Uji Median

^xdxe~xe` Kik Zdrdbcxre`

Odo > < Sle ^xdxe~xe` Hsd ^dbzcm Ekhczckhck 

Odo > Sle ^xdxe~xe` Hsd ^dbzcm Ekhczckhck &^dmekg Ocod~% ?+ Sle Bchedk Sle Bchedk dhdmdf ~dmdf ~dxs zri~chsr udkg zdmekg ~chcrfdkd hdk zdmekg msd~ zckggskddkkud skxs` zckgsledk fezixc~e~ kim udkg bckudxd`dk odfwd hsd ~dbzcm ocod~ xcmdf hexdre` hdre zizsmd~e"zizsmd~e hckgdk bchedk"bchedk udkg ~dbd+ D~sb~e"d~sb~e  D+ Hdxd xcrhere dxd~ hsd ~dbzcm dnd` ocod~ < V 4 4-  V ?  ? - ‡- V k4  k4 - hdk U 4  4 - U ?  ?-  ‡- U k?  k? + O+ ^`dmd zckgs`srdk udkg hegskd`dk ~c`srdkg"`srdkgkud irhekdm+ N+ Qdredocm"qdredocm dnd`kud `ikxeks+ H+ Dzdoemd `chsd zizsmd~e bcbeme`e bchedk udkg ~dbd- bd`d odge bd~ekg"bd~ekg zizsmd~e ~dbd zsmd zcmsdkg z  zcmsdkg z odfwd odfwd ~cosdf fd~em zckgdbdxdkkud d`dk bcmcoefe bchedk `c~cmsrsfdk & grdkh  & grdkh  bchedk % Fezixc~e~"fezixc~e~  D &Hsd ^e~e% F: < @chsd ~dbzcm ocrd~dm hdre zizsmd~e"zizsmd~e udkg ~crszd &ehckxe`%+ F4 < Ckxdf kemde"kemde V  nckhcrskg mcoef oc~dr heodkhekg`dk kemde"kemde U - dxds kemde"kemde U  nckhcrskg mcoef oc~dr heodkhekg`dk kemde"kemde V + Xdrda kudxd & δ   %    δ ^xdxe~xe` Sle  Mdkg`df"mdkg`df skxs` ^xdxe~xe` Sle zdhd Sle Bchedk B chedk eke- ~codgde ocre`sx < 4+ Xckxs`dk Bchedk ~dbzcm gdoskgdk `chsd ~dbzcm+ ?+ @cbshedk osdx ~cosdf xdocm `ikxegck~e - ~czcrxe Xdocm >+8 he odwdf eke Xdocm >+8 Zckudledk hdxd skxs` Sle Bchedk

@chshs`dk Xcrfdhdz Bchedk Gdoskgdk He Dxd~ He Odwdf Lsbmdf

~dbzcm 4 D N D  N 2 k4

? O H O  H 2 k?

Lsbmdf DO NH D  O  N  H 2 k 4  k? 2 K

@cxcrdkgdk < D < Odkud`kud fd~em zckgdbdxdk hdre ~dbzcm 4 udkg mcoef oc~dr hdrezdhd Bchedk Gdoskgdk+

Fdmdbdk ?1 

^xdxe~xe` Kik Zdrdbcxre`

O < N < H <

Odo > < Sle ^xdxe~xe` Hsd ^dbzcm Ekhczckhck 

Odkud`kud fd~em zckgdbdxdk hdre ~dbzcm ? udkg mcoef oc~dr hdrezdhd Bchedk Gdoskgdk+ Odkud`kud fd~em zckgdbdxdk hdre ~dbzcm ~dbzcm 4 udkg mcoef `cnem hdrezdhd Bchedk Gdoskgdk+ Odkud`kud fd~em zckgdbdxdk hdre ~dbzcm ? udkg mcoef `cnem hdrezdhd Bchedk Gdoskgdk+

Xcrldhe Dkg`d ^dbd  Dzdoemd xcrldhe dhd kemde"kemde zckgdbdxdk udkg ~dbd hckgd Bchedk Gdoskgdk- hdzdx hexdkgdke hckgd ~dmdf ~dxs hdre hsd ndrd ocre`sx < d+ Le`d K  oc~dr- hdk le`d fdkud ~che`ex fd~em zckgdbdxdk udkg ~dbd hckgdk Bchedk Gdoskgdk- bd`d oimcf hemd`s`dk zckuekg`erdk dkg`d udkg ~dbd xcr~cosx ~cocmsb bsmde bckgfexskg ~xdxe~xe` sle+ o+ Fd~em zckgdbdxdk udkg ~dbd hckgdk Bchedk Gdoskgdk- oimcf hemd`s`dk zcbodgedk odku`dkud dkg`d udkg ~dbd hckgdk bcmcxd``dk he `cmibzi` dxd~ hdk `cmibzi` odwdf hckgdk ~cgdmd ndrd udkg bskg`ek+ >+ ^cxcmdf hezcrimcf Xdocm @ikxegck~e- Fexskg X ~codgde ~xdxe~xe` sle hckgdk rsbs~ < D X2

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k4

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4    + k ?  

- skxs`  τ  2

@dehdf Zckgdboemdk @czsxs~dk  Hegskd`dk Xdocm ? He~xreos~e Kirbdm Xckxs`dk fdrgd `rexe~ kemde | ocrhd~dr`dk | ocrhd~dr`dk xdrda kudxd

δ

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udkg hedboem+

Ximd`mdf F:- le`d X  mcoef oc~dr hdre fdrgd `rexe~ kemde |  zi~exea dxds X  mcoef `cnem hdre fdrgd `rexe~ kemde | kcgdxea+ | kcgdxea+ Nikxif >+? < _s~cmm h``- bcmdzir`dk kemde"kemde ^xri`c"ekhcv  ~czcrxe udkg xcrmefdx hdmdb Xdocm >+3 skxs` zd~eck"zd~eck udkg hexdkgdke imcf skex re~cx ekadr` bei`drhed  he ~cosdf rsbdf ~d`ex skeqcr~exd~+ @exd ekgek xdfs dzd`df hdxd eke bckuched`dk os`xe udkg bcbdhde skxs` bckskls``dk odfwd bchedk"bchedk `chsd zizsmd~e udkg hewd`eme imcf hdxd `chsd ~dbzcm bcbeme`e zcrochddk zdhd xdrda kudxd δ 2 :+:3 Xdocm >+3 Fdrgd"fdrgd ~xri`c"ekhcv - hdmdb bememexcr- skxs` zd~eck"zd~eck udkg herdwdx he skex re~cx Buindrhedm"  ekadrnxeik ~cosdf rsbdf ~d`ex skeqcr~exd~ Hedgki~e~ Dkxcreir xrdk~bsrd ekadrnxeik hdk dkxcreir kcnri~e~ & V % ?3 4> 5 81 ?3 >: 47 ?: 47 ?: >7 ?3

Ekxcreir xrdk~bsrdm ekadrnxeik hdk ekxcreir kcnri~e~ & U % >4 8> ?4 8? >6 >:

Fdmdbdk ?7 

^xdxe~xe` Kik Zdrdbcxre`

?1 46 >: ?8 ?4

?> ?1 4? ?: >7

?: 44 >? 41 >4

Odo > < Sle ^xdxe~xe` Hsd ^dbzcm Ekhczckhck 

47 >1 38 6 ?1

45 >6 84 16 ?6

?: ?5 4> >? >:

^sbocr ? &457>%- 6"41

Zckucmc~dedk < Fezixc~e~"fezixc~e~  F: < Bchedk kemde ~xri`c"ekhc`~ skxs` ~xri`c"ekhc`~  skxs` zd~eck"zd~eck hckgdk Dkxcreir xrdk~bsrd ekadrnxeik  hdk dkxcreir kcnri~e~  ~dbd hckgdk Bchedk kemde ~xri`c"ekhc`~  skxs` zd~eck"zd~eck hckgdk Ekxcreir xrdk~bsrdm ekadrnxeik  hdk ekxcreir kcnri~e~  F4 < Ckxdf kemde"kemde V nckhcrskg mcoef oc~dr heodkhekg`dk kemde"kemde U- dxds kemde"kemde U nckhcrskg mcoef oc~dr heodkhekg`dk kemde"kemde V+ Xdrda kudxd δ  2 :+:3  ^xdxe~xe` Sle  4+ Bchedk Gdoskgdk hdre 86 hdxd `chsd ~dbzcm hezcrimcf dkxdrd hdxd `c"?8 hdk `c"?3- udexs ?3 + ?1 ?3 hdk ?1- ~cfekggd Bchedk gdoskgdkkud dhdmdf 2 ?3+3 ? ?+ ^cxcmdf hezcrimcf bchedk gdoskgdk- heosdx xdocm `ikxegck~e+ Xdocm >+1 bcbzcrmefdx`dk odkud`kud fd~em zckgdbdxdk hdmdb bd~ekg"bd~ekg ~dbzcm udkg he dxd~ hdk he odwdf ?3+3 Xdocm >+1 Xdocm @ikxegck~e skxs` Nikxif >+? Dkxcreir xrdk~bsrde @chshs`dk Ekadrnxeik hdk dkxcreir Xcrfdhdz ?3+3 Kcnreir He dxd~ 4? He odwdf ?: Lsbmdf >?

>+ Hdre Xdocm >+1 hezcrimcf skxs`  τ  2

^cfekggd hdzdx hezcrimcf X

2

Ekxcreir xrdk~bsrde ekadrnxeik hdk ekxcreir kcnreir 4? 8 41

4? + 4? 86 4? >?

2

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Lsbmdf ?8 ?8 86

:+3: 4? 41

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4

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  >? 41  +

@czsxs~dk  Xdocm ? He~xreos~e Kirbdm- hezcrimcf kemde `rexe~ |  hckgdk xdrda kudxd δ)? 2 :-:3)? 2 :-:?3 dhdmdf ´ 4+51 @drckd X 2 X 2 "?+83 mcoef `cnem hdre fdrgd `rexe~ | 2 | 2 "4+51 - bd`d F : hdzdx heximd`+ @c~ebzsmdk 

Fdmdbdk ?6 

^xdxe~xe` Kik Zdrdbcxre`

Odo > < Sle ^xdxe~xe` Hsd ^dbzcm Ekhczckhck 

Odfwd dhd zcrochddk dkxdrd bchedk"bchedk `chsd zizsmd~e xcr~cosx zdhd xdrda kudxd :+:3

Fdmdbdk ?5