigate the claim a random sample of 300 males in the age group of 40 to 50 are given medical tests. The observed sample results are tabulated below :
|
Ailment Smoking |
Lung ailment |
No Lung ailment |
|
Smokers |
75 |
105 |
|
Non-smokers |
25 |
95 |
On the basis of this information can it be concluded that smoking and lung ailment are independent ?
31. An IQ test was administered to 5 persons before and after they were trained. The results are given below :
|
Candidates : |
I |
II |
III |
IV |
V |
|
IQ before training : |
110 |
120 |
123 |
132 |
125 |
|
IQ after training : |
120 |
118 |
125 |
136 |
121 |
Test whether there is any change in IQ after the training programme.
32. Solve the game by maximin-minimax principle whose pay-off matrix is given by
Player A
|
Player B | |||
|
B 1 |
B 2 |
B 3 | |
|
A 1 |
1 |
3 |
1 |
|
A 2 |
0 |
- 4 |
- 3 |
|
A 3 |
1 |
5 |
- 1 |
33. A truck owner from his past records finds that the maintenance costs per year of a truck whose purchase price is $ 8,000 are as given below :
|
Year : |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
|
Maintenance cost ( in $) |
1,000 |
1,300 |
1,700 |
2,200 |
2,900 |
3,800 |
4,800 |
6,000 |
|
Resale price ( in $ ) |
4,000 |
2,000 |
1,200 |
600 |
500 |
400 |
400 |
400 |
Determine at which time it is profitable to replace the truck.
34. Twenty pieces of cloth out of different rolls contained respectively
1, 4, 3, 2, 5, 4, 6, 7, 2, 3, 2, 5, 7, 6, 4, 5, 2, 1, 3, 8 imperfections. Calculate control limits for suitable control chart.
IV. Answer any two of the following questions :
2 x 10 = 20
35. The following table gives the age and sex distribution and the number of live births occurring in a year in a population :
| ||||||||||||||||||||||||||||||||
|
Compute CBR, GFR & ASFRs. |
36. It is stated that Marshall-Edgeworth index number is a good approximation to the Fishers Ideal index number. Verify this using
|
the following data : | |||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||
|
3 7. Below are given the figures of production ( in thousand quintals ) of a | |||||||||||||||||||||||||||||
|
sugar factory : | ||||||||||||||||
|
a.) Fit a straight line trend to these figures.
b) Estimate the production for the year 2008.
c) Compute the trend values.
|
38. The following mistakes per page were observed in a book : | ||||||||||||
|
Fit a Poisson distribution to the data and test the goodness of fit.
V. Answer any two of the following questions : 2 x 5 = 10
39. X is a normal variate with mean 64 and variance 144. Determine
i) P ( X > 67 )
ii) P ( 60 < X < 66 ).
40. In a random sample of 1000 persons from town A, 400 are found to be consumers of wheat. In a sample of 800 from town B, 400 are found to be consumers of wheat. Do these data reveal a significant difference between town A and town B so far as the proportion of wheat consumers is concerned.
41. The tensile strengths of 8 rods were 8, 3, 12, 14, 7, 13, 9 and 6 tons. Test the hypothesis that the standard deviation is more than
2 tons.
42. A stockist has to supply 400 units of a product every Monday to his customers. He gets the product at Rs. 50 per unit from the manufacturer. The cost of ordering and transportation from the manufacturer is Rs. 75 per order. The cost of carrying inventory is 7-5% per year of the cost of the product. Find
i) Economic lot size
ii) The minimum average cost.
|
Attachment: |
| Earning: Approval pending. |
