shodhganga.inflibnet.ac.inshodhganga.inflibnet.ac.in/bitstream/10603/35100/15/15_appendix.pdf ·...
TRANSCRIPT
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l h1'11 !l' 1<-~ r.n,~l<l r-1-~h'IU J-m
( ) "hli-a Zi: lnlt~ ilnlt t'~-1P~1'1t
( ) ·~ 'ilb n·~ ZZ ll'hiJ U•H1_1-)bl<l: 01 1<-1'1t 11>~
( ) · ~ ~tl<e lJl ZZ llltiJ lrtHtl;lbl<l: L 1'~>1P~1'1t ( ) ·~ J1o ZZ llltl[) lr'~-~tl;lbl<l: Sl !'~-~
"tH 3~h l>1'1i'l(] llltJE) U-aJ'It1'~>ltlr ]'lt}t>3~ 1'~>1P~1'1t t"P ·~ ZZ '11-tlnlt t'~-l'~-ill;lbl<l: Sl ,..,~ t'~-1P~1'1t i~
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(45) li.l:.lih ~-1. '!],'aht~ li-'4!1 qvl-tl. onCiit<ll~ :l:ic.i~ t~t(qctl. ttl.ott (q!J(:'4. '4.:1:it HI..
(a) ~ = G
(b) G;::: X (c) x::;; G
(d) G::;; X
(46) qoCf4ct li.tr\$dl.-tl. '!J,~tht~ li-'4!1 ~u~qt-1 ttl.ott ~,t '4.:1:it nl..
<a> Anti loge=~ ~gxi)
(b) log(Lf; ~gx;)
(c) (Lfx·) Antilog~ xC
(d) A . 1 (Llogf;x;) nt1 og n
(47) ~~dd ~l'l@ rct~t~·~lli.l '!J,~lht~ li.l:.lih ~ttl. ?
(a) G = ~x1x2 ..... x,
(b) G = Vx1x2x3 ..... x,
(c) G=Vx1x2x3 ..... x,
I
(d) G=(x1x2x3 .... x,)"
(48) .fi'll.-ttli.ttlt '!J,~lhH li-1:.1.1.~ li-121 ~l~ fq~l-1. 3~ ?
(a) li.tr\$dl.-tt ~qc1.h-t i:t!J'l ~l,_~tt ~ ::t'l~t <.tqc1.h-t ~h ctl. '!].~tht~ li-'4!1 uNl -1. ~t3ltt. (b) ct.fi Cl.ll"'ttl '!ll!O~ ~-1. :C'4.~ -ttll.
(c) d..fi li.t~dl.li.t c.t~t"6 ~qc:t'l.!!-tl.-tl. C:J'4.lll.ot ttctl. -ttU.
(d) ~tc:Lut.fi li.tttll ~u.l:fi mttt 0. (49) .fi'll..fi li.tr\$dl.-tl. 1>1,
0
(a) (b) 8 (c) 45 (d) 150
(50) lt~l~li.t-t-1 ~'6 li.l\{ ~~ 0 ?
(a) rct:cnt~ (b) ltli.l~ld rct'!tC-t.-1.
(c) ~htu ('q'!l(:t-t
(d) 'llQ,t[b rct'!l(:t.-1.
(51) ~3 li.t~dl.-tt ~q(:t.lb-1. 6, 6, 6, 6, 6,- 0. dl d-l.l '!l(:t-1.l3 ~2(:tl ttllt?
(a) 6 (b) 5 (c) 0 (d) (52) ltli.l~ld rct'!l(:t-t.fi Chli.d ~q'l ~h ?
(a) Jil.m ~-t t!.ltt
(b) Jil.~tl ::t'l~l iltt
(c) ~-t ~ttqt ::t'l'a t!.ltt
(d) Jil.~ll ~l..~ t!.llt
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(53) (a) (b) (c) (d) (54)
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(55) (a) (b) (c) (d) (56)
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"1.,«-1.L ~.SL<Uofi ltL~dJ. li.L2 lFiil~ltL-ti t.tl.oq ltl'4. h~ f:9 ? ~ML~
'II.Q,'-[h ~'11.~-1.
~hLU ~'11.~-1.
llltl~lrt ~'11.~-1.
qo[{,rt ltL~dJ. li.L2 ~hLU ~'11.~-t.fi OL~lrt~'l ltl2i f.lLOf.l ~?l f:9 ?
n
_ Ifi lxi -xl <5x = x c
n
n ilh ltl~dl.i '11.~-tlh q~ ~ rt-tl ~t[ ? ltl~dl.-t[ ~ct~h-t1 ~~ f;9. ltl~dl.-tl ~ct~h-tl. ~lt9l ~~ f;9. ltl~dJ.-t[ ~ct(1.lh-t1 lt~h ~ltl ~tt0Lrt f:9. ltt~dl.-tt ll~t~ ~ttl. '11.~-tth-1. !1.0' tic.Ltt -ttCI..
'II.Q.t( ~'11.(1.-tLh .fi~-tL httL ~?L ct~ uNl. UhLtt ?
Q3-QI 2
QJ +QI X IQQ
Q3-QI
Q3+Q1
Q3-QI
Q3-QI
Q3+Q1
L~d.' -(~) xC
~2Cf2 - cf1 - c~2 x C
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(S2 -St)+(n2 -nt)x n
(S2 -S1)+(n1 -n2)d x C n
(St - 82) + ( n2 - nt )d X C n
-(S1-S2)+(n2 -n1)x
n
(59) .fi~ "'S'talq<a ~l'!@ lqtH~l'il Lq«tl~ 12C1.l tlll.t ?
(a) 4
(b) 35
(c) 32
(d) 16
3 5
3
8 12 17
7 15 20
20
13
(60) ~~ JPU~lct. [q~Et-1. ltll .fi~-tlltttfi l.tLOI.t ~?l 'l.t~f. HL.
(a)
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nt(St +dt)2 +n2(S2 +d2i
nt+n2
n1(S/ +d 12) + n2(S/ +d/)
nt+n2
n2(St + dt)2 + nt(S2 + d2)2
nt +n2
n2(S/ +d12)+n1(S/ +d/)
n2 +nt
24
10
(61) ~~ct. ~l'!rtl Lqct.~~lltl ltut!s' ltut~. ~..t C!l~CH.fi Gltct. 1c£l t!.ll.t ? (a) ~~PU-t
(b) ~lil-t
(c) tl_..-1{
(d) ~l"'rl.t
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(11) (62) ~'1. [q_'blli.dlli.L ~ll<i_ftt Clls-tl t9~l hU (>ll~ <:ic.tti{(!t[ ~LI{ t9 ? (a) ~lc.fi l>ll~ ( ) (b) .{l~.{l l>ll~ ( ) (c) C31.L~.fi l>ll~ ( ) (d) "'fli.Qfi l>ll~ ( ) (63) ~C'tt.d ~l<i_@ lqd~Ql li.l2 ..{l~-tlli.Lt£1. I{LOI{ LqhC:'I.L.fi 'I.L~f.Ofi HL. (a) Q3 + M = M + Q
1 ttlli ( )
(b) QJ - Q, = M ?HI{ ( ) (c) Q3 + Q, = 2M tllli ( ) (d) Q3 - M - Q
1 - M ?-LL!i ( )
(64) ':J,<K-t.L t9~lcttUJ.l ~t<i_ftt fqd~Qt li.t2 f<Pi'i.dLh ul~ctl-;i ~?t h~ ttlli ?
Q3+Q1 (a) Q3-QI ( )
3M-2x (b) s ( )
Q3+Qt-2M (c)
Q3-QI ( )
2x-3M (d) s ( )
li.t~dl-tt ~t<i_ftt cq_d~Qtlli 3 (65) -(Q3- M) = (M -Q1) i9. ctl ~~ li.L~dl hc(l hJ.cttli ? 2
(a) ~'1. Lq'blll. ( ) (b) ~C'tt.d ( ) (c) ~Ql [q_'l>l.li. ( ) (d) f'-t~l{~ ( ) (66) ~lit lq'blll.ctt llt2 -il~-ttllita ht.tl Lq!s<='4. ~t'l{t t9 ? (a) x>M>Z ( ) (b) -
( ) Z>M>x (c) x=M=Z ( ) (d) x~M~Z ( ) (67) c.tLC3~-tl tq'blll.dL!s.fi Clli.d li.L2 .fi~-tl'i.Lt£1. h~ {q_~l-t !iLO!i i9 ? (a) -1 ~ j ~I ( ) (b) -3~j~3 ( ) (c) -1 <j<l ( ) (d) -3 <j <3 ( ) (68) ':J,C<-t.L i9~tctLUJ.l ~l<i_ftt Lqd~Ql.fi Lq'bl'i.dl li.L"Lctl !sU ~'ld-tL C31.L!ilot HctL "'iu~ ? (a) c.ttCJc{l ( ) (b) !slC{ ~1{~'1.
( ) (c) ~hl~ ( ) (d) !sLC{ li.l!r~ ( ) (69) nCx = nCy ~l!i ctl .fi~-tl (q~t-tl. it!s'l 6~ct fq~L-t 'I.L~f. Hl. (a) x + y = n ttlli ( ) (b) x/y = n
( ) (c) x.y = n tllli ( ) {d) x - y = n ( )
( ) Uc•~ l}l'tn'k 1Pb9tlc )'k'klf lll'il1: l'tHtl-)b'M: ll·Ub~ (p) ( ) 1)-)bl3n lPln'k ~llnlbcR: P·t'3n u n·u&~ (:>) ( ) U&~ lP~ nt<' lnll:'M: c1.l.1_?~1~ Pb19P t~t'3n ~ltllf 't> (q) ( ) Ub~ lr~ nrl" lnll:l<e Pbl9P 1l•t'3n ~ltllf 't> (~)
;, ~ "t"?'t!: U&~ cP)'kR: (9L) ( ) cl~1l&'i'c l~ t'3n (I -u) 1~Ub~ cP)'kR: (p) ( ) tlnlbcR: t~Pn (I -u) l~Ub~ cP)'kR: {:>) ( ) 'IJ?b1'3h lPln'k lJ'allnlbcR: l~t'3n 1 + u l~U&~cPJ'hR: (q) ( ) 1)-)bl'3h lPln'k ~lln1bcR: t~Pn u l~U&~ cP)'hR: (~)
'tH '3)'Ch ~1l!l(J hcth U-a)lt~Hil(J )'kl~~~ 1~€1lt lF~ (H)
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l nri'l ~ tl:>?~ llbl9P h~1'k1R: J'kU&~ cPJ'kR: (£L)
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'tH '3)'Ch 1<-~ lllt)!) r.nnlbcR: 1l·t'3h u 'kl1lt 1~U&~ cPJ'kR: (U) ( ) p( I +U) -~ = U.L (p) ( ) p( l-u) + ~ = U.L (:>) ( ) p(I -u) -~ = U.L (q)
' ( ) P(I+U) + ~ = U.L (~)
'tH '3)'Ch l'-1t lllt)!) r.u&~ cll)'k'R: (IL) ( )
vz: = J (p) ( ) l = J (:>) ( ) £ = J (q) ( ) ll = J (~)
l h1h u-n~ ll'kiJ ~ J tP nt'i'l ':::>vz: = 'z:::>vz (OL) (z;I)
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( ) ······x(+A 'XZ+A 'X+A (:>)
( ) ·····,(£+X 'AZ+X 'v+X (q) ( ) ····Hx ',(xx ',(x 'x (~)
l h1m lPJn, ~'IF 9~ l:U&~ cllJltl?: '\.'P h'\."il x llb19ll l:l<t ,< ,h. lt11lt r--ea U&~ cllJltlC ~tt (LL)
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(14) (85) ~.h ltl~dl..fi ~l'1_£Tl ('qct~~L.fi ltUiChltct 42 ~. :Ol-1 qo(<:{c.t.l~ IO ~ ctl Gl.lc[~ltl ~.:{ ~l:{:~ltl ~"j,s'li.
~ 2<:0. ttl~ ? (a) 47 ~.:t 37 ttl~ ( )
(b) 3 7 ~ .:t 4 7 1!.[[ ~ ( )
(c) 37.5 ~.:t 47.5 ttl~ ( )
(d) 47.5 ~.:t 37.5 tl[!{ ( )
(86) ~!s ~l'1_£Tl L<ld~~lltl -tc.t qo[ ~lq(-t,l 0, f.h qo[.fi <:lc.t.l~ 2.5 ~. ~l'1_£Tl ('qct~~l-tl -tl-tlltl -tl-tl qo[.fi ..,
I0.6 ~h ctl. ltLWlL ltt2l qo[i Gl. 14~lltl ~fs ttl~ ? (a) 35.6 ( ) (b) 33. I ( ) (c) 30.6 ( ) (d) 28.I ( ) (87) ~!s ~f'-tctlH ~dd ~l'1_@ f'Ctct~~-tl qo[ 22-26 ~1.~ dl cti ~It: ~ltl ~fs ~2<:1 ttl!i ?
(a) 22 ( ) (b) 26 ( ) (c) 21.5 ( ) (d) 26.5 ( )
(88) ~ q,~c.t..fi A ~.:t s -tl ~·wH ~"j,s'li. 4000 ~.:t 6000 ~1.~ ctlt-tl lttrats ut~.fi [qolct .fi~ ~"'fc.t. ~. dl ctlt-tl ~l~l~l-tl up{.[i. OJ.'?lhH ~2C-t.L ttl~ ?
(a) I : I ( ) (b) 2 : 3 ( ) (c) 3 : 2 ( ) (d) 3 : I ( ) (89) -a 7, 5, I3, X ~.:{ 9 -tl ~ltlct~ lJ.fA{!s 10 ~h dl X .fi Chltct ~2<:fi ttl~ ? (a) IO ( ) (b) I2 ( ) (c) 14 ( ) (d) 16 ( ) (90) ~llULl.fi ~lltl~!s '4.~'l~llltl I6 [qqll!.(f~[~ 'I{U[qc:t. OJ.~l 0, 0, 2, 2, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6,
7, 8 ~. dl ct-tl ~ltl1H lt\.li!s ~2C-t.L ttl~ ? (a) 3 ( ) (b) 4 ( ) (c) 5 ( ) (d) 6 ( ) (9I) ~!s ltl~dl.-tl [!.C-t. I 00 ~1\ClC-t.l!s-tl. 'it5l 20 Cl"ld 4, 40 Cl"ld 5' 30 Cl"ld 6 ~.:t l>t.l!s'li ~ctc:t.l!s-t 7 ~l!i
ctl. ltl~dl.-tl. ~ltt1t~ lJ.l!i~ 12c:t.l. ttl~ ?
(a) 5.3 ( ) (b) 5.4 ( ) (c) 6.I ( ) (d) 6.5 ( )
(92) 1, 2, 3, ....... n =~tc-t.-tl :Hf.G{ ~tttrTl x, 2x nx ~ ctl. ct-tl. ~ltld~ lJ.l~!s ~2c:t.l. ttl~?
(a)
(b)
(c)
(d)
(2n+l)x 3
( 2n+ 1 )x 6
(.!!. )x 2
( n +I )x 2
(
(
(
(
)
)
(93) (a) (b) (c) (d) (94) (a) (b) (c) (d) (95)
(a) (b) (c) (d) (96)
(a) (b) (c) (d) (97)
(a) (b) (c) (d) (98)
(a) (b) (c) (d)
(99)
(a) (b) (c) (d)
(15) oa X, X + 2, X + 4, X + 6, X f· K <tl li.Ui!s 11 t:!.ltt rll lttt.lt ?l~l ~ClC-t.h-tl<tl li.Ui!s ~2~l ttltt?
9 ( ) 11 ( ) 13 ( )
7 ( ) oa X, X + 2, X + 4, X + 6, X ·f 8 <tl li.Ui!s 4 t:!.ltt rll X .{]_ C1sltct ~2Efi tt.ltt ?
0 ( )
4 ( ) ( )
-2 ( ) :1m. ~q~1!f-tt ~ltlrl~ lt\4.!s 20 0. oa "H~ ~ClC-th-ttltl X C1sltct (3~~1'1.l '1.Cll lt\4.!s 22 t:!.ltt rll X ..fi C1sltct ~2Efi ttltt ? -4 ( ) -2 ( ) 4 ( ) +2 ( ) it!s Ulutlltl ~ qo[ <tt I 00 LctEUtiT~ ~t(qlrlltl olut<'l.~ ~~t-tl li.\4.!1 30 0. ~-1 6t qo[-tt 50 l<tattiT~1 it "t Lct'blt{ll.L ~ut<'l.~ ~~t-tl li.\4.!1 60 fJ ct1 ~>t:>1 qo[-tt l<tattiT~1it <lut<'l.~ ~~l-tl lt\4.!1 ~2~1 tt.ltt ?
40 ( ) 45 ( ) 48 ( ) 50 ( ) ?l'il ~L'\@ lctrl~'il'11 ~l<l:_@ ~'j.!~ 45, 40 ~ot 15 <tllt\4.!s ~'j.!ot 2, 2.5 ~ot 2 0. rll ?l~l ~q~1!f-t<tl ~-81. lt\.!{!s !sttl tt~l ? 2.1 ( ) 2.2 ( ) 2.3 ( )
2.4 ( ) 'il'lt ~ClC1.LHL<tl li.\4.!s 27 fJ. oa ctli.i•.(l it!s :t.tctc-t.h-t !st~1 <tl"lctlli.l ~tel rll <tctl lt\4.!s 25 tlltt 0. ct1 !sttl <tl~C-t. ~ctc-t.h<t..fi Dsltct !sO tutt ? 28 26 25 35
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ltl{_Rl!s ~'Wtl 1 ttl 7 '"ll lt\4.!s <tl "'ll 1U~ 100.01, 100.02, 100.03, 100.04, 100.05, 100.06, 100.07 -t1 li.\4.!1 uh1.
100.04 ( ) 100.03 ( ) 100.36 ( ) 100.4 ( )
1 1_!_ <tl ~ltlrl~ lt\4.!s ~2~1 tlltt ? (100)1, 4• 2, -4' 2
(a) 1_!_ ( ) 2
(b) 1.5 ( ) (c) ( ) (d) 1.25 ( )
(16) (1 0 I) I 0 ~Cl.Ellh1.1.L ltut~ 28.2 i9. a& t.h :~-tq<a[H[tfi 1.2 c.t.Lf. H'l dot 2 Cl.~ OJ.qlctl ltutctL 1.Cl.L ltut~ ~2Ell
tt.l~?
(a) 55.2 ( ) (b) 54 ( ) (c) 56 ( ) (d) 27" ( ) (102) ?LqL ~t.'l %t.'l ~~1il.lti :bl~ !Ct.eut(f:bl il.utq<a OJ.qL 50, 50 ~.t 60 i9. a& ll.tt.lt C?ctl.~ ~ltL-t ~.t ?aw
~~Lil.ot ~.4{ ~ ~~til_ Hct[ c.tlt~ ~~T<l ~l'4.Cl.lltl ~lq ctl Lq£l.Lt[;bl ~utq<a OJ.ql1.l (I{L~ct ltut~ ~2C1.l ll.l~ ?
(a) 53.33 ( ) (b) 73.33 ( ) (c) 55 ( ) (d) 65 ( ) {103)~Ll{c.fi ltl~ctl1.L ~ut~tl ~2C1.L tLL~ i9 ·~ 0, 2, 2, 2, -3, 5, -I, 5, 5, -3, 6, 6, 5, 6 (a) 0 ( ) (b) -1.5 ( ) (c) 2 ( ) (d) 3.5 ( )
a a a a a ~ (I04):bl~ ltl~ctl-tl ~Cl.talh1.LJ0'2's'4'6 ~.a& ~L~ctl-ti.ltut~tt.
(a) 21.5 (b) IOO (c) 80 (d) 96
(a) 30 (b) 90 (c) I8 (d) 60 (106)3, 6, -I, -2, -1, 2, I, 0, -1, -4,3 -tl. C>ltf.El~ ~2ta1 tt.L~? (a) -2 (b) -4 (c) 6 (d) -I {1 07) ;bl~ ltl~ctl.1.L ltut~ ~ot lt\-.l.t~tl ~'j.fl~ 3 ~ot 2 i9. ctl C>ltf.CH.fi altct ~2c.fi lll~ ? (a) I (b) 2 (c) 0 (d) 3 {1 08) ;bl~ ltLJl.ctl.lt[ Z - M = 2.5 ~.t ~ut~ I 0 ~h ctl C>ltf.CH Z .{l f?sltct ~2c:ll. tt.l~ ? (a) 11.25 (b) I3.75 (c) 20 (d) 7.5
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(I09) ~ ~Cl.Ellh1.1.l ltut~ "'l·t OJ.'~Lhn. )!tll~ ~'j.!~ 6.5 ~ot 6 ~l~ ctl CJlot ~Cl.Ellh-t.fi altct ~~ ~1~ ? (a) 12 ~.t 3 ( ) (b) 4 ~-i 9 ( ) (c) 6 ~-i 6 ( ) (d) 7 ~-i 6 ( )
(17) (110) x-Z=J <>tot x+Z= 45 rt1 z ·il Ultrt 12at '-llli? (a) 42 (b) 24 (c) 21 (d) 23
(Ill) ltL~rtl-tL 4 <>tctc-t.h-t ~>l-J,:&it I6 :utot 1J t!.L~ rt1 ct-t1 ~~LhL~ ltuth 12c-t.1 e.tl~? (a) 12 (b) 12.5
( ) ( ) ( ) ( )
( ) ( ) ( )
(c) 20 (d) I3
( ) 10
(112) -, x :utot I 0 x -t1 OJ.~LhL~ ltuth I 0 t!.L~ rt1 x ..fi Ultrt hc.fi :utlct~1 ? X
(a) 0.1 ( ) (b) I ( ) (c) 10 ( ) (d) 100 ( )
( 113) 20 "'[email protected] :utL~@ CCtrt~~l-tL ltut!J I I. 5 E9. a& t.h "'tClc:t.Lh-tlt[t.Q 6 t.tlt. htl 2 ctl <ltLOLCllltl :Qt.Lq rt1 -tctt :utctc:t.h-t-1 llltt~trt fct'!lc:t.-t 12~ t!.L~ ?
(a) 23 ( ) (b) 5.05 ( ) (c) 11.0 ( ) (d) 5.75 ( )
(114) :bih ltt~rtl.-t1 ltuth 50 t!.L~ :utot ~c-t.·ti!J 25% t!.L~ rt1 llltt&rt fct'!lc:t.-t ~2~ e.tt~ ? (a) 25 (b) 50 (c) 62.5 (d) 12.5
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) (115) :bih ltl~rtl1 ~hLU fct'!lC-t.-1. 5.2 t!.L ~ :utot ~hm fct'!lc:t.-tlh 0.4 t!.tq rtl ltuth ~2c:t.L f.l.l~ ? (a) 23 ( ) (b) 26 ( ) (c) 13 ( ) (d) 2.08 ( )
(116) :bih ltl~rtlltl X+ s = 48 <>tot X-s = 42 t!.L~ rtl 'llc:t.-tlh hc:t.1 f.l.l~ ? (a) 6.67% (b) 3% (c) 45% (d) 66.7%
(117) :bib ltl~rtl-tl P25 = 20 :utot P75 ' 36 t!.l~ dl ltl~rtl1 'll{J.'-fh fct'!lc:t.-1. ~2~ f.l.l~ ? (a) 16 (b) 56 (c) 0.29 (d) 8
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( (118) :bih ltL~rtllt[ ~c:t. -tct :utctc:t.h-t1 :utot ct-t1 :Lx = 36 :utot :Lx2 = 180t!.L~ rt1 llltL~Lrt fct'!lc:t.-t 12~ '-LL~? (a) 2 ( )
)
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)
(b) 4 ( )
(c) 50 ( ) (d) 3 ( )
.~ ... -,
(18) (1I9) ~~<t.l-!l A -tl N-tl >t'-'H I 00 'blot ll>tl~ld [q~c1.-1. I2 ~. "'fttl~ ~~<t.l-!l B -tl ~-t-tl >tl:.tt!s-tl '1.'4!1 80
'blot J.t>tl~lct ['q~c1.ot 4 ~. ctl. 'blt!s.mu:e~ntt ~lct <mi. ~~<tl-!l !sttl. l?.l.ltt ? (a) A
(b) B
(c) <>t.~ ~~"ll ~
(d) hiS !stl.'l -t mltt
(I20) :b\!1 'btl'{@ [qd~~l'l.l Q3-Q
2 = 2(Q
2-Q
1) dl [q'l>t.'l.dl!s 52~<t.l tlltt ?
(a) -0.66
(b) 0.66
(c) 0.5
(d) 0.33
(I2I) :b\!1 'btl'{@ [qd~~l'l.l >t'4!s 35 'blot C>t.lf.CH 33 ~- dl [q"l'l.dl 5cil. l?.l.llt ? (a) ~~rli
(b) ~-1.
(c) ~~l
(d) <illtct
(122) :bl!s 'l.l~ctl-tl ~C1.-tl~ 18% 19 'blot >tl:.tt!s 25 tl.ltt 'blot C>t.lf.CH 28.5 tl.ttt rll
(a) 4.5
(b) 0. 78
(c) -0.78
(d) -4.5
(I23) I, 2, 3, 4, 4, 4, 5, 6, 8, 9, 10 -tl [q"l'l.rll!s 12C1.l tlltt.
(a) I
(b) 0.6
(c) 0.3
(d) -2.I2
(124) :bl!s 'btl'{@ [qrl~atl..fi f<:l.'l>t.>tn.l -3.3 :Ulot ~Q.tf!s [q~~<t-t II tl.ttt ctl. j ~U.~I.. (a) -O.I5
(b) -0.3
(c) 0.3
(d) O.IO
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[q"l'l.rll!s ~2C1.l l?.l.ltt ? { )
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( ) (I25) :bl!s 'btl'{@ [qd~lll-t.l '1.'4!1
(a) 0.67 I20 <>llf.CH 20 :Ulot J.l>tl(qlrl [q~C-1.-1. I50 tl.ltt dl [q"l'l.rll!s 12C1.l l?.l.ltt ?
(b) I5
(c) I.5
(d) 0.70
? (a) 4 (b) -4
(c) 3 (d) [q"l'l.dl!s ~<!AlRt.!s ~'lrt ~l~ -ttCl.
(I27) 6, 2, 4 :b\ ~l~l :ui!st-tl (J1.tltl0lt(l ~lt~l :ui!s..fi ~2c;fi <i'W{l <>tot ? (a) 4 (b) 6 (c) 3 (d) 8
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(I2S) 9, S, 0, 4 ~ '~m. ~~t-tl (J4.~.tlottll ~L~L ~~.a !zat ~"l>ll.L lt~ ? (19)
(a) 24 ( )
{b) 20 ( ) (c) IS ( ) {d) 30 ( ) {129) nP2 .fi Chn 90 t!Llt nl n .fi 11ltn !zat ttllt ? (a) 9 ( ) (b) I 0 ( )
(c) S ( ) (d) I2 ( )
(130) STATISTICS c.t1:tL"'f :ot~~-tl t3't~.tlot H1 Cot-tnl UtJ.f-t.fi (~ ct <ltl"LL~l~.t :otaf "'f~~ -ttll.) ~"IM{L !zal ttllt ?
{a) I 0 ! ( ) (b) I 0 C I 0 ( )
(c) IOP0 ( )
(d) l0P9 ( )
(I3I) 3 ltl~ld~L~ :ot-1 3 ~~~hL~ ~~ t!L~lt[ h2al ~ct ollocil u~L~.t ! ~til ltt<>Rt :ot-1 ~~~hl~ CLL~LHdl :otLq ?
(a) 36 ( ) (b) 72 ( ) (c) 720 ( ) (d) I44 ( )
(132) "'ll nP2 .fi 11ltn 72 t!L~.tnl nC2
.fi f!ltn !2Eil. ttllt ? (a) 9
( ) (b) 36 ( ) (c) IS ( ) (d) 24 ( )
(I33) nC._2 = 2S t!Llt nl n .fi 11ltn !zc-il ? (a) 6
( ) (b) 7 ( ) (c) s ( ) (d) 9 ( ) (I34) IOP
2 - I OC2 ..{l 11ltn !zc{l. ttL~.t 't
(a) 90 ( ) (b) 45 ( ) (c) ISO ( ) (d) 60 ( ) (135) nPx ..,. nCx = 120 t!Llt nl x ..{l 11ltn !zat ttllt ?
(a) s ( ) (b) 6 ( ) (c) 4 ( ) (d) 5 ( ) (136) nP
2 + nC
2 = 135 t!h ctl n .a n'tn ~2C-il. tlllt ?
(a) IO ( ) (b) 90 ( ) (c) I2 ( ) (d) s ( )
Z\~
(20) (137) ~3 1{il.~i 3 tth., 3 Will :Qtoi 4 C·U<a ~~l ~- d~[e.(l ~h ~ot-ti. ~3 ~~L t!.L~ d ~'ld h2C1.l ll3L~ "4.~~o(l
H'l ~l3L~? (a) 24 ( ) (b) 6 ( ) (c) 18 ( ) (d) 36 ( ) (138) (x+a)8 1 ~ut~ "4.~ b~ t~.h ? (a) 8C4x4a4
( )
(b) 8C5x 3a5 ( )
(c) 8C3x5a3 ( )
(d) 8C4x3a5 ( )
(139) (x+ll) 12 -tl ['qMt~·~t~i h2<:tL "4.f. ~ul. ? (a) II ( ) (b) 12 ( ) (c) 13 ( ) (d) 15 ( ) (140) 10, 6, 2, -2 1 151 "4.f. 3~ I!.LL~ ? (a) 46 ( ) (b) -46 ( ) (c) 64 ( ) (d) -64 ( ) (141) 1 e.£l 50 qul :ouqc.fi 7 q~ ~~L"L Gtto(l U3L~ ctcfi ~W{L<l.L tt~C{LULL h2<'1.L I!.LL~ ? (a) 196 ( ) (b) 14 7 ( ) (c) 7 ( ) (d) 49 ( )
(142) -14 :Qtoi 4 qul 4 tt'i.ld~ ~utb ~~ctl J.li!.L~ :Q!C{C1.lb<1. 3~ tLL~ ? (a) -II ( ) (b) -8 ( ) (c) -12 ( ) (d) 2 ( )
(143) ~3 tt~irt.~ ~~U~t 51 "4.f. 14 :Qt-1 151 "4.~ 44 t~.l.~ rt.l. ~~U1 J.te.t.~ "4.f. h2~ ttL~ ? (a) 5 ( ) (b) 3 ( ) (c) 2 ( ) (d) 6 ( ) (144) 101, 99, 97 .... ~ii!U{ ~2C1.L1 "4.~ 5 I!.Ll~?
(a) 46 ( ) (b) 49 ( ) (c) 50 ( ) (d) 51 ( ) (145) ~b ~~fi1 81 "4.1; 40 ~lll. rt.l. J.ltt~ 15 '4.f.l<tl tt~C{LULL &2<:tl tLLI{ ? (a) 300 ( ) (b) 600 ( ) (c) 350 ( ) (d) 150 ( )
(146) s2S = 145 :Qtoi s24 o= 120 t!.l~ Ill T25 .{1. a~ct h2C.fi I!.LL~ ? (a) 25 (b) 24 (c) 40 (d) 42
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(147) 1/2, l/4, 0, -l/4, -1/2 ...... ~q(l~[ d .fi 11~rt !2c.-t1 tt.L~t ? (21)
{a) 0.5 ( ) (b) 0.25 ( ) (c) -0.25 ( ) (d) -0.5 ( ) {148) 0, 0.33, 0.66, 0.99 ...... <>Wht ~q(\~[ a .fi 11~rt !2c:t1 tll!t ? (a) 0.33 ( )
(b) 0 ( ) (c) -0.33 ( ) {d) 1.65 ( )
{149) :otL1{c:{l ~L~dl. 5, 8, 10, 12, 19, 20, 24, 28, 30, 35'1.L 1dl.!t ~Q.e.fb-.fi i1~rt uhl.. (a) 30 ( ) (b) 8.25 ( ) {c) 28.5 ( ) (d) 28.25 ( )
10
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x=3 (b) -
( ) X=2
(c) -( )
X=4 (d) -
( ) X=5
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n (6t) K=1-3.232log10
n
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n
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4) i1P2 ..fi I:Eli.ct 90 ~ltt. ctl n ..fi I:Eli.ct 12<:0. ~ltt.? (=bt) 9 (('{) 10 (3) 8
5) ~3 =bt.L'!ftt fctct~I?Llii li.I:J..t3 35 =bt.-1. CJt~a3 33 t9. ctl. fct"'.li.ctL1cU ~ltt.? (=bt) ~..-tt, (CJt) It-t (3) ~l?l
5) o, 0.33, 0.66, 0.99 ...... =btl~a ~!?Ulii a ..fi I:Eli.ct 12<:0. ~ltt.?
(=bt) 0.33 (('{) 0 (3) -0.33
7) oill?lltlR.dl-tl. G'4.tt.tol3~cti '4.~ai 3tt.ll{3L~..fi ~lct~dl ~lutcU o&6~? (=bt) lilR.dl-tl ~(-l12(-ll t9 ct ~l~ ~~ o&6~. ( ('{) liLR.dl31.~?1.liUL2ta t9 ct =bt.-1. ct-tl. ~tl ~~?U ~ctl. o&6~ (3) li.LR.dl ~'Kilrlt3 t91 ~l?llrlt3 t9 ct ~!?U ~~ o&6~. Cs) li.LR.rtl-tl ct'4.L~-tl3Ll{~hL..fi lttt.[t.L ~~?U ~c{l o&6~
0 ~ctct =bt.L'!ftt fctct~I?L-tl.li~:.tt.3 ~U.~tctllil2 3~ <;k?L tt.l.ott. t9 ?
(4)
Cs) 12
Cs) 1.65
(=bt) x=B-c(Lcfi_l) (CJt) x=B-c( Lf -1) (3) X=A+LCfi Cs) X=A-c(Lncfi_l) Lf LC[ Lfi
') It-t fct"'.li.ctllii =btl'!ftt ClZ"il t9.sl.36 6f.l% (-iCJtl~(-ll ~l.tt. t9?
(=bt) .Slc,fi ('i.l% (('{) ..fi~..{l.('i.l% (3) G'4.~..fi ('i.L%
I) ~liict~ ~~?U1 G~ct <;k?l '4.~t. 3~1.. (=bt) Tn =a+ (n+1)d (CJt) Tn =a- (n-1)d
(3) Tn =a+ (n -1)d (.s) Tn =a- (n+1)d
) «i<ltl~"t ~ 3tt.lll3l~"il =btl'!ftt fctct~l?l"il =btl~"'. t9 ? (=bt) =bt~ctct (('{) li.l:.tt.~ (3) ~?l.o1UL
) ~3UlULllii =bt qo[-tllOO fct~l~~ ol@lctlii liULCta ~l?l-tlli.\:J..t3 30 t9. =bt.-1. 6t qo[-tl50 lct~l~=btl ~ ~ fct"'.tt.lti
liUL2ta ~l?l-tlli.\:J..t3 60 t9 ctl. ('{~ qo[-tl fct~l~=btl~ liULCta ~J8l-tlli.l:.tt.312(-LL ~ltt.? (=bt) 40 (('{) 45 (3) 48 (.s) 50
.) ~3 ~ =btl~ut '4.~ t.l.~aL "~ =bt.Lt9L" =bt.-1. "~ ct~" =btl.~6ct ctz1 t9t.~ UL1l;l(~ =btl~ t9 ?
{=bt) lil:.tt.3 (CJt) li.l:.tt.~ (3) CJt~a3 (.s) ~~lil:.tt.3 li.LR.rtl-tllil:.tt.3-ti ~t.~lii 8~ct fct~tl-t '4.~t. 3~.
(=bt) L(xi-x)=o (('{) Lxi-x=o (3) L(xi)-Lx=o (.s) Lxi=n+x ~3li.LR.dl-tl =btct(-LL3-t 6, 6, 6, 6, 6 t9. ctl. 21.-tl. ~a-ti312al. ~Ltt.? (=bt) 6 (CJt) 5 (3) 0 (.s) 1
I nCx = nCy ~ltt. ctl...fi~-tl fctltl-tl tHl. G~ct fctltl-1. '4.~t. 3~1.. (=bt) x+y=n~ltt. (CJt) x/y=n (3) x.y=n~Utt. (.s) x-y=n
7) 24C21 = 24Cr ~l~ dl r ...(l. [!ltd h2cll ?.ll~?
(~) r=22 (~) r=3
~) li.LR.ctl--t.Lltl:l.t~--t.i ~t.Gilti G~d (qi:J.L--1. '4.~t. .Hl.
(~) ~La'Ul...Q.ltt.t.~ !tUI:fi !tl~L~ --t.R.
(~) r = 2 (~) r=24
( CJ~.) ~1.~ li.L2L ~ctc:t.l.~--t. ~.t ~1.~ --t.t--t.t ~ctc:t.l.~--~....a ltl:l.t~ '4.~ ~1.~ ~:ct.~ ?.tctl--t.~. (~) 'dsE<.-1.l ~~l Cllutl ~ctc:U~--t.lti ltl:l.t~ ltltfi !tl~l~ --t.R..
(~) d_...(l. OL~ld~ '1.-CJI. ot ~2'4.21. ~.
~) 101,99, 97 ...... ~~U'd,12c:t.L~ '4.t. 5 ?.ll~?
(~) 46 (CJ~.) 49 (~) 50 (~) 51
~"'(S)
(~) nCr= nCn-r (~) nCr= nPr.r! n' (~) nCr=_: r!
(~) nCr= n!(n- r)!
l) STATISTICS CJI.I:tlot ~&1.~--t.l. G'4.~)ot ~~ CJI.--t.dl U%)...(1. (at ct ~l"ll~~ ~~ ot~~ --t.~) ~uttL12cll ?.ll~? (~) 10! (~) 10 C 10 (~) 10P
0 (~) 10P
9
l) ~~.~ Et2--t.l ~--t.~lct[dd ~ct CJ~.-1. ctcUlttR.dl.-1. ~i~~l!tll~lti ~~l--t.l~ ~l.utuflti? (~) ~L'!rd (CJ~.) ~(-1.
(~) ~t.!tl (~) :cllt~
3) ...(1.~--t.Llti~ ~~L ~o&oulti ~t.!tl ct'4.L:ct ~~cut!:~?
(~) :ctlt~--ll ~~let ~~Cll ~l~ ~l~
(~) d'4.l:ct ~out--t.i ~~ltl--ll d'4.l:cl t.~l-tl.l--1. --t.LU ?.ldl ~l~ ~l~ (.~) d'4.l:cl--t.l ~Lttlti ~'t:qLLdl...Q. ~Cll ac(l ~l~ ~l~
(~) d'4.l:cl t.~l-tl.l--1. --t.l~Li ~-1_ !tl~--ll CJI.~lct ~~Cll ~l~ ~l~
~) ~~ lttR.dl--t.Lltl:l.t~ 50 ~1.~ ~-1. ~(-1.--t.i~ 25% ~1.~ ctl. ltltL@Ld [q~(-1.--t.h2~ ?.ll~?
(~) 25 (CJ~.) 50 (~) 62.5 (~) 12.5
;) ~~ ~~U'd, 8~ '4.t. 40 ~1.~ ctl. Jt?.tlt 15 '4.t.l.--t.l. :ct~cttutl.12c:t.l. ?.tt~? (~) 300 (~) 600 (~) 350 (~) 150
5) ~~ lttR.ctl--t.l. ~c:t.--t.i~ 18% ~ ~.t ltl:l.t~ 25 ~1.~ ~.t CJ~.~(-1.~ 28.5 ~1.~ ctl. [C{"'.ltcti~ 12cal. ?.tt~? (~) 4.5 (CJ~.) 0.78 (~) -0.78 (~) -4.5
7) ~~ li.LR.dllti X+ s = 48 ~.t X- s = 42 ~l~ dl ~(-1.--t.i~ 12c:t.L ?.ll~? (~) 6.67% (CJ~.) 3% (~) 45% (~) 66.7%
~) 1 oP 2 - 1 OC2
...a [!ltct 12cll ?.tt ~ ?
(~) 90 (CJ~.) 45 (~) 180 (~) 60
>) '1.-E<-"i.l ~~lctlufllttR.dlltll lt:cll~ltl--t.'d, ~l.o~ ltl'4. ~~ ~ ?
(~) [q~l~ (~) ~Q~~ [q~c:t,--1.
(~) :ct~~LU [q~c:t,--1. (~) ltltl@Ld [q~(-1.--1.
)) ~ ~ctc:t.l.~--t.--t.i ltl:l.t~ ~-1. ~~u~H ltl:l.t~ ~'jz~ 6.5 ~-1. 6 ~1.~ ctl.6l..t ~ctc:t.l.~--~....Q. [!ltct ~~ ~1.~? (~) 12~-1.3 (CJ~.) 4~-1.9 (~) 6~-1.6 (~) 7~-1.6
[) -14 ~ .t 4 q ~ 4 :ct. ltld ~ lt 1:2{~ ~~di Jt ?.llt ~ Cl({l~--1. ~~ ?.ll ~ ?
(~) -11 (CJ~.) -8 (~) -12 (~) 2
2) ...o.~~1.l~i~ ~~u.-n~ ~~~ ~l2-j <-ll~ rctl:tl""l ~~?
(:ut) ~LR.dl...-tl :utctc:t.l.~..-t '{~ ~~ 1 ~~l :utctc-th..-t ~Ll.t ctl. ~~u-n~ ~~~ ltll~ ..-tltl~ll.t. ( CJt) ct. ...a d.ll~l <tl~<-1. :ut.-1. =t'4.'e ""l~. ..
( ~) ct. ...0. ~LR.dl. ~i CJt l:ti ~ :ut Clc:t.L~""ll ""ll G'4.l.tl OL ~dl ""l ~. (,s) :ut.L~ut...O. ~~~~ ltll~ u~Ll.t ~.
3) ~~ ~LR.dl...-tl :ut.Cl<:t.l~""ll I~,~· i· ~· ~ ~. a& ~LR.dl...-tl ~U{=t?-1. 16 ~ll.t dl a ...fi a~ct 12cll ~ll.t ?
(:ut) 21.5 (CJt) 100 (~) so Cs) 96
~) ~~ :ut.L'!rtl rctct~~l~i Q3-Q2 = 2(Q2-Q
1) ctl. rct'bf.~cti~ 12c:t.L ~ll.t?
(:ut) -0.66 (CJt) 0.66 (~) 0.5 (,s) 0.33
5) <t~ict~ ~~0. ~2~ ~ ?
(:ut) ~ :&~~ '4.~l""ll d~lctd :ut<tut ~ll.t ct.cO. ~~o..
(CJt) ~ :&~~ '4.~1...-tl. d~lctd ~~"d~ :ut<tut ~ll.t ct.cO. ~~0.. (~) ~~0...-tl n '4.~1...-tl. <t~ctlutl~ ~utdl. '4.~lctC1l.
Cs) ~~0...-tL :utctc:t.l.~..-tl.-1. <t-Sctl :&~~i ouoctcti ~utdl. ~~0..
>) ~utctdl ~Rt..-tl ~l'4. ctill ~ut3 ~t2 ...0.~..-tl tl~j .&~ fCI.I:tl""l q~ l.tLOl.t ~? (:ut) ~ut~ :utl~ut~ ltll~ ~l3ll.t.
(CJt) 'j«-t.L ~-SL ctlutl qou ~t2 ~ut~ ltlll:filtL~Lctl. ..-t~. ( 3) ct. :ut~ ~ ~l '4. ~ .
(,s) ct....O. OL~ld~~i CJtl:ti ~ :utctc:t.l.~..-tl...-tl. G'4.l.tLOL ~~cu~i :utlctctl. ..-t~. ') ...0.~..-tl G~l~~~l~i~ :ut<tctct <tc:t. '4.~~ ~~1..
(:ut) :ut""ll~'d, (3('"'4.l~""l (CJt) fCI.ttl~:utl.j Cl~""l (~) ~l-[<tl~""ll :uf.'1~Cl (,s) Cll~..-ti....O. ~~l
~ ut~ 12c:t.l. ~ll.t ?
(:ut) 5.3 ( CJt) 5.4 (3) 6.1 (,s) ') Jt~L@Lct fCI.<tc:t...-t ~L2 ...0.~..-tl~i~ (3~ct ~?!. '4.~~ ~~1..
L~di2 (L~di) xc (:ut) ( CJt) ~2Cf2 -cf1 -cf12 x C n
(~) Id-2
(Id· r (,s) s -·+-· =x100 n n X
6.5
(6)
\..
) Jtl{Rt~~~l1 ~ 7..-tl.~ut~..-tl:ut.ll:tl~ 100.01, 100.02, 100.03, 100.04, 100.05, 100.06, 100.07..-tl.~ut~-' ltll ~:tl..
(:ut) 100.04 (CJt) 100.03 (~) 100.36 (,s) 100.4
"L\.. Lol. L .t l tC.. -~ v \ -\ 'v, \... ·. (It, 't:J)
Gn~tt?L
~ih~t~u~,..fi ~~ h~l.2l.
~~t~1 '"lllt : ~tot..U rtt:fi"t :
llutt:i '"lllt : OO' .. lt rtt:fibt :
~ut : Gll~ : h~t ~-1 cto[ : "' ~[rl : l9th~1 I l9th:fi :
. J (9.) (~) (CJt) . c~) . (.s) u ( J 9.) (~) ( CJt) (~) (.s)
(~) (~) (CJt) (~) (,s) (J~) (~). (CJt) (~) (,s) (J) (~) (CJt) (~) (,s) (JJ) (~) (CJt) (~) Cs) ('ll') . (~) ' ' (CJt) (~) Cs) (J'll') (~) (CJt) (~) (,s) ('{) (~) (CJt) (~) (~) (J'{) (~) (CJt) (~) (~) (E) (~) (CJt) (~) Cs) (JE) (~) (CJt) (~) Cs) (-$) (~) (CJt) (~) (~) (J-$) (~) (CJt) (~) (,s) (d (~) (CJt) (~) Cs) (Jd (~) (CJt) (.~) .Cs) (~) (~) (CJt) (~) (,s) (J~) (~) (CJt) (~) (,s) ( 9.0) (~) . ( CJt) (~) (~) ('li'O) (~) (CJt) (~) (~) (9.9.) (~) (CJt) (~) (~) ( 'll'9.) (~) (CJt) (~) ~ (~)
( 9. ~) (~) (CJt) (~) (,s) ('ll'~) (~) (CJt) (~) (,s) ( 9.J) (~) (CJt) (~) (~) ('li'J) (~) (CJt) (~) (~) ( 9. 'll') (~) (CJt) (~) (~) ( 'll''ll') (~) (CJt) (~) Cs) ( 9. '{) (~) (CJt) (~) (,s) ( 'l!''{) (~) (CJt) (~) (,s) ( 9. E) (~) (CJt) (~) (,s) ('li'E) (~) ( CJt) (~) (~) ( 9.-$) (~) (CJt) (~) (,s) ( 'll'-$) (~) (CJt) (~) (~) ( 9.d (~) (CJt) (~) (~) ('ll'd (~) (CJt) (~) (,s) (9.~) (~) (CJt) (~) (~) ('ll'~) (~) (CJt) (~) (~) (~o) (~) (CJt) (~) (~) ('{o) (~) (CJt) (~) Cs) ( ~ 9.) (~) (CJt) ' (~) (~) ('{9.) (~) (CJt) (~) (~) (~~) (~) (CJt) (~) (~) ('{~) (~) (CJt) (~) (~) (~J) (~) (CJt) (~) (~) ('{J) (~) (CJt) (~) (~) ( ~ 'll') (~) (CJt) (~) (~) ( '{'l() (~) (CJt) (~) (~) ( ~ '{) (~) (CJt) (~) (~) ( '{ '{) (~) ( CJt) .. (~) ' (~) (~E) (~) (CJt) (~) (~) ('{E) (~) (CJt) (~) (~) ( ~-$) (~) (CJt) (~) (~) ( '{-$) (~) (CJt) (~) (~) (~d (~) (CJt) (~) (~) ('{d (~) (CJt) (~) (~) (~~) (~) (CJt) (~) (~) ('{~) (~) (CJt) (~) (~) (Jo) (~) (CJt) (~) (~) (Eo) (~) (CJt) (~) (~)
!2-17
&\ -z (;, ---
c~tt) (0 ;3) (~) (0£) (1'1) (;:>h.) (S') (;:>c)
(ltt) (/h.) (ltt) (7c)
(S') (0h.) (~) (0c) (1'1) (;3h.) (1'1) ( ;3 c)
(1'1) (h. h.) (~) (h. c)
(S') (;I_ h.) (~) (;I_ c)
(S') (£h.) (S') (t-c)
.. (ltt) (ch.) (~) (c c) (ltt) ('bh.) (1'1) ( 'b c)
(1'1) (Oh.) (S') (oc)
(1'1) (;::>)I_) (1'1) (;:>'b)
(1'1) ( / ;1_) (~) I (/'b)
(1tt) (0;1_) (S') (0'b)
(~) (;3;1_) (~) (;3'b)
(1'1) (h. ;I_) (ltt) (h. 'b) (S') (;I_ ;I_) (~) (;I_ 'b) ~ (1'1) (£;1_) (1'1) (2'b)
(ltt) (c;l_) .(~) (c 'b) (ltt) ('b;l_) (ltt) ('b'b) (ltt) ( O;l_) (ltt) (O'b)
(1'1) ( ;:l£) (1'1) (;::>) ~--(1'1) (72) (1'1) (/) (1'1) (02) (1tt) (0)
(1tt) ( ;3 £') (ltt) (;3)
(~) (h.£) (ltt) (h.) (1tt) ()I_£) (1'1) (;1_)
(1'1) (22) (1'1) (2) (ltt) (c£) (ltt) (c)
(S') ('b£) (1'1) ('b) f (S') (~) (1'1) (ltt) (S') (~) (1'1) (ltt)
: lF~t~ I tc~t~ : ~JtRo : Jcl:> r~ l&cl)
: clt~ : \1)~
: ~l;lll lt ... ~ : ltll-' f.llnll
: ~l;lll fr~l~ = ltl,... r..na1n~
l]=>ll?: ~~11&fc trl?tlC~ ~~ lr~1161S'~1ltt (
r?.-l
1estion N' Ans 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
~~~~~L~~-~------------------~------
(..2:"\. GAL ~ .l-{l~l rt t tS-ct..t '-bl. .-(1 "~ \ ls ot .u. L <(l~ 5l:w'1~-L ~ ~~~ f ~rt. .u-\. te3'2..
ans_ab_cd 2 8 1 A 28 28 1 A 1 A 1 A 28 28 1 A 1 A 3C 28 28 1 A 28 40 3C 28 40 2 8 3C 40 2 8 28 28 28 1 A 40 3C 40 1 A 28 1 A 3C 1 A 28 28 28 1 A 1 A 1 A 28 40 2 8 3C 1 A 28 2 8 28 1 A
52 1 A 53 4 0 54 4 0 55 2 B 56 2 B 57 4 0 58 1 A 59 2 B 60 1 A
oc:~
' '\Pelf l~-;.. SSbt~ ss~11-t (:t1~.ke 1rlfl1b 1.1~-e tJaeh. ePfcltt> ~ h1~hh., ~ 1h(o 1~hh~
h ... ~ 1bt~ke u-~ u'tl~· rsb1ke ss~tlt 1l--lP1b 'l--1:: ~t:1lt h ... ~ 11:: ·~l-o ~F.> J1.rs tJa1bl~ l-o 'l::fcll'-D SSb1~ SSR!Jllt ~llalt:.~ ~ ·.f;?::ss l--rqfurc t.J1F.> !ltl--1h~ 1::1:: h1~ 1J1.1l~ .)~kl: Pte~ ~ lfSSQl-o
lclt>lcf.> tl--1:: 11:: l(!lt 1b~ ~ 1:: h1~ l-o '1)1.1~ ]lt~-,.h. ~SI!fr.JTC PlceJ ~ L~l:: tln! ~Jl--h1ll1c
LeSS tc~lltre 11::~1h.S) rs~~~ ~~~ t .,..~,h rs~~ t ~'* ss~~ ~ ltt '~l'h. 1~~ h}C1tJ 1::1b. e1b
ss~?~ ~~l--ess l--SS!_fc!rc !Ph.1ke klfe ·@ 1-n.,pc~ 1~rc 1l-o1bh.1~ ~1: bhbke ~ felt-~};) tt~~ '@lr
~.,.h. 1-a~!~fc
'@ ~'' teh.tb fc!h:J-1~ <:t @ ~-.~h.nt 'tt>e~ ~to 11;:~.-.ce~ SS~liJl~-ss~titt~ ~~ lttke ·~ ~h. fetE> l::le lJ<t.elt: Jlt1~1P:C~ltt~ tlaP te~t~}~ln! 'te~r~ 1:: @
lhol~ ]ltlb~ ]lt~l~~ l~hbke ~ ~~~F.> ~ · ~ l)nb 'l}al-o 1ho1~ ]lt1b~ teb1~ ]lt~}h.llt l;:l~hb~
tbt~ lJa'~ '@ l(!lt tb~ h.~ke· '1:\.to.Fe~l=e 'l::,~hb~ h .. ~ fun ~~lt: ll-o~ lt~ ~ ~ ~~i3:cb ~~b
'r~v~ t .,..rc~E>J( 'rcL!f 'el--n!J.!ie~ ·pteb -e~ k lPl:: '@ lelt tb~ h.~~ ~to '1:\,to.Fe~~ 'l::ltl:: 1"!'~ 1~hb~ h .. ~ ~~··ua~ lPlnlt lP!J1lt '\Pe\. lJG~'h. JJatt:.~ ~bJ l: ~ ~ 1ttH> 1lt':)7-1l
JS~tltm .f.Si e l~P @ li~1lt ll-o'Pl}tk lfl?~ lfllb i3.eh '11!J)lt lb~ '1:\.lo.fe~~ l~lfe ~-eb ll:;:hbkl:
11;)?1:: @ l-o~lb li!i ~~h. ~ltl:: l:::ln! '@ ~e Jltl--tsslt lbf. 12 'ssbt~ rs~1lt ~lte 'ePfr.lH> Flte
'hl~bho 11:::1-tl:: '~Jl* ~l]?lb '@ ]t-?~11-n: p·t1b}r~1e ]lt~.~h.llt 11-n: ]F.>rl:: ''t!J)lt 1b~ '1:\,lo,'ft~fe l~lfe
@·ch ~~~P.l ~· lJ'a!ltl:: tM ftllWJ.n: 't~~~F.l li]F.>?t h.~ ~~ ll-o~-'.Pe~ ss~nre-V~)lltlR:
'lh~ 1bl;l hlt~ l~?P lc1F.> ,).~k ~1'-n-1'h1l':.h1 1bp ~1-n: lla~ l~Jhlt '-'-"-~ "-"' IJ" "' ~o:.U<> ;,J UQ"-"' •
hltlt: (llt 1belt> ~.~h.1lt 11-n: Hn.~ln. '@ t1~ \):'It> 11::1c~ lrl:: ~~~1)61,;~ UnH>p~ ,~,.,..l't~ pt?lj~J Fe)p tJae~.h. ·~1rs1~ lJ't.lkl: t'~;)lJ;lmbJ ,,..~~1~ ,I.D ltl:: ss~h~~lt eP~~§)·· ·ss~h-,.nt s-.~h.tlt tkl: ···
'11::~ 'tll!':l)nam~ o o c'c ltH>lcF.> 1l-ol~t'lt>llc li~h~tlt tt'lt~ eft @ ~o1~ Jltlbeli eth~ 'k-h.l'Pl't~
11-n: lJaeh. 1~P.§ 1~ltl:: l}'t.tJ.n: l'.~h.1lt 1~ 1::'~,.. 1~elP~~ ltt~ l::lfe 1):~11:~'1:\kl: 'l}~n
7o o o /€ ~tb1~lt~ '1eRlc ebl>
lt1~1~ ~ ... ~ £C. ~ .. l'JlllC l'_.~ ~l'c~1): F.>~~~~~~.ll~ )'.a~
F.lli~l~tthm Sit~ ?1<?1?~ ... 0 : sst~tlil'l -
jsl~~ ·nc p .. 1llfcl!l~ '1~ : Sikll-cl'l '-'--.. 1.:::
~
l:O.l~h:~
(11-t l }h.llt. 11-'~~,o~s -T :h)lkc:-sr ~11-t lrc
~-~'\~)'?1h
!i~lP~lli.
I'
! ~. ~ r '
'l)!lSS~lr.: ·\Ph.§) '~'~:e.~ ·l}-otliss tc~ lcihjil![ 't;tss~l<t \Ph.§ l~H!!)l~ ·lfll!;: '~h.effilo. lJ. :.f.l'kl: '1? '·IJI. l~P lJ.lh.l~ ~~.lr.: '~.P 11--lh.l~ \l"lltdltl: l~k~lt lfl~ '?-A?.i.§)lli~ .,'t'.,'?l'tc
'?fi(1_]lltl: 'lpl!S~ltl: "f>!~ ·~ :.f.l'kl: 'lf:lj\l~llc.i. l~}ch lt~l'i .,e~\F t l:tc~ll'£ ll-lV:eJbtJ~ '\
}':b lb~ 'lpllf~ltl: l]:lS:~~ 't'IQ:tn;l':ll:\ '>!~i.:l"".:j~ ,~,..:~1!: '~?-tlf: .bllH:.b-:> l'J.AH-~i ~'l!§) "h
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~tructure for table: C:\EXTRA\VACC\finalans.DBF 'lumber of data records: )ate of last update: 23/07/2007 Code Page: :;-ield Field Name Type Width Dec Index Collate Nulls
STUDID Numeric 7 No STUD NAME Character 30 No SCHNAME Character 40 No SCHADD Character 250 No STD Character 5 No
5 AGE Numeric 2 No 7 SEX Character 1 No ~ STD10MARKS Numeric 2 No ) STD11MARKS Numeric 2 No 10 Q1 Numeric 1 No 11 Q2 Numeric 1 No 12 Q3 Numeric 1 No 13 Q4 Numeric 1 No 14 Q5 Numeric 1 No 15 Q6 Numeric 1 No 16 Q7 Numeric 1 No 17 Q8 Numeric 1 No 18 Q9 Numeric 1 No 19 QlO Numeric 1 No w Qll Numeric 1 No n Q12 Numeric 1 No ~2 Q13 Numeric 1 No ~3 Q14 Numeric 1 No ~4 Q15 Numeric 1 No ~5 Q16 Numeric 1 No ~6 Q17 Numeric 1 No n Q18 Numeric 1 No ~8 Q19 Numeric 1 No ~9 Q20 Numeric 1 No w Q21 Numeric 1 No H Q22 Numeric 1 No ~2 Q23 Numeric 1 No B Q24 Numeric 1 No ~4 Q25 Numeric 1 No ~5 Q26 Numeric 1 No ~6 Q27 Numeric 1 No ~7 Q28 Numeric 1 No ~8 Q29 Numeric 1 No ~9 Q30 Numeric 1 No lO Q31 Numeric 1 No
22.3
n Q32 Numeric 1 No l2 Q33 Numeric 1 No l3 Q34 Numeric 1 No l4 Q35 Numeric 1 No l5 Q36 Numeric 1 No ~6 Q37 Numeric 1 No n Q38 Numeric 1 No l8 Q39 Numeric 1 No l9 Q40 Numeric 1 No )0 Q41 Numeric 1 No )1 Q42 Numeric 1 No )2 Q43 Numeric 1 No )3 Q44 Numeric 1 No )4 Q45 Numeric 1 No )5 Q46 Numeric 1 No )6 Q47 Numeric 1 No )7 Q48 Numeric 1 No )8 Q49 Numeric 1 No )9 Q50 Numeric 1 No )0 Q51 Numeric 1 No )1 Q52 Numeric 1 No )2 Q53 Numeric 1 No )3 Q54 Numeric 1 No 54 Q55 Numeric 1 No 55 Q56 Numeric 1 No 56 Q57 Numeric 1 No 57 Q58 Numeric 1 No )8 Q59 Numeric 1 No )9 Q60 Numeric 1 No 70 URB RUR Character 1 No 71 DISTR Character 20 No 72 QT Numeric 10 No 73 QA1 Numeric 1 No 74 QA2 Numeric 1 No 75 QA3 Numeric 1 No 76 QA4 Numeric 1 No 77 QA5 Numeric 1 No 78 QA6 Numeric 1 No 79 QA7 Numeric 1 No w QA8 Numeric 1 No n QA9 Numeric 1 No ~2 QAlO Numeric 1 No B QAll Numeric 1 No ~4 QA12 Numeric 1 No ~5 QA13 Numeric 1 No ~6 QA14 Numeric 1 No
~7 QAIS Numeric I No ~8 QAI6 Numeric I No ~9 QAI7 Numeric I No )0 QAI8 Numeric I No H QAI9 Numeric I No )2 QA20 Numeric I No )3 QA2I Numeric I No )4 QA22 Numeric I No )S QA23 Numeric I No )6 QA24 Numeric 1 No n QA2S Numeric I No )8 QA26 Numeric I No )9 QA27 Numeric 1 No lOO QA28 Numeric I No lOI QA29 Numeric I No l02 QA30 Numeric I No l03 QA3I Numeric I No l04 QA32 Numeric I No lOS QA33 Numeric I No l06 QA34 Numeric I No l07 QA3S Numeric I No l08 QA36 Numeric 1 No l09 QA37 Numeric I No liO QA38 Numeric 1 No lll QA39 Numeric 1 No l12 QA40 Numeric 1 No ll3 QA41 Numeric 1 No l14 QA42 Numeric 1 No liS QA43 Numeric 1 No li6 QA44 Numeric I No li7 QA4S Numeric I No liS QA46 Numeric I No li9 QA47 Numeric 1 No l20 QA48 Numeric 1 No l2I QA49 Numeric 1 No l22 QASO Numeric 1 No l23 QASI Numeric 1 No l24 QAS2 Numeric I No l2S QAS3 Numeric 1 No l26 QAS4 Numeric 1 No l27 QASS Numeric 1 No l28 QAS6 Numeric I No l29 QAS7 Numeric 1 No l30 QAS8 Numeric 1 No l3I QAS9 Numeric I No l32 QA60 Numeric I No
;tructure for table: ~umber of data records: )ate of last update: Code Page: 'ield Field Name
Quest N Rightans
C:\EXTRA\V ACC\anstb.DBF
23/07/2007 1252
Type Numeric Numeric
Width 1 1
Dec No No
Index Collate Nulls
Note: • This program is developed in Visual Foxpro 9.0, before you run this program by
do command, you need to have finaldbf.dbf database table with all the students respective data(Database structure is given in appendix II) and also you need to enter all the right answers of the question in numeric form (i.e. AnsA =1, Ans B = 2, Ans C = 3 and Ans D = 4) anstb.dbf table for all the question no. 's.
• You can enter the data once you have created database structure from visual command windows.
• To created database structure use command "create finaldbf' • To enter the data in to database table use command " use file finaldbf' and "brow
finaldbf' • Once you have enter all the students data, answer given by students in finaldbf
.dbftable and true answer of Multiple choice question having four options in to anstb.dbfthen write down this program in to getans.prg file.
• You will get an output file Microsoft excel format
USE finaldbf IN 0 SELECT finaldbf COPY TO finalans USE finalans IN 0 USE anstb IN 0 PUBLIC ARRAY aarray(1)
SELECT rightans FROM anstb INTO ARRAY aarray
SELECT finalans DO WHILE !EOF()
REPLACE q1 WITH IIF(q1=aarray(1),1,0) REPLACE q2 WITH IIF( q2=aarray(2), 1 ,0) , REPLACE q3 WITH IIF(q3=aarray(3),1,0) REPLACE q4 WITH IIF(q4=aarray(4),1,0) REPLACE q5 WITH IIF(q5=aarray(5),1,0) REPLACE q6 WITH IIF(q6=aarray(6),1,0) REPLACE q7 WITH IIF( q7=aarray(7), 1 ,0) REPLACE q8 WITH IIF(q8=aarray(8),1,0) REPLACE q9 WITH IIF(q9=aarray(9),1,0) REPLACE q10 WITH IIF(q10=aarray(10),1,0) REPLACE q 11 WITH IIF( q 11 =aarray( 11 ), 1 ,0) REPLACE q12 WITH IIF(q12=aarray(12),1,0) REPLACE q13 WITH IIF(q13=aarray(13),1,0) REPLACE q14 WITH IIF(q14=aarray(14),1,0) REPLACE q 15 WITH IIF( q 15=aarray( 15), 1 ,0) REPLACE q 16 WITH IIF( q 16=aarray( 16), 1 ,0) REPLACE q 17 WITH IIF( q 17=aarray( 17), 1 ,0)
REPLACE q18 WITH IIF(q18=aarray(18),1,0) REPLACE q19 WITH IIF(q19=aarray(19),1,0) REPLACE q20 WITH IIF( q20=aarray(20), 1 ,0) REPLACE q21 WITH IIF(q21=aarray(21),1,0) REPLACE q22 WITH IIF(q22=aarray(22),1,0) REPLACE q23 WITH IIF(q23=aarray(23),1,0) REPLACE q24 WITH IIF(q24=aarray(24),1,0) REPLACE q25 WITH IIF( q25=aarray(25), 1 ,0) REPLACE q26 WITH IIF( q26=aarray(26), 1 ,0) REPLACE q27 WITH IIF(q27=aarray(27),1,0) REPLACE q28 WITH IIF(q28=aarray(28),1,0) REPLACE q29 WITH IIF( q29=aarray(29), 1 ,0) REPLACE q30 WITH IIF(q30=aarray(30),1,0) REPLACE q31 WITH IIF( q31 =aarray(31 ), 1 ,0) REPLACE q32 WITH IIF(q32=aarray(32),1,0) REPLACE q33 WITH IIF(q33=aarray(33),1,0) REPLACE q34 WITH IIF(q34=aarray(34),1,0) REPLACE q35 WITH IIF(q35=aarray(35),1,0) REPLACE q36 WITH IIF(q36=aarray(36),1,0) REPLACE q37 WITH IIF(q37=aarray(37),1,0) REPLACE q38 WITH IIF(q38=aarray(38),1,0) REPLACE q39 WITH IIF(q39=aarray(39),1,0) REPLACE q40 WITH IIF(q40=aarray(40),1,0) REPLACE q41 WITH IIF( q41 =aarray( 41 ), 1 ,0) REPLACE q42 WITH IIF(q42=aarray(42),1,0) REPLACE q43 WITH IIF(q43=aarray(43),1,0) REPLACE q44 WITH IIF(q44=aarray(44),1,0) REPLACE q45 WITH IIF(q45=aarray(45),1,0) REPLACE q46 WITH IIF( q46=aarray( 46), 1 ,0) REPLACE q47 WITH IIF(q47=aarray(47),1,0) REPLACE q48 WITH IIF( q48=aarray( 48), 1 ,0) REPLACE q49 WITH IIF(q49=aarray(49),1,0) REPLACE q50 WITH IIF(q50=aarray(50),1,0) REPLACE q51 WITH IIF(q51=aarray(51),1,0) REPLACE q52 WITH IIF(q52=aarray(52),1,0) REPLACE q53 WITH IIF(q53=aarray(53),1,0) REPLACE q54 WITH IIF(q54=aarray(54),1,0) REPLACE q55 WITH IIF(q55=aarray(55),1,0) REPLACE q56 WITH IIF(q56=aarray(56),1,0) REPLACE q57 WITH IIF(q57=aarray(57),1,0) REPLACE q58 WITH IIF(q58=aarray(58),1,0) REPLACE q59 WITH IIF(q59=aarray(59),1,0) REPLACE q60 WITH IIF( q60=aarray( 60), 1 ,0)
SKIP END DO
SELECT finalans COPY TO \getans.xls xls
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Cronbach's alpha
~rom Wikipedia, tbe free encyclopedia
Redirected from Cronbach alpha)
:::ron bach's a (alpha) has an important use as a measure of the reliability of a psychometric instrument. It was first named as alpha by ::ron bach (1951 ), as he had intended to continue with further instruments. It is the extension of an earlier version, the Kuder-Richardson 'onnula 20 (often shortened to KR-20), which is the equivalent for dichotomous items, and Guttman (1945) developed the same quantity mder the name lambda-2. • .. ::ronbach's a is defined as
N ax - ~i=1 aY; , ( 2 N 2)
N- 1 ax .vhere N is the number of components (items or testlets), al- is the variance of the observed total test scores, and(!~ is the variance of
;omponent i for person y.
<\ltematively, the standardized Cronbach's a can also be defined as
!\T' -.. , . r
where N is the number of components (items or testlets) and f is the average of all (Pearson) correlation coefficients between the components.
file:/ /C:\My%20Documents\Cronbach's%20alpha%20-%20Wikipedia, %20the%20free%20en... 8/16/07
SUM
Adds all the numbers in a range of cells.
Syntax
SUM(numberl,number2, ... )
Number!, number2, ... are 1 to 30 arguments for which you want the total value or sum.
COUNT
Counts the number of cells that contain numbers and also numbers within the list of arguments. Use COUNT to get the number of entries in a number field that's in a range or array of numbers.
Syntax
COUNT(valuel,value2, ... )
Valuel, value2, ... are 1 to 30 arguments that can contain or refer to a variety of different types of data, but only numbers are counted.
SUMIF
Adds the cells specified by a given criteria.
Syntax
SUMIF(range,criteria,sum _range)
Range is the range of cells you want evaluated.
Criteria is the criteria in the form of a number, expression, or text that defines which cells will be added. For example, criteria can be expressed as 32, "32", ">32", "apples".
Sum _range are the actual cells to sum.
COUNTIF
' I
Counts the number of cells within a range that meet the given criteria.
Syntax
CO UNTIF( range,criteria)
Range is the range of cells from which you want to count cells.
Criteria is the criteria in the form of a number, expression, or text that defines which cells will be counted. For example, criteria can be expressed as 32, "32", ">32", "apples".
IF
Returns one value if a condition you specify evaluates to TRUE and another value if it evaluates to FALSE.
Use IF to conduct conditional tests on values and formulas.
AVERAGE
Returns the average (arithmetic mean) of the arguments.
Syntax
A VERAGE(numberl,number2, ... )
Numberl, number2, ... are 1 to 30 numeric arguments for which you want the average.
MAX
Returns the largest value in a set of values.
Syntax
MAX(numberl,number2, ... )
Numberl, number2, ... are 1 to 30 numbers for which you want to find the maximum value.
L ...... _ _,,
MIN
Returns the smallest number in a set of values.
Syntax
MIN(numberl,number2, ... )
Numbed, number2, ... are 1 to 30 numbers for which you want to find the minimum value.
STDEV
Estimates standard deviation based on a sample. The standard deviation is a measure of how widely values are dispersed from the average value (the mean).
Syntax
STDEV(numberl,number2, ... )
Numberl, number2, ... are 1 to 30 number arguments corresponding to a sample of a population. You can also use a single array or a reference to an array instead of arguments separated by commas.
CORREL
Returns the correlation coefficient of the arrayl and array2 cell ranges. Use the correlation coefficient to determine the relationship between two properties. For example, you can examine the relationship between a location's average temperature and the use of air conditioners.
Syntax
CORREL( array I ,array2)
Arrayl is a cell range of values.
Array2 is a second cell range of values.
PERCENTRANK
Returns the rank of a value in a data set as a percentage of the data set. This function can be used to evaluate the relative standing of a value within a data set. For example, you can use PERCENTRANK to evaluate the standing of an aptitude test score among all scores for the test.
Syntax
PERCENTRANK( array ,x,significance)
Array is the array or range of data with numeric values that defines relative standing.
X is the value for which you want to know the rank.
Significance is an optional value that identifies the number of significant digits for the returned percentage value. If omitted, PERCENTRANK uses three digits (O.xxx).
RANK
Returns the rank of a number in a list of numbers. The rank of a number is its size relative to other values in a list. (If you were to sort the list, the rank of the number would be its position.)
Syntax
RANK(number,ref,order)
Number is the number whose rank you want to find.
Ref is an array of, or a reference to, a list of numbers. Nonnumeric values in ref are ignored.
Order is a number specifying how to rank number.
• If order is 0 (zero) or omitted, Microsoft Excel ranks number as if ref were a list sorted in descending order.
• If order is any nonzero value, Microsoft Excel ranks number as if ref were a list sorted in ascending order
MEDIAN
Returns the median of the given numbers. The median is the number in the middle of a set of numbers; that is, half the numbers have values that are greater than the median, and half have values that are less.
Syntax
MEDIAN(numberl,number2, ... )
Number!, number2, ... are 1 to 30 numbers for which you want the median.
ABS
Returns the absolute value of a number. The absolute value of a number is the number without its sign.
Syntax
ABS(number)
Number is the real number of which you want the absolute value.
SQRT
Returns a positive square root.
Syntax
SQRT(number)
Number is the number for which you want the square root.
SUMSQ
Returns the sum of the squares of the arguments.
Syntax
2Lf7 __
SUMSQ(numberl,number2, ... )
Numberl, number2, ... are 1 to 30 arguments for which you want the sum of the squares. You can also use a single array or a reference to an array instead of arguments separated by commas.
FREQUENCY
Calculates how often values occur within a range of values, and then returns a vertical array of numbers. For example, use FREQUENCY to count the number of test scores that fall within ranges of scores. Because FREQUENCY returns an array, it must be entered as an array formula.
Syntax
FREQUENCY(~ata_array,bins_array) ·,
Data_ array is an array of or reference to a set of values for which you want to count frequencies. Ifdata_array contains no values, FREQUENCY returns an array ofzeros.
Bins_ array is an array of or reference to intervals into which you want to group the values in data_array. Ifbins_array contains no values, FREQUENCY returns the number of elements in data_array.
MODE
Returns the most frequently occurring, or repetitive, value in an array or range of data. Like MEDIAN, MODE is a location measure.
Syntax
MODE(numberl,number2, ... )
Numberl, number2, ... are 1 to 30 arguments for which you want to calculate the mode. You can also use a single array or a reference to an array instead of arguments separated by commas.
QUARTILE
Returns the quartile of a data set. Quartiles often are used in sales and survey data to
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