მონაცემთა აღწერილობა

13. monacemTa aRweriloba: tabulebis (cxrilebis),

diagramebis, histogramebis ageba

problema, romelsac Cven gamokvlevis am nawilSi vayenebT, mdgomareobs imaSi, rom saukeTeso saxiT warmovaCinoT Cveni samuSaos Sedegebi. Cven unda vipovoT naTeli, mokle, zusti stili, romelic obieqturad asaxavs monacemebs. amave dros Cven unda davexmaroT sxva mkvlevarebs gaigon mniSvneloba an mniSvnelovneba imisa, rac Cven gavarkvieT. sxvagvarad rom vTqvaT, Cven gvinda warmovaCinoT Sedegebi ise, rom is iyos advilad gasagebi. nawilobriv es damokidebulia statis­tikuri analizis gamoyenebaze, romelsac Cven ganvixilavT Semdeg TavSi. magram monacemTa swori interpolaciis warmateba damokidebulia sqema­turi da grafikuli masalis xarisxze, cxrilebisa da diagramebis warmatebul arCevaze, maT gakrveul (mkafio) da naTel agebulebaze.

monacemTa sqematuri da grafikuli aRwerilobis tipebis mraval­ferovneba (mravalsaxeoba) mniSvnelovania da Cven ar SegviZlia SevCerdeT yvelaze an imaTze, romlebic gansakuTrebiT xSirad gvxvdeba. ukeTesia, SeviswavloT ramdenime tipiuri magaliTi. Cven ganvixilavT im wyalqveSa qvebs, romlis Sesaxeb aucilebelia vicodeT rogorc kiTxvis, ise cxrilebis, grafikebis da a.S. momzadebisas. Cven SevexebiT iseT sakiT­xebs, rogoricaa: `rodis unda gamoviyenoT grafikebi? ra aris ukeTesi: cxrili Tu sqema? rogor gamoiyureba cxrili, sqema, diagrama (rogoria maTi struqtura)? rogor SeuZlia maT dagvexmaros sqematuri da grafi­kuli gamosaxulebis masalis gagebaSi?

CamonaTvalTa cxrili

daviwyoT am problemebis Seswavla TqvenTvis ukve nacnobi Camona­TvalTa cxrilidan. CamonaTvalTa cxrili _ es aris kvleviTi monace­me­bis ubralo warmodgena cxrilis saxiT, romelic arsebiTad warmoadgens CamonaTvals. mag. cxrili 13.1. ajamebs amomrCevelTa xmebs demokratebis sasargeblod saprezidento arCevnebze da maT rasobriv kuTvnilebas 1960-1976ww. cxrilis TiToeuli sveti warmoadgens calkeul cvlads (sul oTxi cvladia). is faqti, rom (gv. 375) cxrilSi mocemulia wlis cvladi, romelic ganlagebulia pirvel svetSi, gansazRvravs monacemTa gadmo­cemas TanmimdevrobiT. Tanmimdevroba gvkarnaxobs, rom cxrili agebulia ise, rom vupasuxoT kiTxvas: rogor icvleboda amomrCevelTa xmebi demokratebis sasargeblod saprezidento arCevnebze.

cxrili 13.1.-Si ilustrurebulia cxrilis agebis zogierTi wesi.

cxrili 13.1.

TeTr da Savkanian amomrCevelTa xmebi demokratebis

sasargeblod 1960-1976 w.w., %*

wlebi	demokratebis xmebi	TeTrkaniani demokratebis xmebi	Savkaniani demokratebis xmebi
1960 1964 1968 1972 1976**	50 61 43 40 51	49 59 38 34 48	68 94 58 89 83

* _ monacemebi aziidan, espaneTidan da sxva. marTalia, zangebi, ara­TeTrkanianebi arian monacemTa nakrebSi, romliTac agebulia cxrili, magram amJamindeli analizidan gamoricxulia.

** _ 1976 wlis monacemebi dafuZnebulia samecniero-kvleviTi kompa­niis prognozebis winaswar analizze.

wyaro: am cxrilis monacemebi aRebulia samecniero-kvleviTi kompa­ni­is prognozebis mimoxilvidan, romelic gamoicema oTx weliwadSi erTxel.

yvela cxrili unda iyos TanmimdevrobiT danomrili. soliduri naSromebSi ramdenime danomrili nawilebiT (dusertaciaSi an mraval­Tavian wignSi) es nomrebi unda gamoiyurebodes rogorc cxrili 3.1, 3.2  da a.S. an cxrili III.1, III.2 da a.S. mcire zomis SromebSi sakmarisia numeracia erTi cifriT (cxrili 1, cxrili 2). Tu erT da imave SromaSi cxrilebi mocemulia grafikebTan, sqemebTan da sxva ilustrirebul masalasTan, maSin isini inomreba cal-calke, grafikuli gamosaxuleba gamoisaxeba mag., naxati 1 an naxati 3.1.

TiToeul cxrils unda hqondes saTauri, romelic zustad unda asaxavdes warmodgenili monacemebis Sinaarss. saTauri mkiTxvels unda aZlevdes sakmao informacias, rom gadawyvitos, detalurad gaecnos cxrils Tu ara. mag., cxrili 13.1.-sTvis saTauri: `monacemebi, romlebic asaxavs demokratebis xmebs 1960-1976ww. (gv. 376), monawileobda naxevarze meti amomrCeveli da Savkanianma amomrCevlebma meti xma misces, vidre TeTrkanianebma~ (Seusabamoa, Seuferebelia).

zogadad, saTauri unda asaxavdes ZiriTad cvalebadobas, romelTa Sesaxebac am cxrilSi aris monacemebi. im SemTxvevaSi, rogorc 13.1. cxrilSi aris monacemebi, romelic moicavs gansazRvrul dros, es periodi unda iyos saTaurSi. Tu cxrili mTlianad an nawilobriv Sedgenilia sxva wyaros monacemebis mixedviT, mis qveS unda iyos Semowmebuli maTematikuli wyaro.   

ganmartebiTi miTiTebebi cxrilSi unda aRvniSnoT varskvlaviT an sxva simboloebiT saTauris Semdeg. pirveli miTiTeba (miniSneba), rome­lic exeba cxrilis nawils (Semdeg miniSneba) aRiniSneba pirdapir cxrilSi. miniSneba cxrilis Semdeg moTavsdeba, Semdeg saxeldeba wyaro.

ra unda gvaxsovdes cxrilis Sedgenisas?

1. cxrilis nomeri da saTauri unda movaTavsoT gverdis centrSi an mis marjvena nawilSi da cxrilis odnav zemoT. meore varianti _ movaTavsoT TiToeuli cxrili calkeul gverdze, teqstis im nawilSi, sadac saubaria cxrilze, gamotoveT xazi, dabeWdeT aq _ cxrili 1 didi asoebiT gverdis centrSi, gamotoveT kidev xazi da gaagrZeleT teqsti. orive SemTxvevaSi gareTa sazRvrebi aRniSnoT ori xaziT, SigniTa _ erTiT.

2. Tu SesaZlebelia, moveridoT vertikalur xazebs cxrilis Sig­niT.

3. saTaursa da cxrils Soris saWiroa gamovtovoT ori xazi. kiTxvis gaadvilebis mizniT SeiZleba gamovtovoT erTi xazi. katego­riebis saTaurebi SeZlebisdagvarad mokled unda asaxavdes cvladebs da sidideebs, magram sakmarisad, rom monacemTa mniSvneloba iyos naTeli.

gamocdileba gviCvenebs, rom teqstSi yvela cxrils unda hqondes erTgverdiani ganmarteba. ganmarteba ubralod ar unda imeorebdes cxrilis Sinaarss. cxrilebi ar unda gadavtvirToT cifrebiT da sxva raodenobrivi terminebiT, Tumca zogjer SesaZlebelia maTi (gv. 377) gamoyeneba. ukeTesia cxrilis ganmartebebi naTels hfendes urTierTkavSirebs da mkiTxvelkis yuradRebas miapyrobdes ZiriTad da ara umniSvnelo daskv­nebze. es ganmartebebi SeiZleba gamoviyenoT imisaTvis, rom statistikuri testebis Sedegebs gavukeToT komentireba cxrilis monacemebis safuZ­velze (ix. Tavi 14-16).

Cvens magaliTze dawvrilebiTi ganmarteba SesaZlebelia Seexos saerTo dones da cvlilebebs demokratebisadmi xmis micemis Sesaxeb aRniSnul periodSi da SedarebiTi roli TeTri da Savkaniani amomrCevlebisa. isini SeiZleba Seexos yvela SemCneul msgavsebasa da gansxvavebas. gansakuTrebiT SeiZleba ganvixiloT sakiTxebi cvaleba­dobasa da mudmivobaze (Tuki aseTi arsebobs) cvalebadi variaciebis xasiaTSi, yvela aRniSnul gadaxraSi monacemebi, aseve wyaros saime­doobaSi, saidanac amoRebulia es monacemebi (gv. 378).

wrfivi diagrama

zogjer cxrilebi SeiZleba SevcvaloTYufro martivi da TvalsaCino grafikiT. arsebobs uamravi saSualeba, magram maT Soris yvelaze martivia wrfivi diagrama. wrfivi diagrama aerTianebs yvela mniSvne­lobas erTi xaziT da gvaZlevs SesaZleblobas SevadaroT mniSvnelobebi sxvadasxva xazebis gavlebiT, romlebic gansxvavdeba feriT an gamo­saxulebis maneriT.

diagramaze erTi SexedviT SegviZlia vTqvaT, rom 1960-76ww. demo­kratebs misces saerTod 40-60% xma, rom 1960, 64, 76w.w. maT xma ufro meti misces vidre 1968w. da 72w., TeTrkanianebis xmebi praqtikulad Seefardeba saerTo monacems (TeTrebi gamodiodnen partiidan 1968 da 72w., magram da­brundnen 1976w.) (gv. 378).

zangebis aqtivoba mudmivia da araa damokidebuli partiis warma­tebebsa da Cavardnebze. zogierTi detali cxrilSi ufro TvalnaTelia. mag., diagramaze Zneli SesamCnevia xmebis 50% 1960w. da 51% 1976w.

grafikebi unda gavaformoT iseve, rogorc cxrilebi. TiToeul naxats unda hqondes Tavisi nomeri da zusti saTauri. horizontaluri da vertikaluri RerZi aucilebelia aRvniSnoT da yuradRebiT davakvirdeT, rom TiToeuli sworad da danamdvilebiT Skalirebulia. vertikaluri RerZis dasaxeleba unda movaTavsoT misi gradaciis zemoT. horizontaluri RerZis dasaxeleba diagramis zemoT. Tu horizontaluri RerZis gradacia wlebia, damatebiTi dasaxeleba araa saWiro (Cven magaliTze) Tu ramdenime xazi, maSin diagramis qvemoT vaTavsebT gasaRebs (punqtuaciuri aRwera), Tu aucilebelia, diagramaze SeiZleba movaTavsoT damatebiTi ganmartebiTi testi (gv. 379).

advilia diagramis wakiTxva, roca xazebis raodenoba minimaluria. magram zogjer erT diagramaze SeiZleba iyos ramdenime cvladi mona­cemi. maSin diagrama rac SeiZleba didi unda iyos. Tu xazebi ikveTeba, xazebi unda iyos sxvadasxvanairi gamosaxulebis. gansakuTrebiT xSirad gamoiyeneba Semdegi xazebi:  

________________________

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

. ______ . ______ . ______ .

. . . . . . . . . . . . . . . . . . . . . . . .

_______________________

_______________________

                  (gv. 380).

seqtoruli diagrama da histograma

rogorc CamonaTvalTa cxrili, aseve xazovani diagrama kargia informaciis aRweris da Sejamebis mizniT. monacemTa mcire cvlilebebis SemTxvevaSi SesaZlebelia gamoviyenoT grafikuli xerxi cifrebis analizisa da interpretaciisaTvis. mag., Cven gvainteresebs Savkanianebis da TeTrkanianebis SedarebiTi zemoqmedeba prezidentobis kandidatebis warmatebaze demokratiuli partiis mxridan. Cven gvainteresebs kiTxva, vis daxmarebas (TeTrkanianTa da SavkanianTa) aqvs meti zemoqmedeba demokratebis gamarjvebaze. marTalia Tu ara, rom Savkanianma amomr­Cevlebma moiyvanes jimi karteri TeTr saxlSi 1976w. problemis gamar­ti­vebis mizniT warmovidgenT, rom yoveli xuTi amomrCevelTa kompaniidan, romelsac Cven ganvixilavT, 90% iyo TeTrkaniani, 10% _ zangi. eleqto­ratis zogierT nawils warmoadgenen azielebi da laTinoamerikelebi (gv. 380). Tu SevajerebT amas cxril 13.1-Tan, Cven SegviZlia warmovadginoT amomrCevelTa xmebis komponentebi yvela arCevnebze proporciis saxiT.

rac Seexeba 1976 w., Cven viciT, rom 98% TeTrkaniani amomrCvelebisa xmas aZlevdnen demokratebs da 90% yvela amomrCevlebisa iyo TeTr­kaniani. aviRebT 48%-s 90%-dan, miviRebT, rom 43,2% yvela amomrCevlisa iyo TeTrkaniani (demokratebis amomrCevlebi). aseve zustad viciT, rom 83% Savkaniani amomrCeveli mxars uWerda demokratebs, 10% yvela amomrCevlisa iyos Savkaniani. viRebT 83%-s 10%-dan da vRebulobT, rom 8,3% amomrCevelTa iyo Savkaniani. erTad es cifrebi warmoadgens 51,5% yvela amomrCevels. maT mxari dauWires demokratebs 1976w².

gavagrZeloT Cveni gamoTvlebi. Cven viciT, rom Savkaniani da TeTrkaniani amomrCevlebi 1976w. yvela amomrCevlis 51,5% iyo. rogoria mxardamWerTa prioriteti. es rom gavigoT, ubralod yvela cifrs gavyofT 51,5%-ze (43,2 : 5,1 da 8,3 : 51,5) da miviRebT, rom 1976w. 84% xmebisa demokratebis sasargeblod misces TeTrkanianebma, xolo 16% _ Savka­nia­nebma. msgavsi gamoTvla yvela momdevno arCevnebze gviCvenebs, rom Savkanianebis xmebi Sesabamisad Seadgenda 13, 15, 20 da 23%. 1960, 1964, 1968 da 1972 ww. TeTrkanianebi ki Sesabamisad Seadgenda 87, 85, 80 da 77%. es cifrebi SeiZleba gamovxatoT seqtoruli diagramiT.

seqtoruli diagrama _ iseTi naxatia, romelzec wre warmoadgens gansazRvrul erTianobas da dayofilia segmentebad, rom aCvenos yvela nawilis wili. 13.3 naxatze yvela wre miuTiTebs demokratebisaTvis xmis mimcem pirTa 100%, daStrixuli nawili ki _ Savkanianebis wils.

miaqcieT yuradReba imas, rom saTauri da SeniSvnebi Sesrulebulia da ganTavsebulia ise, rogorc nax. 13.1. da weli miTiTebulia yvela wris qvemoT. procenti SeiZleba miTiTebuli iyos diagramis SigniT an mis gareT. anbanis asoebi diagramis yvela elementis qvemoT uadvilebs mkvlevars diagramis aRweras testSi, mkiTxvels ki _ am diagramis gage­bas.

naxatze SexedvisTanave TvalSi gvxvdeba Savkaniani amomrCevlebis raodenobis zrda 1960-1972 w.w. (Sesabamisad 13% - 23%) da 1976w. Savkaniani amomrCevlebis ricxvis Semcireba. am cifrebis gamoyenebiT Cven SeiZleba SevekamaToT mosazrebas, rom jimi karteri zangebma moiyvanes kabinetSi? piriqiT, is ar iyo damokidebuli zangebis mxardaWeraze.

samwuxarod seqtorul diagramebsac SeuZliaT Segviyvanon Secdo­maSi. amomrCevelTa raodenoba demokratebis sasargeblod icvleba arCev­nebidan arCevnebamde (50% erT wels, 61% - momdevno wels) maSin, roca wris zoma diagramaze ar icvleba. imisaTvis, rom viyoT ara mxolod zustni, aramed srulnic, diagramebi unda icvlebodes zomebSi amomrCevelTa saerTo raodenobis Sesabamisad.

magram sxvadasxva zomis seqtoruli diagramebis vizualuri inter­pretacia gaZnelebulia. adamianebs ubralod ar SeuZliaT amis keTeba. garda amisa, aseT diagramebs SeuZliaT gaaqarwylon Cveni gamokvlevebis efeqturi Txroba. amitom unda vipovoT sxva gza. Tumca seqtoruli diagramebi Zalian gamosadegia. Cven unda gvesmodes monacemebi, romlebic devs grafikuli gamosaxulebis safuZvelSi da Cven unda viyoT darwmunebulni, rom grafika asaxavs monacemebs swored im aspeqtSi, romelSic Cven mas viyenebT (anu kvleviTi sakiTxebis konteqstSi, maga­li­Tad imisaTvis, rom gagvego Savkaniani amomrCevlebis gamudmebuli zrda demokratiul koaliciaSi).

Tu davubrundebiT dasmul problemas, Cven unda vipovoT alter­na­tiuli grafikuli saSualeba, romelic gviCvenebs Savkaniani amomrCev­lebis wils garkveuli wlis ganmavlobaSi, amave dros gaiTvaliswinebs amomrCevelTa saerTo raodenobis cvlilebebs. erTaderTi aseTi saSualebaa svetebis histograma.

svetebis histograma _ es aris grafikuli gamosaxuleba, romelSic simaRle da zogjer sisqe svetebisa gamoxatavs dakvirvebas erT da ramdenime cvladze. histogramaze aRwera ganlagebulia naxatis zemoT. zogjer (gv. 383) histogramebs ganalageben ara vertikalurad, rogorc es 13.3. naxatzea, aramed horizontalurad furclis marcxena mxares. aseT SemTxvevaSi aRwera unda movaTavsoT naxatis qvemoT an marjvniv.

 

naxati 13.3. segmenturi histograma: demokratiuli koaliciis rasobrivi Semadgenloba 1960-1976w.w.

naxati 13.3. Savkaniani amomrCevlebis xmebis raodenoba diagramaze daStrixulia. svetebis sxvadasxva zomisaa, imis mixedviT, Tu ra raodenobis xmebi aqvT miRebuli demokratebs. maTi wili Cans RerZis masStabiT. am naxatiT miRebuli STabeWdileba gansxvavdeba seqtoruli diagramisagan. Cven aq vxedavT, rom Savkanian amomrCevelTa xmebis raodenoba meryeobda, es xdeboda SedarebiT viwro zRvarSi. TeTrkanianTa xmebis raodenoba aRmoCnda ufro cvalebadi, rac dakavSirebulia partiis warmatebasTan. Tu davubrundebiT Cveni gamokvlevis kiTxvas: visi mxardaWera (TeTr Tu SavkanianTa) ufro mniSvnelovania demokratebisaTvis, Cven axla SegviZlia vupasuxoT: orive mxare, oRond Taviseburad. Savkaniani amomrCevlebi Seadgenen SedarebiT mcire, magram yovelTvis mniSvnelovan mxardamWerTa bazas, romelic (gv. 384) SeiZleba aRmoCndes gadamwyveti situaciaSi, rodesac Tanabaria xmaTa raodenoba `mxardamWerebi da mowinaaRmdegeebi~. TeTrkanianebi ufro naklebad saimedoa, Tumca raodenobrivad bevrni arian. amitom maTi mxardaWera ufro mniSvnelovania. sxvagvarad rom vTqvaT, TeTrkanianT roli gadamwyvetia gamarjvebis misaRwevad an demokratebis kandidatebis damarcxebaSi. zanebi praqtikulad yovelTvis exmarebian partias, magram yovelTvis ar arian gadamwyvetni. monacemebi 13.2. naxatze igivea, magram am SemTxvevaSi ufro srulia. daskvnebi am SemTxvevaSi ufro Rrmaa da Cven ufro gvakmayofilebs.

ormxrivi histograma

politikur literaturaSi xSirad gvxvdeba ormxrivi histograma. ormxrivi histograma _ es aris ori mimarTulebiT mdebare grafiki. gamoiyeneba imisaTvis, rom aCvenos normis meryeoba, gamoxatulia cemtraluri xaziT. aseT naxatze centraluri xazi _ es saSualo (gasaSualoebuli) raodenobaa TeTrebisa, romlebic xmas aZlevdnen demokratebs 1960-1976w.w. gamoxatulia %-Si (46%).

urTierTdakavSirebul (urTierTSekavSirebul) niSanTa cxrili

cxrilis es forma gavrcelebulia Tanamedrove politologiur formaTa Soris.

cxrili 13.2.

rasobrivi gansxvavebebi saprezidento arCevnebze 1964w., %

rasobrivi kuTvnileba	kandidatebis xmebi
	demokratebidan	respublikelebi	sul	ricxvi

			%	SemTxvevebi
TeTrebi Savkanianebi yvela amomrCeveli	59 94 61	41 6 39	100 100 100	1350 150 1500

cxrili 13.3.

rasobrivi gansxvavebebi saprezidento arCevnebze 1972w., %

xmis micema kandidatze	rasobrivi kuTvnileba
	TeTrebi	Savkanianebi	yvela amomrCeveli
demokratebidan respublikelebidan sul, % SemTxvevaTa ricxvi	34 66 100 1350	89 11 100 150	40 60 100 1500

(gv. 387)

formatiTa da struqturiT urTierTdakavSirebuli niSnebis cxrili waagavs CamonaTvalTa cxrils, magram SinaarsiT gansxvavdeba misgan.  urTierTdakavSirebuli niSnebis cxrili umetesad dafuZnebulia varaudebze da agebulia ise, rom gaaadvilos CamonaTvalTa urTierTkavSiris Seswavla. cxrili 13.2. ajamebs urTierTkavSirs rasobriv kuTvnilebasa da 1964w. prezidentis arCevnebs Soris. cxrili 13.3 ajamebs igive monacemebs 1972w. orive SemTxvevaSi mocemulia 1500 amomrCevlis hipoTezuri kvlevebi. cxrilebi agebulia ise, rom SevZloT SeviswavloT hipoTeza, Tu ratom aRniSnul wlebSi Savkaniani amomrCevlebi raRaca mizezebis gamo ufro xSirad xmas aZlevdnen demokratebs, vidre TeTrebi.

gadaTvlis TiToeul punqts cxrilSi ewodeba grafa. TiToeuli cxrili Seicavs oTx grafas. cxrilebSi SeiZleba iyos rigebi da svetebi. Tu TiToeuli rigi warmoadgens erTi cvladis gansazRvrul mniSvnelobas, TiToeuli sveti _ meore cvladis mniSvnelobas, e.i. cxrili 13.2. da 13.3. SeiZleba CaiTvalos 2x2 cxrilebad, radganac orive Seicavs 2 rigs da 2 svets.

urTierTdakavSirebuli cxrilebi aigeba ise, rom damoukidebeli da ganmartebiTi cvladebi jamdeba. Cvens SemTxvevaSi aseT cvlads warmoadgens rasobrivi kuTvnileba. es niSnavs imas, rom Tu cvxrili Seicavs procentul ganawilebas, maSin isini dafuZnebuli iqneba 100% Sedegze damoukidebeli cvladze. mag., cxrili 13.2. amtkicebs, rom 1964w. TeTrkanianTa 59% xmas aZlevda demokratebs, magram ara imas, rom 59% demokratebis amomrCevelTa iyvnenYTeTrkanianebi. cxrili I xazze jamdeba procentuli monacemebi yvelasaTvis (100%) TeTri amomrCevlebis, me-2 xazze yvela Savkanian amomrCevelze, me-3 xazze _ yvela amomrCevelze. sveti `SemTxvevaTa raodenoba~ ajamebs respondentebis raodenobas (gv. 388). am svetis monacemebi gansazRvravs sixSiriT ganawilebas. cxrilSi mdebareobis amo mas uwodeben marginalurs.

cxrilebis Seswavlis dros zogadad SeiZleba vTqvaT, Tu ramdenad adastureben monacemebi hipoTezas. mag. 13.2. da 13.3. cxrilidan naTelia, rom Savkaniani amomrCevlebi mudmivad xmas aZlevdnen demokratebs, vidre TeTrebi. 1972w. Savkanianebma meti xma misces demokratebs, maSin roca TeTrebi _ respublikelebs. 1964w., roca orive jgufi xmas aZlevda demokratebs, Savkanianebi ufro saimedo sayrdeni iyo, vidre TeTrebi.  

zogierTi gafrTxileba

erTxel kidev aRvniSnoT cxrilebisa da grafikebis 3 ZiriTadi apseqti:

I _ isini unda iyos TvalsaCino da konstruqciuli;

II _ cxrilebi da grafikebi sworad unda gamoviyenoT;

III _ Tqveni naSromi ar unda iyos gadatvirTuli cxrilebiT da grafi­ke­biT.