Reg. No. :... Sub. Code : R 4 AC 4/ R 4 AR 4/R 4 AN 4/ R 4 AV 4/B 4 AC 4/ B 4 AR 4/B 4 AN 4/B 4 AV 4 B.Com. (CBCS) DEGREE EXAMINATION, NOVEMBER 2014. Fourth Semester Commerce Allied BUSINESS STATISTICS (Also common to B.Com. Computer Application/ B.Com. Vocational Computer Application/ B.Com. Corporate Secretaryship) (For those who joined in July 2008-2011) Time : Three hours Maximum : 75 marks PART A (10 1 = 10 marks) Answer ALL questions. Choose the correct answer : 1. ÒÎ À Põm õk A  zv ß Esø õú ö Ûuº (A) éº (B) Põì (C) ö Í» (D) PõºÀ ºéß
Ws5 The real giant in the development of the theory of statistics is (a) Fisher (b) Gauss (c) Bowley (d) Karl Pearson 2. B ÂÀ EÒÍ ÊzöuõSv iáøóuõp C US õx õ ß kzu Ási øó (A) TöÓk øó (B) ÊUPnUöPk øó (C) ÊUPnUöPk AÀ»x TÖ øó CÁØÔÀ H uý JßÖ (D) CÁØÔÀ GxÄ CÀø» When population under investigation is infinite we should use the (a) sample method (b) census method (c) either census or sample method (d) none of these 3. J ªu õú \ a^μøó μá¼à (A) T.\. << ö.\. < C.\. (B) T.\. > ö.\. > C.\. (C) ö.\. < T.\. < C.\. (D) C.\. < T.\. < ö.\. Page 2
In a moderately assymetrical distribution (a) A.M. < G.M. < H.M. (b) (c) (d) A.M. > G.M. > H.M. G.M. < A.M. < H.M. H.M. < A.M. < G.M. 4. s öuõhº õú upáàpøíu øp õðáuøpõú ]Ó u \μõ\ (A) Pk (B) Cøh{ø» (C) ö UPØ \μõ\ (D) Tmka \μõ\ For dealing with qualitative data, the best average is (a) mode (b) median (c) geometric mean (d) arithmetic mean 5. {PÌuPÄ øç Gß x (A) 0.6754 vmh øç (B) 0.6745 vmh øç (C) 0.6753 vmh øç (D) 0.6475 vmh øç Probable error is (a) 0.6754 S.E. (b) 0.6745 S.E. (c) 0.6753 S.E. (d) 0.6475 S.E. Page 3
Ws5 6. X ØÖ Y BQ CμskUS uzu \μõ\ Pμ x ö ØÓ Â»UP[PÎß ö USz öuõøp ß TmkzöuõøP ä GÛÀ, JmkÓÄU öpêáõúx (A) +1 (B) 1 (C) 0 (D) CøÁ GxĪÀø» If the sum of products of deviations of X and Y from their means is zero, the correlation coefficient shall be (a) +1 (b) 1 (c) 0 (d) None of these 7. {PÌuPÄU öpõòøp À AvP AÍ»õÚ A  zv²hß öuõhº øh Áº (A) éº (B) PõºÀ º\ß (C) ì (D) Põém Much of the development in the theory of probability is associated with (a) Fisher (b) Karl Pearson (c) Bayes (d) Gosset Page 4
8. C {PÌÄPÒ \õº ØÓøÁ GÛÀ CøÁ Cøn x {PÌÁuØPõÚ {PÌuPÄ (A) P A P B (B) P A P B P AB (C) P A P B (D) P A P B If two events are independent, then the probability of their joint occurrence is given by (a) P A P B (b) P A P B P AB (c) P A P B (d) P A P B 9. Ámha \õuøú {øóä ö ÖÁx G õx? (A) P P P 1 (B) P P P 0 12 23 31 Page 5 12 23 31 (C) P P P 1 (D) P P P 0 12 23 21 Circular test is satisfied when 13 23 31 (a) P P P 1 (b) P P P 0 12 23 31 12 23 31 (c) P P P 1 (d) P P P 0 12 23 21 13 23 31
Ws5 10. 2 a bx cx GßÓ Aø öpõsh J ß ia Y \ ß õk CÆÁõÖ AøÇUP kqóx (A) C ia \ ß õk (B) º Põmka \ ß õk (C) ßÖ ia \ ß õk (D) CøÁ GxĪÀø» A polynomial of the form Y a bx cx is called (a) second degree equation (b) linear equation (c) third degree equation (d) none of these PART B (5 5 = 25 marks) Answer ALL questions, choosing either (a) or (b). Answer should not exceed 250 words. 2 11. (A) ÒÎ ¼ß Áøμ øó u P. Auß UQ a ö\ À õkpøíu SÔ kp. Define statistics. Mention its important applications. (B) upáàpøí õs õk ö\ Áuß ÁøPPøÍU TÖP. State the various types of classification of data. Page 6
12. (A) J ]Ó u \μõ\ ß ußø PøÍ ÂÍUSP. Explain the properties of a good average. (B) ßÁ μá¾us Pk PnUQkP : CÚzvß AÍÄ, x : 0 5 5 10 10 15 15 20 20 25 Aø»öÁs, f : 20 24 32 28 CÚzvß AÍÄ, x : 25 30 30 35 35 40 40 45 Aø»öÁs, f : 16 37 10 8 Compute the mode of the following distribution : Size of item, x : 0 5 5 10 10 15 15 20 20 25 Frequency, f : 20 24 32 28 Size of item, x : 25 30 30 35 35 40 40 45 Frequency, f : 16 37 10 8 13. (A) ]uóà ÂÍUP h GßÓõÀ GßÚ? õôpðuqøh EÒÍ JmkÓøÁ AÔÁuØS Ax GÆÁõÖ EuÄQÓx? What is scatter diagram? How does it help us in studying correlation between two variables? Page 7
Ws5 (B) C õh[pîà 10 õnáºpò ö ØÓ v ö spðus Cøh EÒÍ uμ JmkÓÄU öpê 0.2 GÚ PshÔ mhx. BÚõÀ C õh[pðuqøh J õnẠö ØÓ uμ[pîß Âzv õ\ 7 Gß uøs v»õp 9 GÚ uáóõp GkUP mhx Psk iup mhx. \ õú uμ JmkÓÄU öpê GÆÁÍÄ? The coefficient of rank correlation of the marks obtained by 10 students in two subjects was found to be 0.2. But, it was detected that the difference in ranks in the two subjects obtained by one of the students was wrongly taken as 9 instead of 7. What should be the correct rank correlation coefficient? 14. (A) J PoÛ x ØÖ y BQ ÁØÖUQøh EÒÍ JmkÓÄU öpêøáu PnUQk õx ßÁ {ø»ö spøí ö ØÓx; n 30 ; x 120 ; x 2 600 ; y 90, y 2 250 ; xy 356. C Ý ßÚº \ õºus õx, Cμsk upáàpøí CÆÁõÖ μvö kzux. x y 8 10 12 7 Page 8
BÚõÀ AÁØÔß \ õú v PÒ CøÁ õs x y 8 12 10 8 x ØÖ y BQ ÁØÔØQøh EÒÍ \ õú JmkÓÄU öpêøá ö ÖP. A computer while calculating the correlation coefficient x and y obtained the following constants : n 30 ; x 120 ; x 2 600 ; y 90, y 2 250 ; xy 356. It was however, later discovered at the time of checking that it copied down two parts of observation : x y 8 10 12 7 while the correct values were x y 8 12 10 8 Obtain the correct value of the coefficient of correlation between x and y. Page 9
Ws5 (B) ßÁ upáàpî¼ x Jzvø\Ä Â»UP PshÔP áú μ õº H μ áüß x : 8.5 9.2 9.3 8.5 7.2 5.9 y : 60 65 61 74 92 157 áüø» BP ö\ AU Á i\ x : 5.1 6.6 7.7 7.6 8.2 9.2 y : 130 106 58 80 52 45 Compute the coefficient of concurrent deviation between x and y Months : Jan Feb Mar Apr May Jun x : 8.5 9.2 9.3 8.5 7.2 5.9 y : 60 65 61 74 92 157 Months : Jul Aug Sep Oct Nov Dec x : 5.1 6.6 7.7 7.6 8.2 9.2 y : 130 106 58 80 52 45 15. (A) R Ç uμ mkòí \[Q¼z öuõhº AiU SÔ±möhsPøÍ {ø» õú Ai øhu SÔ±möhsPÍõP õøöp. Á h : 2004 2005 2006 2007 2008 \[Q¼z öuõhº AiU SÔ±möhs : 80 110 120 90 140 Page 10
From the chain index numbers given below prepare fixed base index numbers Year : 2004 2005 2006 2007 2008 Chain base index numbers : 80 110 120 90 140 (B) 2002 B Bsøh Ai øh õpu öpõsk J ö õ Îß ö õzu Âø»U SÔ±möhsPÒ R Ç uμ mkòíú. Á h : 2002 2003 2004 2005 2006 2007 2008 SÔ±möhsPÒ : 100 120 190 200 206 230 300 2005 B Bsøh Ai øh õpu öpõsh J v öuõhøμ Aø UP. Taking 2002 as base, the index numbers of wholesale prices of a commodity are given below : Year : 2002 2003 2004 2005 2006 2007 2008 Index Nos. : 100 120 190 200 206 230 300 Construct a new series taking 2005 as base. Page 11
Ws5 PART C (5 8 = 40 marks) Answer ALL questions, choosing either (a) or (b). Answer should not exceed 600 words. 16. (A) ÒÎ À ÂÁμ[PøÍ μv ¼zxU Põmh À ÁÖ C õn ÂÍUP h[pøí ÂÁ UP. Describe the various types of twodimensional diagrams for representation of statistical data. (B) ßÁ upáàpøíz us u mi À ÁiÂÀ ßøÁUP. 2006 B BsiÀ Kº Bø» À ö õzu EÒÍ 3500 öuõè»õîpîà 2400 º J öuõèø\[pzvß A[PzvÚºPÍõP C uúº. ö s öuõè»õîpîß GsoUøP 400 BS. AvÀ 350 º öuõèø\[pzøua \õº uáº& PÍÀ»º. 2007 B BsiÀ öuõèøpçp Áø» õmpîß GsoUøP 3160 BP E º ux. AvÀ 2580 º BsPÒ 2008 B BsiÀ öuõèø\[pzøua \º u öuõè»õíºpò 3600 öuõèø\[pzvà \μõu 400 C uúº. 2008CÀ EÒÍ AøÚzx öuõè»õíºpî¾ 600 ö spò C uúº. AÁºPÎÀ 20 º mk öuõèø\[pzvà \μõuáºpò BÁº. Page 12
Present the following information in a suitable tabular form : In 2006 out of a total of 3500 workers of a factory. 2400 were members of a trade union. The number of women employees was 400 of which 350 did not belong to a trade union. In 2007 the number of union workers increased to 3160 of which 2580 were men. On the other hand, the number of non-union workers fell to 416 of which 56 were women. In 2008 there were 3600 workers who belonged to a trade union and 400 who did not belong to a trade union. Of all the workers in 2006, 600 were women of whom only 20 did not belong to a trade union. 17. (A) R Ç uμ mkòí upáàpî¼ x Y «uõú X ØÖ X «uõú Y BQ öuõhº õusa \ ß õkpøíu PnUQkP. Âø» (¹.) : 10 12 13 12 16 15 uøá õú öuõøp : 40 38 43 45 37 43 Âø» ¹. 20 BP C US õx C UPU Ti uøáø v kp. Page 13
Ws5 Calculate the two regression equations of X on Y and Y on X from the data given below, taking deviations from actual means of X and Y Price (Rs.) : 10 12 13 12 16 15 Amount demanded : 40 38 43 45 37 43 Estimate the likely demand when the price is 20. (B) ßÁ mi ¼¼ x, PõºÀ º\Ûß øó À JmkÓÄU öpêøáu PnUQkP. X : 6 2 10 4 8 Y : 9 11? 8 7 X ØÖ Y öuõhº\îß Tmka \μõ\ øó 6 ØÖ 8 BS. From the following table, calculate the coefficient of correlation by Karl Pearson s method. X : 6 2 10 4 8 Y : 9 11? 8 7 Arithmetic mean of X and Y series are 6 and 8 respectively. Page 14
18. (A) J ø 10 xpøíu öpõskòíx. AÁØÔÀ Cμsk ]Á, ßÖ Fuõ ØÖ 5 P õs. \ Áõ øó À ø ¼ x ßÖ xpò GkUP mhú. ßÁ ÁÚÁØÔØS {PÌuPÄ GßÚ? (i) ßÖ xpð öáæ ÁÖ {Ó[PÒ (ii) C xpò J μ {Ó (iii) AøÚzx xpð J μ {Ó. A bag contains ten balls. Two of which are red, three blue and five black. Three balls are drawn at random from the bag, that is, every ball has an equal chance of being included in the three. What is the probability that : (i) the three balls are of different colours, (ii) the two balls are of the same colour, and (iii) the balls are all of the same colour. (B) C PøhPÒ E mh mhú. ßÁ ÚÁØÔØS {PÌuPÄ PshÔP. (i) PøhPÎß «uõú GsoUøP ö õzu 8 (ii) PøhPÎß «uõú GsPÎß ö õzu 8US AvP Page 15
Ws5 (iii) C PøhPÐ J μ Gsøn Põs UQßÓÚ (iv) PøhPÎß «uõú GsPÎß ö õzu 13 (v) PøhPÎß «uõú GsPÎß ö õzu 5US SøÓÄ. Two dice are thrown, find the probability that (i) the total of the numbers on the dice is 8 (ii) the total of the numbers on the dice is greater than 8 (iii) both the dice show the same numbers (iv) the total of the numbers on the dice is 13 (v) the total of the numbers on the dice is less than 5. 19. (A) 52 ^mkpò öpõsh ßÓõPU Pø»UP mh ^mkupmk JßÔ¼ x C ^mkpò \ Áõ øó À GkUP mhú. AøÁ (i) (ii) Cμsk HéõP Cμsk ]Á õp (iii) SøÓ ux J HéõP C uøpõú {PÌuPÄ GßÚ? Page 16
Two cards are drawn at random from a wellshuffled pack of 52 cards. What is the probability that : (i) both are aces, (ii) both are red, (iii) at least one is an ace? (B) J ÒÎ À PnUS A, B ØÖ C GßÓ ßÖ õnáºpðus uμ mhx. AUPnUøPz wº uøpõú AÁºPÐøh Áõ øó 1/5, 1/3 ØÖ 2/3 BS. PnUøPz wºä ö\ ÁuØPõÚ {PÌuPÄ GßÚ? (i) AÁºPÎÀ SøÓ u m\ J Áº (ii) AÁºPÎÀ J Á ªÀø» (iii) AÁºPÒ AøÚÁ PnUøPz wºä ö\ ÁuØPõÚ {PÌuPÄ GßÚ? A problem in Statistics is given to three students, A, B and C whose chances of solving it are 1/5, 1/3 and 2/3 respectively. What is the probability that the problem will be solved by (i) at least one of them (ii) none of them (iii) all of them. Page 17
Ws5 20. (A) ßÁ upáàpðus J º Põmøh ö õ zv 2010 BsiØPõÚ ÂØ øúø v kp. Á h : 2000 2001 2002 2003 2004 2005 2006 2007 ÂØ øú : 100 105 109 96 102 108 112 114 Fit a straight line to the following data and estimate the sales for the year 2010 : Year : 2000 2001 2002 2003 2004 2005 2006 2007 Sales : 100 105 109 96 102 108 112 114 (B) «a]ö ÁºUP øó À õus v PøÍU PshÔ x 2008 B BsiØPõÚ EØ zvø v kp. Á h : 2001 2002 2003 2004 2005 2006 2007 EØ zv : 9 12 14 16 20 26 35 Fit the trend values by the method of least squares and estimate the production for the year 2008 : Year : 2001 2002 2003 2004 2005 2006 2007 Production : 9 12 14 16 20 26 35 Page 18