Ma Quartiles a Deta Yokha: Kumvetsetsa Kwakuya kwa Gawo la Deta mu Ziwerengero
Limodzi mwa mfundo zazikulu mu ziwerengero ndi kugawa deta m'magawo atatu. Magawo atatu amagwiritsidwa ntchito kumvetsetsa kugawa deta mwatsatanetsatane osati kungoyang'ana pakati kapena pakati. M'nkhaniyi, tikambirana za magawo atatu a deta imodzi, momwe tingawawerengere, ndi momwe amagwiritsidwira ntchito m'njira zosiyanasiyana zosanthula deta.
Kodi Quartile ndi chiyani?
Ma Quartiles ndi ma values enieni omwe amagawa deta yosankhidwa m'magawo anayi ofanana. Mwachidule, ma Quartiles ndi magulu a deta yosankhidwa, ndipo gawo lililonse limaphimba pafupifupi 25% ya deta.
Ma Quartiles ali ndi zizindikiro zitatu zazikulu:
1. Gawo loyamba (Q1): limagawa 25% yocheperako ya deta kuchokera ku zina zonse.
2. Gawo lachiwiri la magawo anayi (Q2) kapena lapakati: limagawa deta m'magawo awiri ofanana, 50% ya deta ili pansi pa mtengo uwu ndipo 50% ili pamwamba pa mtengo uwu.
3. Gawo lachitatu (Q3): limagawa 25% ya data yapamwamba kwambiri kuchokera ku zina zonse.
Gawo lililonse la magawo anayi limayimira gawo linalake la deta ndipo lili ndi ntchito zosiyanasiyana, kuyambira kufotokozera deta mpaka kusanthula kwapadera.
Momwe Mungawerengere Ma Quartiles
Kuti muwerenge ma quartiles, gawo loyamba ndikusankha deta motsatira dongosolo lokwera. Tiyeni tiwone njira zatsatanetsatane zowerengera ma quartiles pa seti imodzi ya data:
Kusanja Deta
Tiyerekeze kuti tili ndi deta yotsatirayi:
`7, 15, 36, 39, 40, 41, 42, 43, 47, 49`
Gawo loyamba ndikuwonetsetsa kuti deta yasankhidwa:
`7, 15, 36, 39, 40, 41, 42, 43, 47, 49`
Kudziwa Udindo wa Quartile
Kenako, timapeza malo a quartile. Kuti mupeze deta ya kukula \( N \):
– Malo Q1 = \( \frac{(N+1)}{4} \)
– Malo Q2 = \( \frac{(N+1)}{2} \)
– Malo Q3 = \( \frac{3(N+1)}{4} \)
Pa deta yathu (N=10):
– Malo Q1 = \( \frac{(10+1)}{4} = 2.75 \)
– Malo Q2 = \( \frac{(10+1)}{2} = 5.5 \)
– Malo Q3 = \( \frac{3(10+1)}{4} = 8.25 \)
Kusakaniza Ma Quartiles
Ngati malo a quartile ndi nambala ya decimal, ndiye kuti timaphatikiza pakati pa mitengo iwiri ya data yoyandikana.
– Q1 (Udindo 2.75):
Phatikizani mfundo za data mu malo achiwiri `15` ndi malo achitatu `36`.
Q1 = 15 + 0.75 (36 - 15) = 15 + 0.75 21 = 15 + 15.75 = 30.75
– Q2 (Wapakati pa malo 5.5):
Phatikizani mfundo za data mu malo achiwiri `40` ndi malo achitatu `41`.
Q2 = 40 + 0.5 (41 – 40) = 40 + 0.5 1 = 40.5
– Q3 (Udindo 8.25):
Phatikizani mfundo za data mu malo achiwiri `43` ndi malo achitatu `47`.
Q3 = 43 + 0.25 (47 - 43) = 43 + 0.25 4 = 43 + 1 = 44
Kotero, magawo anayi a deta yathu ndi awa:
– Q1 = 30.75
– Q2 = 40.5
– Q3 = 44
Kugwiritsa Ntchito kwa Quartile
Kufotokozera kwa Ziwerengero
Ma Quartile amagwiritsidwa ntchito ngati gawo la mafotokozedwe a ziwerengero kuti apereke chithunzithunzi cha kufalikira kwa deta. Kudziwa ma Quartile kumatithandiza kumvetsetsa bwino kusinthasintha, kulinganika, ndi kufalikira kwa deta.
Kusanthula Kwapadera
Ma Quartiles ndi othandiza kwambiri pozindikira zinthu zopanda pake. Ma Outliers ndi zinthu za data zomwe sizili kutali ndi zambiri mwa deta. Kuti mupeze zinthu zopanda pake, njira ya "Interquartile Range (IQR)" imagwiritsidwa ntchito nthawi zambiri.
IQR imawerengedwa ngati kusiyana pakati pa Q3 ndi Q1:
\[ \malemba{IQR} = Q3 – Q1 \]
Mitengo ya deta imaonedwa kuti ndi yosiyana ngati ili pansi pa \( Q1-1.5 \times \text{IQR} \) kapena pamwamba pa \( Q3+1.5 \times \text{IQR} \).
Mu deta yomwe ili pamwambapa:
– IQR = 44 – 30.75 = 13.25
– Malire otsika a zinthu zosafunikira = Q1 – 1.5 IQR = 30.75 – 1.5 13.25 = 30.75 – 19.875 = 10.875
– Malire apamwamba a zinthu zopanda pake = Q3 + 1.5 IQR = 44 + 1.5 13.25 = 44 + 19.875 = 63.875
Chifukwa chake, mitengo ya data yomwe ili pansi pa 10.875 kapena kupitirira 63.875 imaonedwa kuti ndi yopanda phindu. Popeza deta yathu ili mkati mwa unyinji umenewo, palibe yopanda phindu.
Kusamalira Deta Kovuta
Kupatula kugwiritsidwa ntchito mu deta yosavuta, ma quartiles angagwiritsidwenso ntchito ku ma data ovuta kwambiri. Mwachitsanzo, pakusanthula zachuma, ma quartiles angathandize kuzindikira momwe masheya enaake amagwirira ntchito pamsika. Mu maphunziro, ma quartiles angagwiritsidwe ntchito kuzindikira momwe ophunzira amagwirira ntchito pamaphunziro pa mayeso enaake.
Box Plot
Chida chimodzi chowonetsera chomwe chimagwiritsa ntchito ma quartiles ndi Box Plot kapena Tukey Box Plot. Box Plot imapereka chithunzi cha zidule zisanu zofunika mu deta: mtengo wocheperako, quartile yoyamba (Q1), wapakati (Q2), quartile yachitatu (Q3), ndi mtengo wokulirapo. Njira yosavuta yodziwira ma outliers ndikugwiritsa ntchito Box Plot, pomwe ma outliers nthawi zambiri amawonetsedwa ngati mfundo kunja kwa "ndevu" (mizere yobisika pakati pa minimum, Q1, Q3, ndi maximum).
Mapeto
Kuwerengera ndi kumvetsetsa ma quartiles mu deta imodzi kumapereka chidziwitso chakuya pa kapangidwe ka deta, kufalikira kwake, komanso kukhalapo kapena kusakhalapo kwa ma outliers. Pa ntchito zosiyanasiyana, kuyambira kufotokozera kosavuta kwa ziwerengero mpaka kusanthula kovuta kwambiri monga kuzindikira kwa outlier ndi kugwiritsa ntchito ma box plots, ma quartiles amachita gawo lofunikira pakusanthula ndi kutanthauzira deta. Ndi chida ichi, kusanthula deta kumakhala kolongosoka komanso kopatsa chidziwitso, kutsegulira njira yodziwira mwakuya komanso kupeza zinthu zofunikira m'magawo osiyanasiyana ophunzirira. Ma Quartiles samangothandiza kufotokozera ziwerengero komanso amapereka chidziwitso chofunikira chofunikira popanga zisankho zoyendetsedwa ndi deta.
Kumvetsetsa bwino ma quartiles ndi momwe amagwiritsidwira ntchito posanthula deta ndi luso lofunika lomwe lingagwiritsidwe ntchito m'njira zosiyanasiyana, kuyambira kafukufuku mpaka bizinesi, zomwe zimatipangitsa kukhala anzeru pakusanthula ndi kutanthauzira deta.
