Additional Mathematics Project Work 2013 (Form 5): Statistics
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Transcript of Additional Mathematics Project Work 2013 (Form 5): Statistics
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ADDGTGIJAM FATL@FATGBR^XIK@BT SIXO 8>12
Jaf`; Caj Fgjc Kgajc
Bmass; 0E
G)B Ji; 751114&18&57
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Gjtridubtgij
S` stud`jts taogjc Addgtgijam Fatl`fatgbs ar` r`qugr`d ti barry iut a prik`bt wiro
wlgm` w` ar` gj Eirf 0* S` ar` ti bifpm`t` ijmy IJ@ taso has`d ij statgstgbs* Tlgs prik`bt baj
h` dij` gj criups ir gjdgvgduammy- ajd G cmadmy bliis` ti di tlgs gjdgvgduammy* Ppij bifpm`tgij
ie tl` Addgtgijam Fatl`fatgbs ^rik`bt Siro- w` ar` ti cagj vamuahm` `xp`rg`jb`s ajd ahm` ti;
Appmy ajd adapt a varg`ty ie prihm`f simvgjc strat`cg`s ti simv` riutgj` ajd jij&riutgj`prihm`fs*
@xp`rg`jb` bmassriif `jvgrijf`jts wlgbl ar` blamm`jcgjc- gjt`r`stgjc ajd f`ajgjceumajd l`jb` gfpriv` tl`gr tlgjogjc sogmms*
@xp`rg`jb` bmassriif `jvgrijf`jts wl`r` ojiwm`dc` ajs sogmms ar` appmg`d gjf`ajgjceum ways gj simvgjc r`am&mge` prihm`fs*
@xp`rg`jb` bmassriif `jvgrijf`jts wl`r` `xpr`ssgjc ij`s fatl`fatgbam tlgjogjc-r`asijgjc ajd biffujgbatgij ar` lgclmy `jbiurac`d ajd `xp`bt`d*
@xp`rg`jb` bmassriif `jvgrijf`jts tlat stgfumat`s ajd `jlajb`s `ee`btgv` m`arjgjc* Abqugr` `ee`btgv` fatl`fatgbam biffujgbatgij tlriucl iram ajd wrgtgjc- ajd ti us` tl`
majcuac` ie fatl`fatgbs ti `xpr`ss fatl`fatgbam gd`as birr`btmy ajd pr`bgs`my*
@jlajb` abqugsgtgij ie fatl`fatgbam ojiwm`dc` ajd sogmms tlriucl prihm`f&simvgjc gjways tlat gjbr`as` gjt`r`st ajd bijegd`jb`*
^r`par` iurs`mv`s eir tl` d`fajd ie iur eutur` ujd`rtaogjcs ajd gj wiropmab`* X`amgz` tlat fatl`fatgbs gs aj gfpirtajt ajd piw`reum tiim gj simvgjc r`am&mge` prihm`fs
ajd l`jb` d`v`mip pisgtgv` attgtud` tiwards fatl`fatgbs*
Tragj iurs`mv`s jit ijmy ti h` gjd`p`jd`jt m`arj`rs hut amsi ti bimmahirat`- ti biip`rat`-ajd ti slar` ojiwm`dc` gj aj `jcacgjc ajd l`amtly `jvgrijf`jt *
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Ps` t`bljimicy `sp`bgammy tl` GBT appriprgat`my ajd `ee`btgv`my* Tragj iurs`mv`s ti appr`bgat` tl` gjtrgjsgb vamu`s ie fatl`fatgbs ajd ti h`bif` fir`
br`atgv` ajd gjjivatgv`*
X`amgz` tl` gfpirtajb` ajd tl` h`auty ie fatl`fatgbs* S` ar` `xp`bt`d ti suhfgt tl`prik`bt wiro wgtlgj tlr`` w``os erif tl` egrst day tl` taso gs h`gjc adfgjgst r`d ti us*
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Hrg`e Lgstiry ie Rtatgstgbs
Hy tl` 1
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Rtatgstgbs tiday
Durgjc tl` 8>tl b`jtury- tl` br`atgij ie pr`bgs` gjstruf`jts eir acrgbumturam r`s`arbl-
puhmgb l`amtl bijb`rjs ,`pgd`fgimicy- hgistatgstgbs- `tb*'- gjdustrgam quamgty bijtrim- ajd
`bijifgb ajd sibgam purpis`s ,uj`fpmiyf`jt rat`- `bijif`try- `tb*' j`b`ssgtat`d suhstajtgam
advajb`s gj statgstgbam prabtgb`s*
Tiday tl` us` ie statgstgb las hriad`j`d ear h`yijd gts irgcgj* Gjdgvgduams ajd
ircajgzatgijs us` statgstgbs ti ujd`rstajd data ajd fao` gjeirf`d d`bgsgijs tlriucliut tl`
jaturam ajd sibgam sbg`jb`s- f`dgbgj`s- husgj`ss- ajd itl`r ar`a*
Rtatgstgbs ar` c`j`rammy r`card`d jit as tl` suheg`md ie fatl`fatgbs hut ratl`r as a
dgstgjbt- ammg`d- eg`md* Fajy ujgv`rsgtg`s fagjtagj s`parat` fatl`fatgbs ajd statgstgb d`partf`jts*
Rtatgstgb gs amsi tauclt gj d`partf`jt as dgv`rs` as psyblimicy- `dubatgij ajd puhmgb l`amtl*
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F`aj
Tl` f`aj gs wlat gj `v`ryday bijv`rsatgij gs bamm`d tl` av`rac`* Gt gs bambumat`d hysgfpmy
addgjc tl` vamu`s ie amm tl` vamgd bas`s tic`tl`r ajd dgvgdgjc hy tl` jufh`rie vamgd bas`s*
Tl` f`aj gs aj gjt`rvam)ratgi f`asur` ie b`jtram t`jd`jby* Gts bambumatgij r`qugr`s
tlat tl` attrghut`s ie tl` vargahm` r`pr`s`jt a juf`rgb sbam`
Fid`
Tl` fid` gs tl` attrghut` ie a vargahm` tlat ibburs fist iet`j gj tl` data s`t*
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Eir ujcriup`d data- w` baj egjd fid` hy egjdgjc tl` fidam bmass ajd draw tl` fidam bmass ajd
twi bmass`s adkab`jt ti tl` fidam bmass* Twi mgj`s erif tl` adkab`jt w` briss`d ti egjd tl`
gjt`rs`btgij* Tl` gjt`rs`btgij vamu` gs ojiwj as tl` fid`*
F`dgaj
Tl` f`dgaj gs a f`asur` ie b`jtram t`jd`jby* Gt gd`jtgeg`s tl` vamu` ie tl` fgddm` bas` wl`j tl`
bas`s lav` h``j pmab`d gj ird`r ir gj mgj` erif miw ti lgcl* Tl` fgddm` ie tl` mgj` gs as ear erif
h`gjc `xtr`f` as yiu baj c`t*
Tl`r` ar` as fajy bas`s gj mgj` gj erijt ie tl` fgddm` bas` as h`lgjd tl` fgddm` bas`* Tl`
f`dgaj gs tl` attrghut` us`d hy tlat fgddm` bas`* Sl`j yiu ojiw tl` vamu` ie tl` f`dgaj- yiu
ojiw tlat at m`ast lame tl` bas`s lad tlat vamu` ir a lgcl`r vamu`- wlgm` at m`ast lame tl` bas`s lad
tlat vamu` ir a miw`r vamu`*
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Xajc`
Tl` dgstajb` h`tw``j tl` fgjgfuf ajd tl` faxgfuf gs bamm`d tl` rajc`* Tl` marc`r tl` vamu` ie
tl` rajc`- tl` fir` dgsp`rs`d tl` bas`s ar` ij tl` vargahm`? tl` sfamm`r tl` vamu` ie tl` rajc`- tl`
m`ss dgsp`rs`d ,tl` fir` bijb`jtrat`d' tl` bas`s ar` ij tl` vargahm`
Xajc` 6 faxgfuf vamu`fgjgfuf vamu`
Gjt`rquartgm` Xajc`
Gjt`rquartgm` rajc` ,GQX' gs tl` dgstajb` h`tw``j tl` 30tl p`rb`jtgm` ajd tl` 80tl p`rb`jtgm`* Tl`
GQX gs `ss`jtgammy tl` rajc` ie tl` fgddm` 0>% ie tl` data* H`baus` gt us`s tl` fgddm` 0>%- tl`
GQX gs jit aee`bt`d hy iutmg`rs ir `xtr`f` vamu`s*
GQX 6 Rtajdard D`vgatgij
Tl` stajdard d`vgatgij t`mms yiu tl` apprixgfat` av`rac` dgstajb` ie bas`s erif tl` f`aj* Tlgs
gs `asg`r ti bifpr`l`jd tlaj tl` squar`d dgstajb` ie bas`s erif tl` f`aj* Tl` stajdard d`vgatgij
gs dgr`btmy r`mat`d ti tl` vargajb`*
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Ge yiu ojiw tl` vamu` ie tl` vargajb`- yiu baj `asgmy egcur` iut tl` vamu` ie tl` stajdard
d`vgatgij* Tl` r`v`rs` gs amsi tru`* Ge yiu ojiw tl` vamu` ie tl` stajdard d`vgatgij- yiu baj
`asgmy bambumat` tl` vamu` ie tl` vargajb`* Tl` stajdard d`vgatgij gs tl` squar` riit ie tl`
vargajb`*
,h' Eir `abl typ` ie f`asur` ie b`jtram t`jd`jby stat`d gj ,a'- cgv` `xafpm`s ie tl`gr us`s gj
dagmy mge`*
Ps`s ie f`aj
F`aj baj h` us`d ti s`` tl` av`rac` faro ie tl` bmass ihtagj`d* Tlgs av`rac` l`mps ti s`` liw
fajy stud`jts ar` ahiv` av`rac`- liw fajy ar` av`rac` stud`jts ajd liw fajy ar` h`miw
av`rac`s* Tl` t`abl`r trg`s ti l`mp tl` av`rac` ajd h`miw av`rac` stud`jts ti sbir` fir` crad`s
gj eutur`* Gj a eabtiry- tl` f`aj ie tl` wac`s l`mps tl` autlirgtg`s ti ojiw ge tl` wiro`rs# w`mear`
gs fagjtagj`d* Gt amsi l`mps ti bifpar` tl` samarg`s ie tl` `fpmiy``s ie tl` dgee`r`jt bifpajg`s*
Gj sam`s- tl` av`rac` sam`s gj tl` dgstrgbt l`mp tl` sam`s fajac`r ti pmaj eir gjbr`asgjc tl` sam`s gj
tl` eutur`* Tl` civ`rjf`jt tao`s tl` av`rac` gjbif` ajd `xp`js` ie tl` bgtgz`js ti ojiw
wl`tl`r tl` bgtgz`js rgclts ar` fagjtagj`d* Tl` eafgmy egjds tl` av`rac` ie tl`gr `xp`js`s ti
hamajb` tl`gr egjajb`* Tl` av`rac` pridubtgij ie acrgbumturam biffidgtg`s- tl` gjdustrgam ciids-
tl` av`rac` xpirts ajd gfpirts l`mp tl` biujtry ti s`` tl`gr d`v`mipf`jts*
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Ps`s ie f`dgaj
F`dgaj gs tl` fgddm` vamu`* Gt l`mps us ti s`` hitl tl` sgd`s ie tl` fgddm` vamu`* Gt dgvgd`s tl`
gjeirfatgij gjti twi `quam parts- ij` part m`ss`r tlaj f`dgaj ajd tl` itl`r fir` tlaj tl`
f`dgaj* F`dgaj gs bambumat`d aet`r arrajcgjc tl` gjeirfatgij gj asb`jdgjc ird`r ir d`sb`jdgjc
ird`r* F`dgaj gs us`d ti egjd tl` stud`jts wli sbir`s m`ss ir fir` tlaj tl` fgddm` vamu`*
F`dgaj gs bambumat`d ti egjd tl` dgstrghutgij ie tl` wac`s* Gt gs bambumat`d ti egjd tl` l`gclt ie tl`
pmay`rs- gj tl` pigjts sbir`d hy pmay`rs gj a s`rg`s ie fatbl`s- ti egjd tl` fgddm` vamu` ie tl`
ac`s ie tl` stud`jts gj a bmass `tb* F`dgaj amsi d`t`rfgj`s tl` piv`rty mgj`*
Ps`s ie fid`
Gt gs us`d ti bambumat` tl` er`qu`jby ie tl` arrgvam ie tl` puhmgb trajspirt- tl` er`qu`jby ie tl`
caf`s wij hy a t`af ie pmay`rs- tl` er`qu`jby ie tl` j``ds ie aj gjeajt* Tl` fid` gs amsi s``j
gj bambumatgij ie tl` wac`s- gj tl` jufh`r ie t`m`plij` bamms r`b`gv`d gj a fgjut` hy tl`
t`m`plij` d`partf`jt- tl` er`qu`jby ie tl` vgsgtirs- tl` er`qu`jby ie tl` patg`jts vgsgtgjc tl`
lispgtams- tl` fid` ie trav`m `tb*
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^AXT 8
1* C`t yiur bmass faros ie ajy suhk`bt gj ij` `xafgjatgij)t`st* Attabl tl` faro sl``t*Faro sl``t ie 0Es ^lysgbs `xafgjatgij
1* Adrg`m Mg Blg Tao 33
8* Amaj Adaf Owaj 51
2* Hryaj Madgsmaus 05
4* Bl`jc Oajc Ogaj 47
0* Blgj ^gj Quaj 03
5* Blujc Bg Fgjc 01
3* @dwgj Mau Oio Uug 5>
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27* Jur Ryalgdal hgjtg Ahdum Xaslgd 47
4>* Jur Ryalgral hgjtg Ahdum Xaslgd 42
41* Jur Ryaqgra Lajajg` hgjtg [agjam 23
48* ^ajc Waj 00
42* Xilajg Arpa 0>
44* Rammy Mag Lu`y Mgj 3140* Rlargeal Fargajg Lahgh Lafgd 45
45* Rl``ja Mg`w S`g Rluaj 53
43* Rl`mm` Taj Bl`w Mgjc 52
Titam , ' 8 554
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8* ,a' F`aj
,h' F`dgaj
, ' F`dgaj faro6 007
Fid` 6 03*0
, '
, '
,' 6 03*0
>
8
4
5
18
1> 17 8> 87 2> 27 4> 47 0> 07 5> & 57 3> &37 & 77
Er`qu`jby
Bmass Faros
0E stud`jts# faros eir ^lysgbs @xafgjatgij
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,ggg' F`dgaj
F`tlid 1; F`dgaj eirfuma
F`dgaj faro 6 03*82
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>
0
1>
10
8>
80
2>
20
4>
40
0>
> 8> 4> 5> 1>> 18>
Bufumatgv`Er`qu`jby
Bmass Faros
F`tlid 8; Icgv` Crapl
0E stud`jts faros eir ^lysgbs @xafgjatgij
F`dgaj faro has`d ij tl` icgv` crapl 6 0
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,gv' Rtajdard d`vgatgij
F`tlid 1; Rtajdard d`vgatgij eirfuma
F`tlid 8; Bambumatir
1* Bmgbo ij tl` FID@ huttij twgb`* ^r`ss huttij 1 ti bliis` RD* Tlgs puts tl`bambumatir gj Rtatgstgbs Fid`*
8* O`y gj tl` egrst data- x- wlgbl gs 4*0 gjti tl` bambumatir* ^r`ss tl` RLGET huttij- ajdeimmiws hy tl` - huttij*
2* Aet`r tlat- o`y gj tl` er`qu`jby ie tl` data 4*0- wlgbl gs >*4* ^r`ss tl` F/ huttij*0* O`y gj tl` r`st ie tl` data hy r`p`atgjc st`ps 8- 2 ajd 4*5* Aet`r o`ygjc gj amm tl` data- pr`ss RLGET huttij acagj*3* ^r`ss huttij 8**Tl` ajsw`r sliw`d ij tl` bambumatir gs 13*2>*
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,v' Gjt`rquartgm` Xajc`
F`tlid 1; Gjt`rquartgm` Xajc` Eirfuma
GQX 6 GQX 6
6 81*25
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>
0
1>
10
8>
80
2>
20
4>
40
0>
> 8> 4> 5> 1>> 18>
Bufumatgv`Er`qu`j
by
Bmass Faros
F`tlid 8; Icgv` Crapl
0E stud`jts faros eir ^lysgbs @xafgjatgij
Has`d ij tl` icgv` crapl-
GQX 6
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,h' Has`d ij yiur ajsw`rs erif 2,a' ahiv`- stat` tl` fist appriprgat` f`asur` ie b`jtram
t`jd`jby tlat r`em`bt tl` p`reirfajb` ie yiur bmass* Cgv` yiur r`asijs*
Has`d ij fy ajsw`rs erif 2,a'- tl` f`aj gs a fir` sugtahm` f`asur` ie b`jtram t`jd`jby
h`baus` gt r`em`bts tl` b`jtram vamu` ariujd wlgbl tl` data s``fs ti bmust`r* Tl` fid` gs
jit sugtahm` h`baus` tl` data di`s jit s``f ti bmust`r ahiut fid`* Tl` f`dgaj gs amsi jit
tlat sugtahm` as gt ijmy sliws tl` fgddm` vamu` ie tl` wlim` data*
,b' F`asur` ie dgsp`rsgij gs a f`asur`f`jt us`d ti d`t`rfgj` liw ear tl` vamu`s ie data
ar` spr`ad iut erif gts av`rac` vamu`*
@xpmagj tl` advajtac`s ie usgjc stajdard d`vgatgij bifpar`d ti gjt`rquartgm` rajc` as tl`
h`tt`r f`asur` ie dgsp`rsgij
Rtajdard d`vgatgij ,RD' gs tl` fist biffijmy us`d f`asur` ie dgsp`rsgij* Gt gs a
f`asur` ie spr`ad ie data ahiut tl` f`aj* RD gs tl` squar` riit ie suf ie squar`d
d`vgatgij erif tl` f`aj dgvgd`d hy tl` jufh`r ie ihs`rvatgijs*
Gj hitl tl`s` eirfumas j & 1 gs us`d gjst`ad ie j gj tl` d`jifgjatir- as tlgs pridub`s a
fir` abburat` `stgfat` ie pipumatgij RD*
Tl` r`asij wly RD gs a v`ry us`eum f`asur` ie dgsp`rsgij gs tlat- ge tl` ihs`rvatgijs ar`
erif a jirfam dgstrghutgij- tl`j 5
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ihs`rvatgijs mg` h`tw``j f`aj 8 RD ajd 77*3% ie ihs`rvatgijs mg` h`tw``j f`aj 2
RD
Tl` itl`r advajtac` ie RD gs tlat amijc wgtl f`aj gt baj h` us`d ti d`t`bt so`wj`ss*
Gjt`rquartgm` rajc` gs d`egj`d as tl` dgee`r`jb` h`tw``j tl` 80tl
ajd 30tl
p`rb`jtgm` ,amsi
bamm`d tl` egrst ajd tlgrd quartgm`'* L`jb` tl` gjt`rquartgm` rajc` d`sbrgh`s tl` fgddm` 0>%
ie ihs`rvatgijs* Ge tl` gjt`rquartgm` rajc` gs marc` gt f`ajs tlat tl` fgddm` 0>% ie
ihs`rvatgijs ar` spab`d wgd` apart*
Tl` fagj dgsadvajtac` gj usgjc gjt`rquartgm` rajc` as a f`asur` ie dgsp`rsgij gs tlat gt gs
jit af`jahm` ti fatl`fatgbam fajgpumatgij*
Tl` stajdard d`vgatgij cgv`s a f`asur` ie dgsp`rsgij ie tl` data ahiut tl` f`aj* A dgr`bt
ajamicy wiumd h` tlat ie tl` gjt`rquartgm` rajc`- wlgbl cgv`s a f`asur` ie dgsp`rsgij
ahiut tl` f`dgaj* Liw`v`r- tl` stajdard d`vgatgij gs c`j`rammy fir` us`eum tlaj tl`
gjt`rquartgm` rajc` as gt gjbmud`s amm data gj gts bambumatgij* Tl` gjt`rquartgm` rajc` gs
titammy d`p`jd`jt ij kust twi vamu`s ajd gcjir`s amm tl` itl`r ihs`rvatgijs gj tl` data*
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Tlgs r`dub`s tl` abburaby gt `xtr`f` vamu` gs pr`s`jt gj tl` data* Rgjb` tl` faros di`s
jit bijtagj ajy `xtr`f` vamu`- stajdard d`vgatgij cgv` a h`tt`r f`asur`s bifpar`d ti
gjt`rquartgm` rajc`*
4* ,a' S` baj bambumat` f`aj- f`dgaj- fid` ajd stajdard d`vgatgijs usgjc hitl criup`d
ajd ujcriup`d data* Liw`v`r- tl`r` ar` stgmm dgee`r`jb`s h`tw``j tl` ajsw`r ie tl`
bambumatgij* Eir aj `xafpm`- tl` egjam ajsw`r ie tl` f`aj gj ujcriup`d data gs 05*5* Hitl ie tl` ajsw`rs dgee`r wgtl a
vamu` ie >*4
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Egrst- eir `xafpm`- wl`j pr`s`jtgjc a marc` s`rg`s ie data- gt gs fir` pr`e`rahm` ti us`
criup`d data as criup`d data gs w`mm arrajc`d ajd gt gs `asg`r eir us ti ihs`rv`* M`ss
tgf` ajd `j`rcy wgmm h` j``d`d gj biujtgjc tl` data `abl ti bambumat` f`aj-
f`dgaj- fid` ajd stajdard d`vgatgij ie tl` data*
Liw`v`r- gt gs fir` pr`e`rahm` ti us` ujcriup`d data wlgm` egjdgjc r`sumts durgjc aj
gjv`stgcatgij* Tlgs gs h`baus` amm tl` data ar` us`d hut jit gj criup`d data* Tlus- gt wgmm
cgv` a fir` abburat` r`sumt*
Mastmy- criup`d data gs amsi fir` pr`e`rahm` durgjc bmassgegbatgij- d`t`rfgjgjc
rajc` ajd fistmy wl`j tl` jufh`r ie data gs egx`d* Ge tl` jufh`r ie data gs egx`d ir gt
bijtagjs aj `xtr`f` vamu` wlgbl gt gs lard ti h` criup`d- gt gs h`tt`r ti us` aj ujcriup`d
data*
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^AXT 2
1* Wiur t`abl`r wgmm add 2 faros eir `abl stud`jt gj yiur bmass eir bifpm`tgjc amm tl`gr
assgcjf`jts* Fao` a bijk`btur` eir tl` j`w vamu`s ie tl` eimmiwgjc;
,a' F`aj
J`w f`aj 6 05*8> / 2
6 07*8>
A H B D 1 4*0 3*0 > >
8 14*0 13*0 8 20
2 84*0 83*0 1 83*0
4 24*0 23*0 0 1 530
< 34*0 33*0 3 048*0
7 74*0 73*0 > > 43 8 3
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,h' Fid`
Fid` 6 03*0
J`w fid` 6 03*0/2
6 5>*0
Bmass Gjt`rvams ,Faros' Er`qu`jby-218 >
1288 8
8228 1
2248 0
4208 3
0258 11
52 & 38 1>
3> &37 3
& 77 >
,
'
J`w fid`
-
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F`tlid 8; Icgv` Crapl
0E stud`jts faros eir ^lysgbs @xafgjatgij
F`dgaj faros has`d ij tl` icgv` crapl 6 5>*2
>
0
1>
10
8>
80
2>
20
4>
40
0>
> 8> 4> 5> 1>>
Bufumatgv`
Er`
qu`jby
Bmass Faros
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,d' Gjt`rquartgm` Xajc`
GQX 6 81*25
F`tlid 1; Gjt`rquartgm` Xajc` Eirfuma
GQX 6 GQX 6
6 81*25
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>
0
1>
10
8>
80
2>
20
4>
40
0>
> 8> 4> 5> 1>>
Bufumatgv`
Er`qu
`jby
Bmass Faros
F`tlid 8; Icgv` Crapl
0E stud`jts faros eir ^lysgbs @xafgjatgij
Has`d ij tl` icgv` crapl-
GQX 6
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,`' Rtajdard d`vgatgij
Bmass Gjt`rvam ,Faros' Fgdpigjt- Er`qu`jby- 2 18 3*0 > > >12 88 13*0 8 20 518*0
82 28 83*0 1 83*0 305*80
22 48 23*0 0 121*80
42 08 43*0 3 228*0 10 372*30
02 58 03*0 11 528*0 25 25 530 40 058*0
32 42*30
580
72 1>8 73*0 > > >
Titam 470 43 8 3
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8* A j`w stud`jt las kust `jrimm`d gj yiur bmass* Tl` stud`jt sbir`d 73% gj lgs)l`r eirf`r
sbliim* Ge tl` stud`jts faro gs tao`j gjti abbiujt gj tl` ajamysgs ie yiur sbliim `xafgjatgij
ir t`st- bambumat` tl` f`aj ajd tl` j`w stajdard d`vgatgij*
J`w F`aj 6 5>*>>
Bmass Gjt`rvam ,Faros' Fgdpigjt- Er`qu`jby- 2 18 3*0 > > >12 88 13*0 8 20 518*0
82 28 83*0 1 83*0 305*80
22 48 23*0 0 121*80
42 08 43*0 3 228*0 10 372*30
02 58 03*0 11 528*0 25 25 530 40 058*0
32 42*30
580
72 1>8 73*0 1 73*0 7 0>5*80
Titam 470 4< 8
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J`w stajdard d`vgatgij 6 13*73>
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Eurtl`r @xpmiratgij
1* Tl` tip 8>% ie tl` stud`jts gj yiur bmass wgmm h` award`d hy tl` suhk`bt t`abl`r*Bambumat` tl` miw`st faro eir tlgs criup ie stud`jts hy usgjc craplgbam ajd bambumatgij
f`tlids*
Bambumatgij;
stud`jts4 stud`jts 6 2< stud`jts
, ' , ' 1
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Craplgbam f`tlid;
0E stud`jts faros eir ^lysgbs @xafgjatgij
Fgjgjuf faro ti h` award`d has`d ij tl` icgv` 6 38
>
1>
8>
2>
4>
0>
5>
> 8> 4> 5> 1>> 18>
Bufumatgv`Er`qu`jby
Bmass Faros