(4) n + 1. n+1. (1) 2n 1 (2) 2 (3) n 1 2 (1) 1 (2) 3 (1) 23 (2) 25 (3) 27 (4) 30

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1 CHCK YOUR GRASP STATISTICS XRCIS-I Arthmetc mea, weghted mea, Combed mea. Mea of the frst terms of the A.P. a, (a + d), (a + d),... s- a d () ( )d a a + ( ) d a + d. The A.M. of frst eve atural umber s - ( + ) () +. The A.M. of C 0, C, C,... C s - () If the mea of umbers 7,, 89, 07, s 8, the the mea of umbers 0,, 8, 0, wll be- 80 () If the mea of observatos,,... s, the the sum of devatos of observatos from mea s :- 0 (). I a frequecy dst., f d s devato of varates d from a umber ad mea = +, the s :- Lower lmt () Assumed mea Number of observato Class terval. The A.M. of observato s. If the sum of observatos s K, the the mea of remag observatos s- K K () K ( )K. The mea of values,,,... whch have frequeces,,,... resp., s :- (). The sum of squares of devato of varates from ther A.M. s always :- Zero () Mmum Mamum Nothg ca be sad. If the mea of followg feq. dst. s., the the value of f s :- Noe of these. The mea of 9 terms s. f oe ew term s f f added ad mea become, the the value of ew term s :- () () Noe of these 7. If the mea of frst atural umbers s equal to 7. The weghted mea (W.M.) s computed by the formula? 7, the s equal to- w W.M. = () W.M. 0 () w 8. oe of these w w The mea of frst three terms s ad mea of W.M. = W.M.= et two terms s 8. The mea of all the fve terms w 9. s- 8. The weghted mea of frst atural umbers whe. ().0.. ther weghts are equal to correspodg atural umber, s :- If the mea of fve observatos, +, +, + ad + 8 s, the the mea of last three () obsevatos s- () 7 ()( ) 0. The mea of a set of umbers s. If each umber Noe of these s decreased by, the mea of the ew set s- 9. The average come of a group of persos s () ad that of aother group s y. If the umber of. The mea of 0 observatos s. If ts two persos of both group are the rato :, the average come of combed group s :- observatos 0 ad are deleted, the the mea of the remag observatos s- + y + y () () + y 8 oe of these Noe of these 7 NOD ()\DATA\0\KOTA\J-ADVANCD\SMP\MATHS\UNIT#0\NG\PART-\0-STATISTICS\.X

2 NOD ()\DATA\0\KOTA\J-ADVANCD\SMP\MATHS\UNIT#0\NG\PART-\0-STATISTICS\.X 0. I a group of studets, the mea weght of boys s kg. ad mea weght of grls s kg. If the mea weght of all studets of group s kg, the the rato of the umber of boys ad grls the group s :- : () : : : Geometrc mea, Harmoc mea. The G.M. of postve terms,,... s :- (... ) () (... ) (... ) / Noe of these. The G.M. of umbers,, 0, 0, s :-.8 () Noe of these. The geometrc mea of the frst terms of the seres a, ar, ar,..., s- ar / () ar ar ( )/ ar. If G ad G are geometrc mea of two seres of szes ad resp. ad G s geometrc mea of ther combed seres, the log G s equal to :- log G + log G () log G + log G logg logg logg logg. The Harmoc mea of, 7, 8, 0, s- () The H.M. of the umbers,, s :- () / 7. The H.M. of followg freq. dst. s :- 9 f 9 () 7. Noe of these 8. A boy goes to school from hs home at a speed of km/hr. ad comes back at a speed of y km/hr. the the average speed of the boy s :- y km / hr y km / hr y () y km / hr Meda, Mode y km / hr y 9. The meda of a arraged seres of eve observatos, wll be :- () th term th term th term Mea of th terms 0. The meda of the umbers,,, 8, 0, 9,, s :- 8 () Meda of the followg freq. dst. 0 7 f () 0 8. Noe of these. Meda s depedet of chage of :- oly Org () oly Scale Org ad scale both Nether org or scale. A seres whch have umbers three 's, four 's, fve 's, eght 7's, seve 8's ad s 9's the the mode of umbers s :- 9 () 8 7. Mode of the followg freqecy dstrbuto : f : () 8 0. The mode of the followg freq. dst s :- Class f 7 8 ().8 7. Noe of these

3 Symmetrc ad asymmetrc dstrbuto, Rage. For a ormal dst :- mea = meda () meda = mode mea = mode mea = meda = mode 7. The relatoshp betwee mea, meda ad mode for a moderately skewed dstrbuto s- mode = meda mea () mode = meda mea mode = meda mea mode = meda mea 8. The rage of observatos,,, 9, 8, 7,,, 7,, s :- () 7. Mea Devato 9. The mea devato of a frequecy dst. s equal to :- d () d Varace ad Stadard Devato. The varate ad u are related by u a the h correct relato betwee ad u s :- h () h u h h u. The S.D. of the frst atural umbers s- (). The varace of observatos,, 0,, s :- 8.8 () Noe of these 7. If 0 ( ) ad 0 u ( ) 8 the the u fd f d 0. Mea devato from the mea for the observato, 0, s- () oe of these. Mea devato of the observatos 70,,,,,,,, 8, 8 from meda s :- 7.8 () Mea devato of observatos from ther mea s., the coeffcet of mea devato s :- 0. () 0.. Noe of these. The mea devato from meda s greater tha the mea devato from ay other cetral value () less tha the mea devato from ay other cetral value equal to the mea devato from ay other cetral value mamum f all values are postve S.D. of observatos,... 0 s :- () Noe of these 8. The S.D. of 7 scored,,,,,, 7 s- () 7 oe of these 9. The varace of seres a, a + d, a + d,..., a + d s :- ( ) d ( ) d () ( ) d ( ) d 0. Varace s depedet of chage of- oly org () oly scale org ad scale both oe of these NOD ()\DATA\0\KOTA\J-ADVANCD\SMP\MATHS\UNIT#0\NG\PART-\0-STATISTICS\.X

4 . If the coeffcet of varato ad stadard devato of a dstrbuto are 0% ad 0 respectvely, the ts mea s- 0 () 0 0 Noe of these. If each observato of a dst. whose S.D. s, s creased by, the the varace of the ew observatos s - () + +. The varace of,,, 8, 0 s- 8 () 8 oe of these. If each observato of a dst., whose varace s, s multpled by, the the S.D. of the ew ew observatos s- (). The stadard devato of varate s. The stadard devato of the varate where a, b, c are costats s- a c a c a () c a Noe of these b, c NOD ()\DATA\0\KOTA\J-ADVANCD\SMP\MATHS\UNIT#0\NG\PART-\0-STATISTICS\.X ANSWR-KY CHCK YOUR GRASP XRCIS-I Que As. Que As. Que As. 7

5 BRAIN TASRS STATISTICS XRCIS-II. The A.M. of the seres,,, 8,,..., s- (). If the mea of observatos,,,... s 9. The observatos 9,, 8, 0,, +, 7, 78, 8, 9 are arraged ascedg order ad ther meda s the the value of s :- (). 0. If the mode of a dstrbuto s 8 ad the mea s 8 (), the s equal to- (). The weghted mea of frst atural umbers whose weghts are equal, s :- () ( ) ( ). The average age of a group of me ad wome s 0years. If average age of me s ad that of wome s 7, the the percetage of wome the group s- 0 () The geometrc mea of the observatos,, 8,,, s- / () 7/ Noe of these. The H.M. of the recprocal of frst atural umbers s :- ()... Noe of these 7. Product of postve umbers s ut. The sum of these umbers ca ot be less tha- () oe of these 8. The A.M. of frst terms of the seres..,..7,.7.9,..., s () If the mea ad S.D. of observatos,,... are ad resp, the the sum of squares of observatos s :- ( + ) () ( ) ( ) Noe of these. The varace of observatos 8,,,,, s :- ().. Noe of these. If the mea of a set of observatos,,..., 0 s 0, the the mea of +, + 8, +,..., 0 + 0, the meda s- s- () 8 0. The mea of values 0,,,..., whe ther weghts are, C, C,..., C, resp., s () ( ). The G.M. of frst atural umbers s :- () (!) (!) / Noe of these. If a varable takes the dscrete values +, 7,,,, +,, + ( > 0), the the meda of these values- () 7. The S.D. of frst odd atural umbers s :- () NOD ()\DATA\0\KOTA\J-ADVANCD\SMP\MATHS\UNIT#0\NG\PART-\0-STATISTICS\.X

6 8. If the sum ad sum of squares of 0 observatos are ad 8 resp., the, The S.D. of observatos s :- () 9. The mea of values of a dstrbuto s. If ts frst value s creased by, secod by,... the the mea of ew values wll be- () / + Noe of these 0. The mea of the seres,,..., s X. If s replaced by, the the ew mea s- X () X 7. The S.D. of the followg freq. dst. :- Class f 7.8 () The mea of a dst. s. f ts coeffcet of varato s 8%. The the S.D. of the dst. s :-. ().. Noe of these 9. The mea of a set of observatos s. If each observato s dvded by, ( 0) ad the s creased by 0, the the mea of the ew set s 0 () 0 0 NOD ()\DATA\0\KOTA\J-ADVANCD\SMP\MATHS\UNIT#0\NG\PART-\0-STATISTICS\.X ( )X X. Let G ad G be the geometrc meas of two seres,,..., ad y, y... y respectvely. If G s the geometrc mea of seres /y, =,,...,, the G s equal to- G G () log G /log G log (G /G ) G /G. The mea devato of the umbers,,,, s- 0 ()... If mea = ( meda mode), the the value of s- () / /. A ma speds equal ammout o purchasg three kds of pes at the rate Rs/pe, 0 Rs/pe, 0 Rs/pe, the average cost of oe pe s :- 0 Rs () Rs 0 Rs 7 Noe of these. The meda of observato s 0. f each observatos greater tha the meda are creased by, the the meda of the observatos wll be- 0 () + 0/ 0/. The coeffcet of rage of the followg dstrbuto 0,,, 9, 8,, 0. () The average age of a teacher ad three studets s 0 years. If all studets are of equal age ad the dfferece betwee the age of the teacher ad that of a studet s 0 years, the the age of the teacher years () 0 years years years. If a, b, c are ay three postve umbers, the the least value of (a + b+ c) a b c () 9 Noe of these. Meda of C 0, C, C,..., C (whe s eve) s- C () C C Noe of these. The mea devato from mea of observatos, 0,, 0,...8 s :-.7 () Noe of these. If stadard devato of varate s 0, the varace of the varate ( 0 + ) wll be- 0 () s- s-

7 . The S.D. of the umbers,,,... 7 s- () 7 Noe of these. The sum of the squares of devato of 0 observatos from ther mea 0 s 0, the coeffcet of varato s- 0% () 0% 0% Noe of these 7. The meda ad stadard devato (S.D.) of a dstrbuto wll be, If each term s creased by - meda ad S.D. wll creased by () meda wll creased by but S.D. wll rema same meda wll rema same but S.D. wll creased by meda ad S.D. wll rema same 8. If X ad X are the meas of two seres such that X < X ad X s the mea of the combed seres, the- X < X () X > X X < X < X X = X X 9. The meda of 9 observatos of a group s 0. If two observatos wth values 8 ad are further cluded, the the meda of the ew group of observato wll be 8 () 0 0. The coeffcet of mea devato from meda of observatos 0,,, 90, 8, 7 s :-. () 0. Noe of these. A group of 0 observatos has mea ad S.D.. aother group of 0 observatos has mea ad S.D., the the S.D. of combed group of 0 observatos s :- () Noe of these. For the values,... 0 of a dstrbuto < < <... < 00 < 0. The mea devato of ths dstrbuto wth respect to a umber k wll be mmum whe k s equal to- () I ay dscrete seres (whe all the value are ot same) the relatoshp betwee M.D. about mea ad S.D. s- M.D. = S.D. () M.D. > S.D. M.D. < S.D. M.D. S.D. ANSWR-KY BRAIN TASRS XRCIS-II Que As. Que As. Que. As. 0 NOD ()\DATA\0\KOTA\J-ADVANCD\SMP\MATHS\UNIT#0\NG\PART-\0-STATISTICS\.X

8 PRVIOUS YAR QUSTIONS STATISTICS XRCIS-III NOD ()\DATA\0\KOTA\J-ADVANCD\SMP\MATHS\UNIT#0\NG\PART-\0-STATISTICS\.X. The mea of Mathematcs marks of 00 studets of a class s 7. If the umber of boys s 70 ad the mea of ther marks s 7. The the mea of the marks of grls the class wll be- [AI-00] 0 () 8. I a epermet wth observatos of, the followg results were avalable = 80, = 70. Oe observato that was 0 was foud to be wrog ad t was replaced by t's correct value 0. The the corrected varace s- [AI-00] 8. () The mea ad varace of a radom varable X havg a bomal dstrbuto are ad respectvely. The P(X = ) s- [AI-00] () 8. The meda of a set of 9 dstct observatos s 0.. If each of the largest four observatos of the set s creased by, the the meda of the ew set- [AI-00] remas the same as that of the orgal set () s creased by s decreased by s two tmes the orgal meda. Cosder the followg statemets- [AI-00] (a) Mode ca be computed from hstogram (b) meda s ot depedet of chage of scale (c) varace s depedet of chage of org ad scale whch of these are correct- oly (a) ad (b) () oly (b) oly (a) (a), (b) ad (c). I a seres of observatos, half of them equal a ad remag half equal a. If the stadard devato of the observatos s, the a equals- () [AI-00] 7. The mea ad the varace of a bomal dstrbuto are ad respectvely. The the probablty of sucesses s- [AI-00] 8 () If a frequecy dstrbuto, the mea ad meda are ad respectvely, the ts mode s appromately- [AI-00].0 () Let,,..., be observatos such that 00 ad 80. The a possble value of amog the followg s- [AI-00] () Suppose a polulato A has 00 observatos 0, 0, ad other polulato B has 00 observatos,, If V A ad V B represet the varace of two populato respectvely the V V A B s- [AI-00] 9/ () /9 /. The average marks of boys a class ad that of grls s. The average marks of boys ad grls combed s 0 the the parcetage of boys the class s- [AI-007] 0 () The mea of the umbers a, b, 8,, 0 s ad the varace s.80 the whch oe of the followg gves possble values of a ad b? [AI-008] a = 0, b = 7 () a =, b = a =, b = a =, b =. Statemet : The varace of frst eve atural umbers s. Statemet : The sum of frst atural umbers s ( ) ad the sum of squares of frst atural umbers s ( ) ( ). [AI-009] Statemet s true, Statemet s false. () Statemet s false, Statemet s true. Statemet s true, Statemet s true ; Statemet s a correct eplaato for Statemet. Statemet s true, Statemet s true ; Statemet s ot a correct eplaato for statemet.

9 . If the mea devato of the umbers, + d, + d,..., + 00d from ther mea s, the that d s equal to :- [AI-009] 0. () For two data sets each of sze s, the varaces are gve to be ad ad the correspodg meas are gve to be ad respectvely, the the varace of the combed data set s :- () [AI-00]. If the mea devato about the meda of the umbers a, a,..., 0a s 0, the a equals:- [AI-0] () 7. A scetst s weghg each of 0 fshes. Ther mea weght worked out s 0 gm ad a stadard devato of gm. Later, t was foud that the measurg scale was msalged ad always uder reported every fsh weght by gm. The correct mea ad stadard devato ( gm) of fshes are respectvely : [AI-0] 8, (),, 8, 8. Let,,..., be observatos, ad let be ther arthmetc mea ad be ther varace. Statemet : Varace of,,..., s. Statemet : Arthmetc mea of,,..., s. [AI-0] Statemet s true, Statemet s false. () Statemet s false, Statemet s true. Statemet s true, Statemet s true ; Statemet s a correct eplaato for Statemet. Statemet s true, Statemet s true ; Statemet s ot a correct eplaato for Statemet. PRVIOUS YARS QUSTIONS ANSWR-KY XRCIS-III Q u e A s Q u e. 7 8 A s NOD ()\DATA\0\KOTA\J-ADVANCD\SMP\MATHS\UNIT#0\NG\PART-\0-STATISTICS\.X