MaQuartiles eData Rimwe Chete: Kunzwisisa Kwakadzama kweDhaurirano reData muStatistics
Imwe yepfungwa huru muhuwandu ndeyekupatsanura data kuita makota. Makota anoshandiswa kunzwisisa kugoverwa kwedata zvakadzama pane kungotarisa pakati kana pakati. Muchinyorwa chino, tichakurukura makota edata rimwe chete, maitiro ekuaverenga, uye mashandisirwo awo mumamiriro akasiyana-siyana ekuongorora data.
Chii chinonzi Quartile?
MaQuartiles ndiwo ma "specific values" anogovanisa data rakarongeka kuita zvikamu zvina zvakaenzana. Zvichitaurwa zviri nyore, maQuartiles mapoka edata rakarongeka, uye quartile yega yega inofukidza inenge 25% yedata.
Makota ane zviratidzo zvikuru zvitatu:
1. Chikamu chekutanga (Q1): chinoparadzanisa 25% yakaderera yedata kubva kune mamwe.
2. Chikamu chechipiri (Q2) kana kuti Median: chinokamura data kuita zvikamu zviviri zvakaenzana, 50% yedata iri pasi peiyi kukosha uye 50% iri pamusoro peiyi kukosha.
3. Chikamu chechitatu chedata (Q3): chinoparadzanisa 25% yepamusoro yedata kubva kune mamwe ese.
Chikamu chimwe nechimwe chekota chinomiririra chikamu chakati chedata uye chine mashandisirwo akasiyana-siyana, kubva pakutsanangurwa kwedata kusvika pakuongorora kwekunze.
Maitiro Ekuverenga Makota
Kuti uverenge makota, danho rekutanga nderekuronga data nenzira iri kukwira. Ngatitarisei matanho akadzama ekuverenga makota padata rimwe chete:
Kuronga Data
Ngatitii tine data rinotevera:
`7, 15, 36, 39, 40, 41, 42, 43, 47, 49`
Danho rekutanga nderekuona kuti data rakarongeka:
`7, 15, 36, 39, 40, 41, 42, 43, 47, 49`
Kusarudza Nzvimbo yeMakota
Tevere, tinosarudza nzvimbo dzemakota mana. Kuti uwane data rehukuru \( N \):
– Nzvimbo Q1 = \( \frac{(N+1)}{4} \)
– Nzvimbo Q2 = \( \frac{(N+1)}{2} \)
– Nzvimbo Q3 = \( \frac{3(N+1)}{4} \)
Kune data redu (N=10):
– Nzvimbo Q1 = \( \frac{(10+1)}{4} = 2.75 \)
– Nzvimbo Q2 = \( \frac{(10+1)}{2} = 5.5 \)
– Nzvimbo Q3 = \( \frac{3(10+1)}{4} = 8.25 \)
Kubatanidza Makota
Kana nzvimbo yekota iri nhamba yedesimali, saka tinobatanidza pakati pema data maviri ari pedyo.
– Q1 (Chinzvimbo 2.75):
Sanganisa data values munzvimbo yechipiri `15` uye nzvimbo yechitatu `36`.
Q1 = 15 + 0.75 (36 - 15) = 15 + 0.75 21 = 15 + 15.75 = 30.75
– Q2 (Pakati penzvimbo 5.5):
Sanganisa data values munzvimbo yechipiri `40` uye nzvimbo yechitatu `41`.
Q2 = 40 + 0.5 (41 – 40) = 40 + 0.5 1 = 40.5
– Q3 (Chinzvimbo 8.25):
Sanganisa data values munzvimbo yechipiri `43` uye nzvimbo yechitatu `47`.
Q3 = 43 + 0.25 (47 - 43) = 43 + 0.25 4 = 43 + 1 = 44
Saka, zvikamu zvina zvedata redu ndeizvi:
– Q1 = 30.75
– Q2 = 40.5
– Q3 = 44
Kushandiswa kweQuartile
Tsananguro yeZviverengero
MaQuartiles anoshandiswa sechikamu chetsananguro dzezviverengero kuti ape ruzivo rwakakwana rwekugoverwa kwedata. Kuziva maQuartiles kunotibvumira kunzwisisa zviri nani kuenderana, kuenzana, uye kupararira kwedata.
Ongororo Yekunze
MaQuartiles anobatsirawo zvikuru pakuona zvinhu zvisingawanikwe. Zvinhu zvisingawanikwi idata rakawanda riri kure neruzhinji rwedata. Kuti uone zvinhu zvisingawanikwi, nzira ye "Interquartile Range (IQR)" inowanzo shandiswa.
IQR inoverengerwa semusiyano uripo pakati peQ3 neQ1:
\[ \mashoko{IQR} = Mubvunzo 3 – Mubvunzo 1 \]
Data values inoonekwa seisina kunaka kana iri pasi pe \( Q1-1.5 \times \text{IQR} \) kana pamusoro \( Q3+1.5 \times \text{IQR} \).
Mudhatabhesi riri pamusoro apa:
– IQR = 44 – 30.75 = 13.25
- Muganho wakaderera wezvisingashande = Q1 - 1.5 IQR = 30.75 - 1.5 13.25 = 30.75 - 19.875 = 10.875
– Muganho wepamusoro wezvisingashande = Q3 + 1.5 IQR = 44 + 1.5 13.25 = 44 + 19.875 = 63.875
Saka, data values riri pasi pe10.875 kana kupfuura 63.875 rinoonekwa serisingakoshi. Sezvo data redu riri mukati mehuwandu ihwohwo, hapana data risingakoshi.
Kubata Data Kwakaomarara
Kunze kwekushandiswa mudata riri nyore, maquartiles anogonawo kushandiswa kumadata akaomarara. Mukuongororwa kwemari, semuenzaniso, maquartiles anogona kubatsira kuona mashandiro emasheya akati wandei mumusika. Mudzidzo, maquartiles anogona kushandiswa kuona mashandiro evadzidzi muzvidzidzo mubvunzo yakati.
Bhokisi Plot
Chimwe chishandiso chekuona chinoshandisa maquartiles iBox Plot kana kuti Tukey Box Plot. Box Plot inopa mufananidzo wemifananidzo wepfupiso shanu dzakakosha mudata: minimum value, first quartile (Q1), median (Q2), third quartile (Q3), uye maximum value. Nzira iri nyore yekuona outliers ndeyekushandisa Box Plot, uko outliers dzinowanzo ratidzwa semapoinzi ari kunze kwe "whiskers" (mitsetse ine mumvuri pakati pe minimum, Q1, Q3, uye maximum).
Mhedziso
Kuverenga nekunzwisisa maquartiles mudata rimwe chete kunopa ruzivo rwakadzama pamusoro pemaumbirwo edata, kugoverwa kwaro, uye kuvapo kana kusavapo kwezvisingawanikwe. Mumashandisirwo akasiyana-siyana, kubva kutsananguro dziri nyore dzezviverengero kusvika kuongororo dzakaoma dzakadai sekuona zvisingawanikwi uye kushandiswa kwemabhokisi, maquartiles anoita basa rakakosha mukuongorora nedudzira data. Nechishandiso ichi, kuongorora data kunova kwakarongeka uye kunopa ruzivo, kuchigadzira nzira yekunzwisisa kwakadzama uye kuwana zvine musoro mune dzakasiyana siyana dzekudzidza. Maquartiles haangobatsiri chete tsananguro dzezviverengero asiwo anopa ruzivo rwakakosha rwakakosha pakuita sarudzo dzinotungamirirwa nedata.
Kunzwisisa kwakasimba kwezvikamu zvina uye mashandisirwo azvo mukuongorora data hunyanzvi hunokosha hunogona kushandiswa mumamiriro akasiyana-siyana anoshanda, kubva pakutsvagisa kusvika kubhizinesi, zvichitiita vakachenjera pakuongorora nekududzira data.
