Pre University Board 2010 P.U.C. Commerce (SEBA) Statistics - Question Paper
Code No. 31
Total No. of Questions : 42 ]
Total No. of Printed Pages : 16 ]
March, 2010
( Kannada and English Versions )
Time : 3 Hours 15 Minutes ] [ Max. Marks : 100
( Kannada Version )
: i) od Xerort Xdosrtoddo.
ii) d.qad rtraXedddrart>o d>eA,udodo.
iii) ysod 0y do3n > 3eO,3
I. X> 0> d,&rt>o 3 O: 10 x 1 = 10
co ZJ <*L ot _o
1. ed bo-6-boSd odo do<d o
ot
2. dd ddrX@ d odd) 121 wAd. ado $ds)odo Xa.
3. ooo dod/ra ,2ifpdd dodoaooaXo ,3;do udoO.
4. Uo3od/ udosdran odo dsdd} Xa.
5. add a3d} o ,os,Ooo Ao3 dado doe ?
6. ,sd/6 dd) dd ,-s,OAo3 d 3 ndoXd ,odaeo3 0do ?
7. ao3 dedd odo dertdo
ot
8. $dd , <do rto}sod 0oddeo ?
9. adjd\ds3 3,ed <do d ( Value ) 0do ?
10. ,so,d rtora aoo3;rad0 defi&d aoo3;ra X,oo d, n>
6 V co V oOk _o
dedPO3X@ /d)do 0odo d , O.
- B
II. X>A zd)dadd JO : 10 x 2 = 20
11. odo aarj ddrd0c.3, odo saortd0 4,000 edoJ rt>o ,oad. doe0 50 d&rt>0 dortoa &aod saooado ad&.dosa d.
CO >J _0
d/J dodra ddd 0r ( M.M.R. ) XodoaDO (1,000 X@).
12. oXd zd)dadd 0dzb > 0r doo.
13. P 01 ( L ) = 108 doJ P 01 ( P ) = 110 wdd, P 01 ( F ) 0r XodoaiO.
14. X;dod d< d a$,J <oo da.za.a do Jo odo dad} Xa.
ZJ cp co ot <=i 6 6 -e
15. zd aod rt >0 ad d aJ d} oo dpe,a aJ d} n ddartoJd ?
16. aoJ ,adz,w aJd} o , da, o doJo a< 0%jdoJd ?
17. odo d OeX\o naJ, do Jo adodrrt > o da6za6a&.
18. dj-ed ( x 2 ) d oeX\o >o , doo& 0y, o ,doo,daA 0dti3 ao n > o d oo.
19. $ X , - XX 2 % = 2-7 do Jo SE $ XX , - XX 2 % = 1-3 wdart , 5% <ya, r
v127 -e v 1 2 7 7 oO
do&,d0 <ao dOeX.n ado., $da,odeo ?
eo co oOk a- Zs
20. ,d>deeo X,do aa ,do,_woo da6za6a&.
21. odo ooJ,d 0dde ddrd ,dX$ d do Jo ,oJ adr}a d rt>o
-> IS -e 2
XjdodaA d&. 10,000 doJo d&. 10,200 wAd d, da&rX ,da,O d o ?
y -0 CO 7 2
22. odo d, a JzOya d;5,oo0 dead} oiartoo yadradartod 0>rt3b
-o ZJzJ co
ad d yad ran > o
ot
- C
8 x 5 = 40
23. X> A sa6,Qo , ort, odoX dd o XooaoO :
|
(rrt>Q ) |
&,oZ6 |
,o4 |
|
15 - 19 |
50,000 |
1,000 |
|
20 - 24 |
60,000 |
7,000 |
|
25 - 29 |
45,000 |
8,000 |
|
30 - 34 |
40,000 |
5,000 |
|
35 - 39 |
30,000 |
900 |
|
40 - 44 |
25,000 |
100 |
|
45 - 49 |
20,000 |
50 |
24. ,a6oX doY >eyartod /d)ad b otn > o doO.
|
25. X> A sa oS X, tyaSo rtora ,>a,oXd o XodoaoO : -e v ti o <=t | ||||||||||||||||||||
|
26. X> A ya< S,ert 5 drrt > <a , da, Ort > o XooaoO :
|
6 | |
|
2000 |
10 |
|
2001 |
15 |
|
2002 |
18 |
|
2003 |
21 |
|
2004 |
25 |
|
2005 |
30 |
|
2006 |
33 |
|
2007 |
40 |
|
2008 |
50 |
27. odo ddddd, d)d@ ,dd,O 03 3 dododod- w dddS, 500
d&rt$d, 0dOj d)n>Y
i) </d)de 3 d),rt $dod)a<
J
ii) dad 0d do 3 d do3 d ?
YJ -e
28. 4 3dd3 do.d <d dra.rt > o 64 , < aot, dAd. 3 doecdA dod >Oe3,3
6 CO 6 t S' ok
wd , oZ6rt > o dodoaoO.
29. 60 ad, n > , odo bj0Y d;/dd , oZ6oo n doa, do3o. dj/dd ,dd,O do3o ao3 a< do ddoddA 40 do3o 3 wAdo3 d. 5% <yd,dr
_o _o _o oUs,
dodS, dj/dd ,od,Odoo 35 a@o3 {db ddode 0odo dOeb.
30. X>n d.dod d3d od, 5% <yd,dr do&.dS 0ddo ,do&,rt> dd3rt>0
eJ -q-6 eJ co eo co
rtoradodrt > 0 ( I.Q. ) d> n dd dftd :
|
d .3d.,adde 0odo d Oe3,b. > > oOk | |||||||||
|
|
31. 3 d Sedo dd < do3o 3 d Sedo o3 d 5 add.arn > oa do3 _D t> * Cp -0 | ||||||||||||||||||
|
3 dSedoo add.arrt > oa do3 rtododrt > o d ,3 doe 0odo d Oe3,b.
6 * cp -0 <=t 24 -C ok
32. rtod0 doJo Xadd0 rtod JJ,do daeA X>A a,edoo
co_oco&5c{, Zs <=t
aa&.
|
d,rae>k - B | ||||||||||||||||||||
|
33. Xaod d da. 10,000 dod odo ooJ,do wd0,co odo yZFoo d. - dodo-ado dji<, da. 100 d . - adr} d rt>o
-o ZJ t li
|
rrt>3 |
>r}e> trt>o (d&.rt>0 ) ti v r? ' |
|
1 |
300 |
|
2 |
500 |
|
3 |
900 |
|
4 |
1000 |
|
5 |
1500 |
|
6 |
2000 |
|
7 |
2500 |
|
8 |
3000 |
& ooJ,do d0,deXo ?
34. d,od nd) 5 dod 6 d,ort> ,uz,0 ( X ) doJo ( R )
<=t &J co
|
&rtoo ,oZ6 |
1 |
2 |
3 |
4 |
5 |
6 |
|
,-d,Q ( X ) |
10 |
11 |
10 |
12 |
15 |
18 |
|
&d6& ( R ) |
5 |
7 |
4 |
9 |
6 |
5 |
X - X\0 aoojjra ort > 0r XodoQoO. (A 2 = 0577 0odo aead )
- D
IV. /d)d 0do 44 Oft : 2 x 10 = 20
35. X> 3oQo 0dd TO,drt> ao3 dodra drt > r XodQo, e&ft :
co
| ||||||||||||||||||||||||||||||||||
|
36. X> ft oQoti do3o ds*r _0 _D S | ||||||||||||||||||||||||||||||||||
6 <=i
|
&rt>3 -C |
zS ( df.) | |||
|
2005 |
2008 |
2005 |
2008 | |
|
A |
10 |
12 |
5 |
7 |
|
B |
20 |
21 |
6 |
9 |
|
C |
5 |
6 |
2 |
5 |
|
D |
8 |
8 |
5 |
6 |
|
37. X> A y< ,ert y = a + bx d , d> deo doo , dooft do3o rt>o XodQoO : | ||||||||||||||||
|
2009 e d rd d/d&d o oraft.
<=t
38. odo 1000 adrrt> ,ro,O Jdd) 55 S.mp do Jo aoJ ao 3 S.np dj,d/w aJd}00, 0,D,'0 d.
6 <=t -0
i) 48 S.njOrt $AoJ dado
ii) 57 3.ns,o do Jo 65 3.ns,ort > dod
iii) 60 S.njOrt $AoJ o
J>dd)> adFrt > , oZ6rt > r dodoaoO.
>ri - E
V. d>A zd3d 0-d: drtrt Job :
2 x 5 = 10
39. oo d J o , OT, O 2 rfeddPOJ d,0n $d /dddA WObd odo
eJ co
i) /dd dedad d ,on
ii) .odd 2 deddpOJ d >o
<=t
40. odo ra,d o 1000 , < aovbdrt J doeco.nOTA 550 , <
6 <=t & &
ad. 5% 53f do&jd d) <d)dJdAdoe 0odo 3ed/ra, de ?
41. odo n d d odo dd d ,oabd 77 d J n > o d> n dd oAd :
CO CO
|
Q |
da |
,edo |
doort> |
od |
rtodo |
a | |
|
8 |
10 |
11 |
13 |
14 |
6 |
15 |
d J n >o ddd 0o a rt> , do ddzrad ,oabdoe 0odo 5%
co co ZJ co *
oO ao co wA
42. odo d , > da&rX deaXoo 1000 wAd. d, d , > , < doo d.
_o Zs >
10 wAd. , dXort> , ort,d d ad r } d dd) ty, drX, , < do 20% dod)do. ,a&;3 ddd) d>. 100 wdd, i) wrX oX<Xd aead deaX dOd/ra
'
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. Mention a source of vital statistics.
2. The price index number for the current year is 121. Give your conclusion.
3. Write the formula for computing Laspeyres quantity index number.
4. Give an example for seasonal variation.
5. Is mean of Binomial Distribution less than variance ?
6. What is the probability that a normal variate takes a value greater than its mean ?
7. Mention a use of Standard Error.
8. What is confidence coefficient ?
9. What is the value of a fair game ?
10. Name the control chart used in case of defectives in Statistical Quality Control.
II. Answer any ten of the following questions : 10 x 2 = 20
11. In a community in a specific year 4000 live births occurred. In the case of 50 of above, the mothers died due to child birth. Compute M.M.R. ( per 1000 ).
12. Write any two limitations of index number.
13. If P01(L) = 108 and P01(P) = 110, find P01( F).
14. Define irregular variation and give an example.
15. Under what conditions does Binomial distribution tend to Poisson distribution ?
16. What are the mean and variance of Standard Normal distribution ?
17. Define size and power of a test.
18. Mention any two conditions in fitting "2 test of goodness of fit.
19. If (x : - X2) = 2-7 and SE (x : - X2) = 1-3 what would you conclude at 5% level of significance for right tail test ?
20. Define Linear Programming Problem.
21. If the depreciation cost and the cumulative maintenance cost for an equipment for the second year are Rs. 10,000 and Rs. 10,200 respectively, what is the annual average cost ?
22. Mention two types of causes for variation in a manufacturing process.
III. Answer any eight of the following questions : 8 x 5 = 40
23. From the following data calculate Total Fertility Rate :
|
Age ( Yrs.) |
Female Population |
No. of Live Births |
|
15 19 |
50,000 |
1,000 |
|
20 24 |
60,000 |
7,000 |
|
25 29 |
45,000 |
8,000 |
|
30 34 |
40,000 |
5,000 |
|
35 39 |
30,000 |
900 |
|
40 44 |
25,000 |
100 |
|
45 49 |
20,000 |
50 |
24. Mention any five steps in the construction of index numbers.
25. Calculate Paasches Quantity Index number from the following data :
|
Items |
A |
B |
C |
D |
|
Base year Quantity |
10 |
7 |
5 |
10 |
|
Current year Quantity |
11 |
8 |
7 |
15 |
|
Current year Price |
50 |
30 |
20 |
10 |
26. Find 5 yearly moving averages for the following time series
|
Year |
Value |
|
2000 |
10 |
|
2001 |
15 |
|
2002 |
18 |
|
2003 |
21 |
|
2004 |
25 |
|
2005 |
30 |
|
2006 |
33 |
|
2007 |
40 |
|
2008 |
50 |
27. In a textbook, on an average 0-3 mistake per page is found. If there are 500 pages in that textbook, in how many pages will there be
i) no mistakes
ii) at least two mistakes ?
28. 4 unbiased coins are tossed 64 times. Calculate the expected frequencies for the number of heads obtained.
29. On 60 different days the numbers of passengers in a bus were noted. The mean & S.D. of the number of passengers was found to be 40 and 3 respectively. At 5% level of significance, test the hypothesis that the mean number of passengers in the bus is more than 35.
30. For the following data test whether there is any significant difference in the population proportion at 5% level of significance :
|
Size |
Proportion | |
|
Sample I |
100 |
0-02 |
|
Sample II |
110 |
0-01 |
|
31. I.Q. of 5 students before & after training are given below : | ||||||||||||||||||
|
Test whether the training of students increases I.Q. ( Take a = 1% )
32. Solve the following game by maximin-minimax principle :
|
Player B | |||||
|
Bi |
b3 |
B4 | |||
|
A |
0 |
5 |
4 |
2 | |
|
Player A |
A2 |
- 1 |
0 |
- 2 |
- 3 |
|
A3 |
- 3 |
1 |
- 3 |
0 | |
33. A factory is thinking of replacing a machine whose purchase price is Rs. 10,000. Its resale value is Rs. 100. The maintenance costs are given below :
|
Year |
Maintenance Cost ( Rs. ) |
|
1 |
300 |
|
2 |
500 |
|
3 |
900 |
|
4 |
1000 |
|
5 |
1500 |
|
6 |
2000 |
|
7 |
2500 |
|
8 |
3000 |
When should the machine be replaced ?
|
5 each : | |||||||||||||||||||||
|
Find the control limits for X-chart. ( Given A2 = 0 577 )
IV. Answer any two of the following questions : 2 x 10 = 20
35. For the following two villages compute Standardized Death Rates & comment :
|
Age ( Yrs.) |
Standard Population |
Village A |
Village B | ||
|
Population |
Deaths |
Population |
Deaths | ||
|
0 20 |
20,000 |
8,000 |
128 |
4,000 |
72 |
|
20 50 |
30,000 |
13,000 |
65 |
9,000 |
54 |
|
50 70 |
35,000 |
10,000 |
140 |
7,000 |
98 |
|
70 & above |
15,000 |
4,000 |
252 |
3,000 |
129 |
36. Calculate Dorbisch-Bowley and Marshall-Edgeworth price index numbers for the following data :
|
Items |
Price ( Rs. ) |
Quantity | ||
|
2005 |
2008 |
2005 |
2008 | |
|
A |
10 |
12 |
5 |
7 |
|
B |
20 |
21 |
6 |
9 |
|
C |
5 |
6 |
2 |
5 |
|
D |
8 |
8 |
5 |
6 |
37. For the following time series fit a linear trend of the type y = a + bx and obtain trend values :
|
Year |
Sales |
|
2001 |
80 |
|
2002 |
100 |
|
2003 |
110 |
|
2004 |
120 |
|
2005 |
140 |
|
2006 |
150 |
|
2007 |
168 |
Estimate the sales in 2009.
38. The weights of 1000 students are normally distributed with mean 55 kg & standard deviation 3 kg. Find the number of students with weight
i) less than 48 kg
ii) between 57 kg & 65 kg
iii) more than 60 kg.
SECTION - E
V. Answer any two of the following questions
39. On an average a box contains 2 defective items. Find the probability that a randomly selected box has
i) no defective items
ii) at the most 2 defective items.
40. A coin is tossed 1000 times and head turns up 550 times. Can we conclude at 5% level of significance that the coin is unbiased ?
41. 77 accidents that have occurred in a city in a week are given below :
|
Day |
Sun |
Mon |
Tue |
Wed |
Thu |
Fri |
Sat |
|
Accidents |
8 |
10 |
11 |
13 |
14 |
6 |
15 |
Test at 5% level of significance that the accidents occur uniformly throughout the week.
42. The annual demand for an item is 1000 units. Capital cost is Rs. 10 per unit. Inventory carrying cost is 20% of capital cost per annum. If set-up cost is Rs. 100, determine
i) EOQ
ii) Minimum annual average cost.
|
Attachment: |
| Earning: Approval pending. |
