Transcript Mean, Median, and Mode

“arsebobs sicrue, mtknari sicrue da statistika”
anu
rogor aiZulo ricxvebi gamcnon
yvelaferi, rac gainteresebs
nino arCvaZe
ratom aris saWiro statistika?
radganac xSirad faqtebi daujerebelia!
magaliTad, ratom rekavs yovelTvis telefoni maSin, rodesac saabazanoSi xarT?
ratom gamoviyenoT statistika?
monacemTa analizisas mizani martivia: gakeTdes myari daskvnebi SezRuduli monacemebis
analizis safuZvelze.
amisaTvis saWiroa 2 problemis gadaWra:
 Sedegebis miRwevas SesaZloa xeli SeuSalos biologiuri procesebis cvalebadobam da
eqsperimentis msvlelobisas daSvebulma uzustobebma;
 adamianis gonebas warmatebiT SeuZlia modelebis moZieba, Tundac SemTxveviT
monacemTa Soris.
Cveni bunebrivi swrafvaa (gvsurs! gansakuTrebiT
sakuTar monacemebTan muSaobisas!) davaskvnaT, rom
gamovlenili gansxvaveba realuria da minimumamde
daviyvanoT SemTxveviTi cdomilebebis roli.
statistikuri midgoma gicavT aseTi Secdomisagan.
ratom gamoviyenoT statistika?
statistikuri analizi aucilebelia, roca gamovlenili sxvaoba mcirea eqsperimentul uzustobebTan
da biologiur variabelobasTan SedarebiT.
zogierTi mecnieri fiqrobs, rom aRwevs dasaxul mizans, iyenebs ra daxvewil eqsperimentul
sistemas biologiuri variabelobis gareSe, minimaluri uzustobebiT;
maT unda icodnen:
 Tu statistika dasWirdaT sakuTari eqsperimentis SefasebisaTvis, maTi eqsperimenti
mcdaria!
 Tu Sedegebi TvalnaTliv metyveleben? eqsperimenti warmatebiT SeiZleba gagrZeldes!
Sedegebis adeqvaturi analizisaTvis saWiroa statistikis ZiriTadi
principebis codna
statistikis ZiriTadi debulebebis gacnobisas SevecdebiT yuradReba maT praqtikul
gamoyenebaze gavamaxviloT, kerZod, aqcenti gavakeToT biomecnierebebis dargSi
gamoyenebul statistikur meTodebze
statistikis ZiriTadi idea martivia:
Tqven gsurT gamoiyenoT monacemTa SedarebiT mcire raodenoba zogadi daskvnebisaTvis
am mizniT statistikosebma SeimuSaves martivi modeli:
 dauSviT, rom arsebobs monacemTa didi populacia da Tqveni monacemebi (e.w. ““SerCeva”) SemTxveviTad iqna amokrebili aRniSnuli populaciidan. gaanalizeT Tqveni SerCeva da gamoiyeneT albaTobis kanonebi mTel
populaciaze Sedegebis gasavrceleblad.
aRniSnuli modeli sifrTxiliT unda iqnas gamoyenebuli zogierT SemTxvevaSi.
 magaliTad, xarisxis kontrolisaTvis gamiznuli SerCeva realurad SemTxveviT iqneba amokrebili didi populaciidan. klinikuri eqsperimentebi ar moicavs pacientebis SemTxveviTad SerCeul amonakrebs, magram xSirad da ara
yovelTvis SesaZloa Seswavlili ESerCevis Sedegebis eqstrapolacia msgavsi tipis pacientebis ufro did populaciaze.
tipiur eqsperimentSi Tqven realurad ar axdenT SerCevas didi populaciidan, magram gsurT Tqveni monacemebis eqstrapolacia ufro zogadi daskvnebis gamosatanad.
SerCevisa da populaciis koncefciebi SeiZleba gamoiyenoT, roca gadawyvetT, rom:
 Tqvens mier mopovebuli monacemebi aris SerCeva
 monacemebi, romlebsac Tqven miiRebdiT eqsperimentis dausruleblad gagrZelebis SemTxvevaSi aris populacia.
problema is gaxlavT, rom statistikuri daskvnebi SeiZleba exebodes mxolod im populacias, romlisaganac moxda SerCeva, Tqven ki xSirad gsurT daskvnebis gamotana, romlebic vrceldeba aRniSnuli populaciis farglebs gareT.
magaliTisaTvis, Tqven CaatareT eqsperimenti samjer. samive SemTxvevaSi gamoiyeneT erTi da igive tipis ujredebi, igive buferi da igive xelsawyo. statistikuri daskvnebi saSualebas gaZlevT gaakeToT daskvnebi imis Taobaze, Tu
ra Sedegs miiRebdiT igive resursebis (obieqti, pirobebi da xelsawyoebi) gamoyenebit cdis mravaljer ganmeorebisas.
albaT survili geqnebaT, gaakeToT eqstrapolacia, Tu ra Sedegebi iqneboda Tuki vinme sxva gaimeorebda eqsperiments sxva tipis ujredebze, sxva buferisa da xelsawyoebis gamoyenebiT.
samwuxarod statistikuri gamoTvlebi amis SesaZleblobas ar iZleva –- am sakiTxSi is Tqven ver dagexmarebaT.
ganzogadebisaTvis Tqven unda gamoiyenoT mecnieruli analizi da intuicia!
SerCevis MmeTodi
populacia
SerCeva
statistika
Pparametri
SerCeva da populacia
 populacia – Seswavlis yvela obieqti, dakvirvebis yvela SesaZlo SedegTa simravle
 SeCeva – - obieqtebis garkveuli jgufi, populaciidan analizisaTvis amorCeuli
nawili
 parametri – - axasiaTebs populacias
 statistika – - axasiaTebs SerCevas
8
monacemTa tipebi

cvladi – - populaciis an SerCevis maxasiaTebeli, romelic Cveni interesis sagans
warmoadgens

monacemebi – - cvladebis dakvirvebuli mniSvnelobebi

raodenobrivi monacemebi – - ricxviTia
Tvisobrivi monacemebi - kategoriulia

9
monacemTa tipebi
Data
Categorical
(Qualitative)
Numerical
(Quantitative)
Discrete
Continuous
10
Tvisobrivi monacemebi
raodenobrivi monacemebi
asaki – Semosavali
55
42
75000
68000
.
.
.
.
wonis mateba
persona daojax/ an dauojaxeb.
1
2
3
ki
ara
ki
.
.
Tvisobrivi monacemebidan .
Pprofesori
.
SesaZlebelia mxolod ama Tu im kategoriaSi moxvedrili
1
2
3
.
.
monacemebis proporciis gansazRvra
+10
+5
.
.
leqtori
aAsistenti aAsocirebuli sruli
15
25%
25
41.67%
rangi
lLeqtori
sruli
Aasistenti
.
.
sul
5
15
8.33% 25%
60
11
monacemTa tipis codna aucilebelia
swori statistikuri testis SerCevisaTvis

zog SemTxvevaSi aseve mniSvnelovania imis codna, SesaZlebelia Tu ara monacemTa ranJireba
calkeuli tipis monacemebisaTvis arsebobs analizis dasaSvebi forma:

raodenobrivi monacemebisaTvis –- ariTmetikuli gamoTvlebi
 Tvisobrivi monacemebisaTvis – - calkeul kategoriaSi dakvirvebaTa raodenobis gansazRvra
 ranJirebul monacemebze –- ranJirebis procesze damyarebuli gamoTvlebi
12
statistikuri damuSavebis sawyis etapze, Sedegebis analizisaTvis Sesabamisi statistikuri testis SerCevis mizniT aucilebelia
ganisazRvros eqsperimentuli cvladebis tipi
ricxviTi monacemebi:
diskretuli monacemebi
uwyveti tipis monacemebi
kategoriuli monacemebi:
nominaluri
atributuli
ordinaluri
arsebobs eqsperimentuli cvladebis 3 tipi:
gazomvis 4 tipis skala (Stanley Smith
Stevens, 1946)
kategoriuli
nominaluri
mag. sqesi: memdr./mamr.
gazomvis susti formaa
ricxvebi gamoiyeneba
subieqtebis, obieqtebis
an Tvisebis
klasifikaciisaTvis
ricxviTi
ordinaruli, anu
ranguli
mag. mosaxleobis
social-ekonomikuri
statusi: 1-dabali,
2-saSualo, 3-maRali,
4-umaRlesi. ricxvebs
aqvT garkveuli
maTematikuri mniSvneloba –
3-Si gaerTianebuli
individebi statusiT
ufro maRla dganan,
vidre me-2 jgufSi.Y
intervaluri
mag., Termometrs aqvs aTvlis wertili tis matebis Sesafaseblad,
magram es wertili
ar miuTiTebs t-is
0 mniSvnelobaze,
mis saerTod
ararsebobaze
fardobiTi
aqvs namdvili 0,
mag., Semosavali,
Svilebis raodenoba,
dakisrebuli
gadasaxadi
kategoriuli
nominaluri skala
gazomvis nominaluri skalis gamoyenebiT
Sefasebuli cvladebi aris nominaluri anu
kategoriuli cvladebi
ordinaruli skala
gazomvis ordinaruli skalis gamoyenebiT
Sefasebuli cvladebi aseve kategoriuli cvladebia,
romlebic warmodgenilia ranJirebuli saxiT (ranguli
cvladebi). mag. cxenebis doRSi finiSTan misvlis
Tanmimdevroba, romelic ar miuTiTebs konkretul
droze (pirveli, more da a.S.), avadmyofobis
nominaluri anu kategoriul cvladebi
nominalur anu kategoriul cvladebs sxvanairad atributuls uwodeben.
nominaluri skalis gamoyenebiT miRebuli nominaluri cvladebis calkeuli
mniSvnelobebi klasificirdeba kategoriebad. isini ar warmoadgens ricxvebs.
isini sityvebia. mag., sqesi (mdedrobiTi an mamrobiTi), genotipi (AA, Aa, aa),
janmrTelobis mdgomareoba (avadmyofi/janmrTeli), aseve avadmyofobis
tipebi, mcenareTa saxeobebi. maTze ariTmetikuli operaciebi sruli uazrobaa.
nominaluri cvladebi xSirad gamoiyeneba klasifikaciisaTvis, raTa moxdes
klasebis Sedareba.
advilad dainaxavT gansxvavebas ricxviT da nominalur cvladebs Soris, Tuki
warmoidgenT TiToeuli laboratoriuli dakvirvebis Sedegebs. Tu zomavT
izopodebis Tavis siganes, konkretuli monacemi SeiZleba iyos 3.41 mm.
cxadia, rom cvladi ricxviTia. izopodebis sqessze dakvirvebis Sedegi SeiZleba
iyos mdedri an mamri - is nominaluri cvladia.
SesaZlebelia ricxviTi cvladis gadayvana nominalur cvladSi, Tuki individebs
davyofT mcire zomis klasebad sazRvrebis gaTvaliswinebiT. mag. Tu Tqven
swavlobT qolesterinis donesa da sisxlis wnevas Soris kavSirs, SegiZliaT
gazomoT qolesterinis done (ricxviTi cvladi), Semdeg gayoT cdis pirebi 2
jgufad (qolesterinis dabali da maRali donis mqone individebi – nominaluri
ordinaruli anu ranguli cvladebi
ordinaruli skalis gamoyenebiT fasdeba ordinaruli cvladebi - maTi
mniSvnelobebi SesaZloa ganTavdes ranJirebuli wesiT, mciredan
didisaken, imis miuxedavad, cnobilia Tu ara maTi zusti mniSvnelobebi.
biologiaSi isini naklebad gamoiyeneba martivi mizezisda gamo – aseTi
cvladebis SefasebisaTvis gankuTvnili statistikuri testebi (e.w.
‘araparametruli testebi’) ricxviTi cvladebisaTvis gankuTvnil statistikur
testebTan SedarebiT ar iZleva srulyofil informacias monacemTa Sesaxeb.
• magaliTad, Tqven dazomeT izipodebis Sejgufebis dro da naxeT, rom maTi
umetesoba gancalkevda 1-2 wuTis ganmavlobaSi. 2 izopodi, mamri, darCa jgufSi
30 wuTis ganmavlobSi.
Tuki monacemT analizisaTvis Tqven gamoiyenebT ricxviTi monacemebis
damuSavebisaTvis gankuTvnil statistikur tests, mamri izopodebis saSualo dro
aRniSnuli ori monacemis CarTvis gamo mniSvnelovnad gadaaWarbebs
mdedrebisas da gansxvaveba mdedrebsa da mamrebs Soris aRmoCndeba
statistikurad sarwmuno. Tuki monacemebs warmoadgenT ranJirebulad da maT
daamuSavebT araparametruli wesiT, bolo da bolos wina izopodis monacemebi
nakleb gavlenas moaxdens saerTo Sedegebze da Sesabamisad, ar miiRebT mcdar
“sarwmuno” gansxvavebas, radganac is realurad ar arsebobs
ricxviTi monacemebi
rogorc saxelwodeba migviTiTebs, aseTi tipis monacemebi gazomvadia da yovelTvis aqvs ricxviTi mniSvneloba. mag., sigrZe, wona, simkvrive, pH. gazomvisas maTi
SesaZlo mniSvnelobebi limitirebulia sazomi xelsawyoebis sizustiT. cvladebi, romlebic ricxobrivad gamoisaxeba (mag. baqteriebis raodenoba petris jamze), cnobilia
metrikuli, diskretuli cvladebis saxelwodebiT da maTi gaanalizebis meTodebi iseTivea, rogoric uwyveti tipis monacemebis (wona, sigrZe, dro, temperatura, sisxlis
wneva da .aS.) SemTxvevaSi.
Tumca saWiroa garkveuli sifrTxilis gamoCena: daTvlis SemTxvevaSi xSirad saqme gvaqvs nominalur cvladTan. baqteriebis raodenoba petris jamze ricxviTi
monacemia (mag., 87 kolonia erT jamze da 92 kolonia meoreze), Tumca Tu gvaqvs sxvadasxva saxis koloniebi da viTvliT TiToeuli maTganis raodenobas, saqme
gvaqvs nominalur tipis monacemTan: “kolonia 1” da “kolonia 2”. aseT SemTxvevaSi SegviZlia nominaluri monacemebi gamovxatoT ricxviTi mniSvnelobiT, magram
isini mainc nominalurad rCebian.
SesaZloa gazomili sidide warmoadgendes ricxviT monacems maSinac ki, rodesac maTi mniSvneloba ganisazRvreba eqsperimentatoris mier. Tuki gavzrdiT baqteriebs
sxvadasxva jamze manozas gansxvavebuli koncentraciis areze, manozas koncentracia iqneba ricxviTi monacemi misi Cvens mier SerCevis SemTvevaSic ki.
ricxviTi monacemebi
intervaluri skala
gazomvis intervaluir skalis gamoyenebiT
Sefasebuli cvladebi aris intervaluri cvladebi
(mag., temperatura celsiusebSi an faregeitebSi
(mxolod ara kelvinebSi)). maT or mniSvnelobas
Soris arsebul sxvaobas datvirTva aqvs im kuTxiT,
rom mag., 1000C da 900C temperaturas Soris
iseTive intervalia, rac 900C da 800C Soris.
fardobiTi skala
 fardobiTi skala xSirad gamoiyeneba biologiaSi, mag., gulis cemaTa sixSire wuTSi, anda
leikociebis raodenoba sisxlis 1 mililitrSi.
 Tuki fardobaSi monawile mniSvneli ar warmoadgens biologiuri variaciis magaliTs (am
SemTxvevaSi wuTi anda mililitri), fardobiTi skalis gamoyenebiT miRebuli monacemebi
SesaZloa damuSavdes rogorc ricxviTi cvladebi,
 magram Tuki mricxvelic da mniSvnelic biologiuria, sasurvelia iseTi statistikuri testis
gamoyeneba, romelic gamijnavs am or cvlads (mag., sqesi da sxeulis zoma). mag., Tuki
gsurT daadginoT mamr izopodebs aqvT Tu ara ufro didi Tavi, vidre mdedrebs, albaT gayofT
Tavis zomas sxeulis sigrZeze da SeadarebT am fardobas mamrebsa da mdedrebSi. Tumca,
ukeTesi iqneba cvladebis gamijvna da TiToeuli maTganis regresiuli mrudis Sedareba.
 fardobiT cvladebs iseTive Tvisebebi aqvT, rogorc intervalurs, magram damatebiT aqvT
mkafiod gansazRvruli 0. Tuki cvladis mniSvneloba nulia, is ar arsebobs.
magaliTad, wona, simaRle, fermentebis aqtivoba fardobiTi cvladebia.
 temperatura (farengeitebSi an cesliusebSi) ar aris fardobiTi cvladi – maTi nulovani
mniSvneloba ar miuTiTebs temperaturis ararsebobaze, Tumca kelvinebSi gamosaxuli
temperatura fardobiTia – misi 0 realurad niSnavs temperaturis ararsebobas.
 fardobiT cvladebTan muSaobisas, intervaluri cvladebisagan gansxvavebiT, SegiZliaT
SeafasoT maTi fardoba. mag., 4 grami orjer metia, vidre 2 grami, radganac wona
fardobiTi cvladia.
ra kategoriaa feri? zogierT eqsperimentSi is nominaluria, magram Tuki mas
gamovsaxavT Sesabamisi talRis sigrZiT, feri iqneba fardobiTi cvladi.
cirkularuli cvladebi
ricxviTi cvladebis specialuri tipia cikluri cvladebi. maT aqvT Tviseba - udidesi da umciresi mniSvneloba erTmaneTis
gverdigver xvdeba, xSirad nulovani mniSvneloba sruliad pirobiTia. yvelaze naTeli magaliTi aseTi tipis cvladebisa biologiaSi aris
dRis dro, weliwadis dro, kompasis mimarTuleba. Tuki Tqven zomavT weliwads dReebSi, I dRe SeiZleba iyos 1 ianvari,
gazafxulis bunioba; romeli dRec ar unda aarCioT, I dRis momijnave iqneba erTis mxriv II dRe da meores mxriv 365-e dRe.
Tuki Tqven ganixilavT mxolod ciklis monakveTs, cirkularuli cvladebi xdeba ricxviTi cvladebi.
araerTmniSvnelovani cvladebi
Tuki Tqven gaqvT Zalze mcire mniSvnelobebis mqone ricxviTi cvladebi, SesaZloa Zneli iyos garkveva is ricxviTi cvladia Tu
nominaluri.
magaliTisaTvis, Tuki Tu Tqven adarebT baqteriebis zrdas 2 sxvadasxva areze (manozas 0 mM da 20 mM koncentraciisas) da
gaqvT baqteriaTa gansxvavebuli zrda areTa calkeul koncentraciaze, aseT SemTxvevaSi Tqven SegiZliaT ganixiloT manozas
koncentracia, rogorc nominaluri cvladi (mniSvnelobiT “manozas arseboba” da “manozas ararseboba”) da gaaanalizoT Sedegebi
martivi t-testis gamoyenebiT. magram Tuki Tqven saeqsperimentod iyenebT manozas 10 gansxvavebul koncentracias, isini unda
ganixiloT, rogorc ricxviTi cvladi da miRebuli Sedegebi gaaanalizoT wrfivi regresiis gamoyenebiT.
sazomi sistemebi
ratom viyenebT sazom sistemebs?
• mecnierebs sWirdebaT
• monacemTa aRwerisa da gacvlis universaluri sistema
(saerTaSoriso (SI) sazomi erTeulebi)
ra izomeba sazomi sistemebiT
• grami (g) –- wonis sazomi erTeuli
• litri (l) -– siTxis moculobis sazomi
• metri –(m) - sigrZisa da manZilis sazomi
• celsiusi - temperatura
sazomTa konvertaciis sqema (safexurebis meTodi)
Kkilo
1000 hHeqto
erT.
100 dDeka
erT.
10
erT.
mcire erTeulSi gadasayvanad Sesabamisad
gadaanacvleT marjvniv mZime an gaamravleT
ZiriTadi
erTeuli
Ddeci
0.1
erT.
santi
0.01
erT.
mcire erTeulSi gadasayvanad Sesabamad
gadaanacvleT marcxniv mZime an gayaviT
Mmili
0.001
erT.
gamoviyenoT safexurebis meTodi:
1000 mg = ______ g
safexuri 1: gansazRvreT kibis ra mimarTulebiT gadaadgildebiT
safexuri 2: gansazRvreT ramdeni safexuria miligramidan gramamde
safexuri 3: gadaanacvleT mZime imdeni erTeuliT da im mimarTulebiT,
rac ganisazRvra 1 da 2 safexuriT
(zemoT Tu qvemoT)
1 g
1000 mg = ______
gamoviyenoT safexurebis meTodi:
.15 L = __________ ml
safexuri 1: gansazRvreT kibis ra mimarTulebiT gadaadgildebiT
safexuri 2: gansazRvreT ramdeni safexuria miligramidan gramamde
safexuri 3: gadaanacvleT mZime imdeni erTeuliT da im mimarTulebiT,
rac ganisazRvra 1 da 2 safexuriT
(zemoT Tu qvemoT)
150
.15 L = __________
ml
sazomi erTeulebi
erTeuli
simbolo
ras zomavs
metri
m
sigrZe
grami
g
wona
litri
L
moculoba
celsiusi
C
temperatura
pPrefiqsi
Kilo
Deci
Centi
Milli
Micro
Nano
Pico
simbolo
k
ZiriTadi erTeuli
*
d
c
m
µ
n
p
** * biologiaSi gamoyenebuli ZiriTadi sazomi erTeulebia : metri, grami an litri
103 = 1,000 (aTasi)
faqtori
10-1 = 0.1 (meaTedi)
10-2 = 0.01 (measedi)
10-3 = 0.001 (meaTasedi)
10-6 = 0.000001 (memilionedi)
10-9 = 0.000000001 (mebilionedi)
10-12 = 0.000000000001 (metrilionedi)
ivarjiSeT!
decilitri mililitrze mcirea/////////didia
mikrometri metrze mcirea//didia
jer
jer
nanometri milimetrrze mcirea//didia
jer
decigrmi mikrogramze mcirea//didia
jer
gadaiyvane:
 6 decilitri litrebSi
 0.8 kilogrami gramebSi
 42 mikrolitri litrebSi
 897 santimrtri metrebSi
 5,684 milimetri metrebSi
 4 mililitri microlitrebSi
 87 mikrometri santimetrebSi
 206 nanogrami pikogramebSi
 4.5 santilitri mikrolitrebSi
 34,567 milimetri nanometrebSi
 3.09 microgrami miligramebSi
sigrZisa da manZilis erTeulebi
mMetrikuli eqvivalentebi
1 km = 1000 m; 1 m = 100 cm = 1000 mm = 10^6 um = 10^9 nm
sazomi erTeuli
milimetri
santimetri
santimetri
metri
metri
metri
kilometri
kilometri
mravldeba
inglisuri erTeuli
0.0394
0.394
0.0328
39.4
3.28
1.1
3,281
0.621
inCi (in)
inCi
futi (ft)
inCi
futi
iardi (yd)
futi
mili (mi)
inglisuri eqvivalentebi
1 mi = 1,760 yd = 5,281 ft; 1 yd = 3 ft = 36 in
inglisuri erTeuli
mravldeba
= sazomi erTeuli
inCi (in)
inCi
inCi
futi (ft)
iardi (yd)
iardi
mili (mi)
25.4
2.54
0.254
30.48
91.44
0.9144
1.609
milimetri
santimetri
metri
santimetri
santimetri
metri
kilometri
wonis erTeulebi
mMetrikuli eqvivalentebi
1 mt (metric ton) = 1000 kg = 2,205 lb
1 kg = 1000 g = 2.205 lb = 35.2802 oz
1 g = 1000 mg = 10^6 ng = 10^9 pg
sazomi erTeuli
grami (g)
kilogrami (kg)
metruli tona (mt)
mravldeba
inglisuri erTeuli
0.035
uUncia (oz)
2.2
1.102
tona (t)
funti (lb)
inglisuri eqvivalentebi
1 ton = 2000 lb = 907.2 kg or 0.9072 mt
1 lb = 16 oz = 0.4536 kg = 453.6 g
inglisuri erTeuli
mravldeba
= sazomi erTeuli
uUncia (oz)
28
grami (g)
funti (lb)
0.4536
kilogrami (kg)
tona (t)
0.9072
metruli tona (mt)
siTxis moculobis erTeulebi
mMetrikuli eqvivalentebi
1 L = 1000 ml = 2.113 pt (pints) = 1.06 qt (quarts) = 0.264 US gal
1 ml (or cm^3) = 1000 ul = 0.03 fl oz (fluid ounces)
sazomi erTeuli
mravldeba
inglisuri erTeuli
mililitri (ml)
0.02957
Txevadi uncia (fl oz)
litri(L)
2.13
pinta (pt)
litri (L)
1.0567
kvarta (qt)
inglisuri eqvivalentebi
inglisuri erTeuli
1 US gal = 4 qt = 8 pt = 128 fl oz = 3.785 L
1 qt = 2 pt = 32 fl oz = 946.4 ml or 0.9464 L
1 pt = 16 fl oz = 473.2 ml or 0.213 L
1 fl oz = 29.57 ml
mravldeba
= sazomi erTeuli
Cais kovzi(tsp)
5
mililitri (ml)
sadilis kovzi (tbsp)
15
mililitri
Txevadi uncia (fl oz)
29.57
mililitri
Wiqa (c)
0.24
litri (L)
pinta (pt)
0.4732
litri
kvarta (qt)
US galoni (US gal)
0.9464
3.785
litri
litri
temperaturis sazomi erTeulebi
temperaturis eqvivalentebi
K =kKelvini || C = celciusi || F = Ffarengeiti
0 K = -273.15 C = absoluturi nuli (molekulebis moZraoba wydeba)
273.15 K = 0 C = 32 F = wylis gayinvis / yinulis dnobis temperatura
373.15 K = 100 C = 212 F = wylis duRilis temperatura
fFarengeitis konvertacia celsiusSi
(F - 32) x 5/9 = C
celsiusis - C konvertacia farengeitebSi - F
(C x 9/5 ) + 32 = degrees F
koncentraciis sazomi erTeulebi
koncentracia, rogorc wesi , asaxavs masa/ moculobis damokidebulebas
procentuloba (%)
= gr sxsnarisa / 100 ml gamxsnelSi;
M
molarul koncentraciaSi gadasayvanad grami mravldeba 10-ze da iyofa xsnaris molekulur masaze
= moli xsnarisa litr gamxsnelSi
magaliTad,
1 M = 1 moli/litri sadac
molaruli koncentracia
anu
molaroba (M)
1 moli (mole) = 6.023 x 10^23 molekula
= 1 molekuluri masa (MW)
~ 1 formula masa (FW)
dabal koncentraciebze muSaobisas molaroba SeiZleba gamoisaxos milimolebSi (mM ),
sadac 1 mM = 10-3 M
mineralizacia, marilianoba
= xsnariebis saerTo masa (gr) zRvis wylis kilogramze.
rogorc wesi, gamoisaxeba ppt – Si ("parts per thousand")
sanapiro wylebSi aris 30-32 g xsnari/kg = 30-32 ppt marilianoba
monacemi = signali + xmauri
signali = is, rasac vzomavT
xmauri = cdomilebebi gazomvisas
Tuki xmauri SemTxveviTia, SerCevis zrdasTan erTad is
mcirdeba da rCeba mxolod signali
eqsperimentuli variaciebi
mecniereba, gazomvebi,
cdomilebebi da Secdomebi
gazomvebi da cdomilebebi
• samecniero eqsperimentebi xSirad moiTxovs
gazomvebs
• gazomvebis Sedegebi iSviaTad aris erTnairi
• gazomvebis Sedegebi yovelTvis gansxvavdeba
realuri, “namdvili” mniSvnelobisagan
• “namdvili” mniSvneloba is mniSvnelobaa, romelic
miiReboda gazomvaTa idealurad Catarebis pirobebSi
da radganac idealuri gazomva ar arsebobs, “namdvili
mniSvnelobac” ararealuria
• realuri mniSvnelobisagan gadaxras Secdoma
Secdomis wyaroebi
gazomvisas Secdomebis 2 ZiriTadi wyaroa:
• xelsawyoebis mgrZnobelobis zRvari
• cudad dagegmili eqsperimenti an sazomi
xelsawyoebis defeqti
Secdomebi SeiZleba iyos:
– SemTxveviTi;
– sistematuri (regularuli,
meToduri)
39
SemTxveviTi Secdomebi”:
arsebobs yovelTvis
gazomvebi xSirad warmodgenilia ase:
• wyaro:
– operatoris Secdoma
– cvlileba saeqsperimento garemoSi
•
rogor daviyvanoT minimumazde?
– gaimeoreT gazomvebi da gamoTvaleT saSualo
gazomvis Sedegi ± SemTxveviTi Secdoma
SemTxveviTi Secdoma ar axdens gavlenas saSualoze, adgili aqvs
mxolod variabelurobas
40
sistematuri Secdomebi
Cveulebrivad aqvs adgili
gazomvebi xSirad warmodgenilia ase:
• wyaro:
– instrumentuli, fizikuri Tu adamianuri resursebis
limiti
mag. xelsawyos araswori kalibrireba
•
gazomvis Sedegi + SemTxveviTi Secdoma
rogor daviyvanoT minimumazde?
– swori kalibrireba
– xarisxiani xelsawyoebi
an
gazomvis Sedegi - SemTxveviTi Secdoma
SemTxveviTi Secdoma gavlenas axdena saSualoze!
mas gadaxra ewodeba
41
sizuste da akuratuloba gazomvebisas
• sizuste
ramdenad ganmeorebadia
gazomvebi
• akuratuloba
ramdena axlosaa
gazomvebi realurTan
42
gansazRvreba
akuratuloba da
sizuste …sityvebs
TiTqos erTnairi
datvirTva aqvT...
sad aris sxvaoba?
Accuracy
and Precision...
gansazRvreba : akuratuloba
eqsperimentSi saWiroa gaTvaliswinebul iqnas sazomi xelsawyoebis akuratuloba,
magaliTad,
ZviradRirebuli Termometri ufro akuratulad gazomavs
temperaturas - gazomvis Sedegi axlos iqneba realurTan.
aseTi xelsawyo ufro mgrZnobiare iqneba temperaturis mciredi cvlilebis
mimarT
gansazRvreba : sizuste
sizuste dakavSirebulia sazomi xelsawyos umciresi danayofis fasTan, mag.,
saxazaviT gazomvisas:
milimetriani danayofis mqone saxazavi ufro zusti iqneba
vidre santimetriani
aseTi saxazavi mogvcems myar monacemebs gazomvaTa gameorebisas
gazomvis sizuste
≈ 26.13 cm
 bolo cifri aris mixlovebiTi
estimate.
 sizuste limitirebulia instrumentiT
46
gansazRvreba : sizuste
menzura
aiwona A sasworze
3-jer
For example,
2 balances:
Sedegebia: 73 g, 77 g, 71 g
amrigad, sazRvrebia
A
= 71 g – 77 g = 6 g
Semdeg menzura aiwona meore B sasworze 3-jer
Sedegebia: 75 g, 73 g, 74 g
amrigad, sazRvrebia
B
= 73 g – 75 g = 2 g
B saswori ukeTesi sizustisaa, misi gazomvis Sedegebi axlos dgas erTmaneTTan
akuratulobis da suzustis Sedareba
gaviazroT sakiTxi xis panelis gazomvis magaliTze
0
namdvili
mniSvneloba
panelis sigrZes aqvs namdvili mniSvneloba
da
Cven SegviZlia gavzomoT is
akuratulobis da suzustis Sedareba
0
zusti (dajgufebuli), magram araakuratuli
true
value
0
0
akuratuli (saSualod) magram arazusti
akuratuli da zusti
mizanSi srola: akuratuloba da sizuste
•
araakuratuli
arazusti
warmoidgineT adamiani, romelic isvris mizanSi.
akuratuli
arazusti
araakuratuli
zusti
akuratuli
zusti
50
samecniero monacemebi
mecnierebs yovelTvis sWirdebaT zusti da akuratuli
eqsperimentuli Sedegebi
Tumca sizuste da akuratuloba
limitirebulia xolme
monacemTa mopovebis
meTodebiTa da xerxebiT
51
rogor movepyroT Secdomebs?
 pirvel rigSi gamovavlinoT isini da SevafasoT maTi xarisxi
 SevecadoT SevamciroT Secdomebi
rogor?
– ukeTesi xelsawyoebiT
– eqsperimentis ukeTesad dagegmviT
– Sedegebis raodenobis zrdiT
52
cudi ambavi…...…
• ara aqvs mniSvneloba, rogor kargad
asrulebT amocanas… - Secdomebi
iqneba yovelTvis!
• ismis SekiTxva - – rogor moveqceT
maT?
gamoviyenoT statistika!
53
yvelaze mniSvnelovani, rasac aucileblad unda miaqcios yuradReba studentma samecniero saqmianobis
dawyebisas, xSirad yuradRebis miRma rCeba – is, rom samecniero eqspeiments garkveulwila Tan axlavs
gaurkvevloba.
buneba arasodes tyuis, magram mecnierebis survili Caataron eqssperimenti da moaxdinon Sedegebis
interpretacia xSirad winaaRmdegobebs awydeba. ramdeni dro dauxarjavT maT rom mieRoT 60%-iani
sarwmunooba!
studentebi acnobiereben eqsperimentul monacemebSi Secdomebis arsebobis SesaZleblobas Teoriuli codnis
safuZvelze an awydebian maT pirveli praqtikuli amocanis Sesrulebisas, Tumca amas eqsperimentis Cavardnad
Tvlian da srulyofilad ar aanalizeben maT - ZiriTadi koncepciebis safuZvelze daskvnebis gamotanas swavla
sWirdeba.
roca gaqvT problemebi eqsperimentis msvlelobisas:
1.
2.
3.
4.
5.
6.
SeamowmeT testi;
SeamowmeT analizi;
dafiqrdiT da Sedegsac miaRwevT!
hkiTxeT kolegebs sxva eqsperimentebis Sedegebis Sesaxeb;
moaxdineT urTierTgamomricxavi faqtebis sistematizacia;
gaakeTeT adeqvaturi daskvnebi!
rodesac yvelaferi swori gziT midis
1.
2.
aRaraferi iRonoT
CainiSneT miRweuli da gaagrZeleT saqmianoba
3.


aRar gaimeoroT sistematuri Secdomebi:
es alogikuria
es safrTxes Seuqmnis Tqvens gulmodginebas
Slide 56
waxaliseba
silabusis TemaTa daZlevaSi yvelaze
warmatebul
4 students
dadga dro SeasruloT saSinao davalebebi!