Momwe Mungawerengere Ma Quartiles, Deciles, ndi Percentiles mu Statistical Data
Mu ziwerengero, nthawi zambiri timafunika kudziwa malo a mtengo mkati mwa deta. Kungowerengera mean kapena median sikukwanira, chifukwa miyeso iyi imalephera kufotokoza momwe deta imagawidwira komanso momwe kuwona kumafananizira ndi ena. Apa ndi pomwe ma quartiles, ma deciles, ndi ma percentiles amagwira ntchito. Izi zitatu ndi miyeso ya malo yomwe imagawa deta yosankhidwa m'magawo ofanana. Nkhaniyi ikufotokoza matanthauzo, masitepe onse, ndi momwe mungawerengere ma quartiles, ma deciles, ndi ma percentiles a deta imodzi ndi yamagulu.
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1. Lingaliro Loyambira: Deta Iyenera Kusanjidwa
Tisanawerenge ma quartiles, ma deciles, kapena ma percentiles, gawo lofunika kwambiri ndikusankha deta kuyambira yaying'ono mpaka yayikulu. Deta ikasankhidwa, titha kudziwa komwe ma quartiles, ma deciles, kapena ma percentiles ali kutengera malo awo owerengera.
Mwambiri:
- Ma Quartiles amagawa deta m'magawo anayi.
- Ma deciles amagawa deta m'magawo 10.
- Ma percentiles amagawa deta m'magawo 100.
M'machitidwe, ma quartiles, ma deciles, ndi ma percentiles nthawi zambiri amagwiritsidwa ntchito pofufuza zigoli za mayeso, deta ya ndalama, miyeso ya anthropometric (kutalika/kulemera), ndi kuwunika magwiridwe antchito.
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2. Momwe Mungawerengere Ma Quartiles (Q1, Q2, Q3)
A. Ma Quartiles mu Deta Imodzi (Osagawidwa m'magulu)
Ma Quartiles amakhala ndi:
– Q1: gawo lotsika la magawo anayi (25% ya deta ili pansi pake)
– Q2: wapakati (50%)
– Q3: gawo lapamwamba la magawo atatu (75%)
Masitepe owerengera ma quartiles a deta imodzi:
1. Sanjani deta.
2. Werengerani malo a quartile pogwiritsa ntchito njira ya malo:
– Malo Q1 = \((n+1)/4\)
– Malo Q2 = \(2(n+1)/4\) kapena \((n+1)/2\)
– Malo Q3 = \(3(n+1)/4\)
Ngati malo ndi nambala yeniyeni, tengani mtengo womwe uli pamalowo. Ngati malowo ndi kachigawo, phatikizani (tengani mtengo womwe uli pakati pa mfundo ziwiri zapafupi za deta).
Chitsanzo chachidule:
Deta yosankhidwa: 4, 6, 7, 8, 10, 12, 13, 15 (n = 8)
Malo Q1 = (8+1)/4 = 2,25 → ali pakati pa deta yachiwiri ndi yachitatu.
Kotero Q1 ili pakati pa 6 ndi 7. Kutanthauzira:
Q1 = 6 + 0,25(7−6) = 6,25.
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B. Ma Quartiles mu Deta Yogawidwa (Kugawa Ma Frequency)
Pa deta yolumikizidwa m'magulu (monga nthawi ya makalasi), ma quartiles amawerengedwa pogwiritsa ntchito fomula iyi:
\[
Q_k = L + \left( \frac{\left(\frac{k}{4}n – F\right)}{f} \right) \times c
\]
Zambiri:
– \(Q_k\): kth quartile (k = 1,2,3)
– \(L\): m'mphepete mwa kalasi ya quartile
– \(n\): chiwerengero cha deta (mafupipafupi onse)
– \(F\): kuchuluka kwa ma cumulative frequency isanafike kalasi ya quartile
– \(f\): mafupipafupi mu kalasi ya quartile
– \(c\): kutalika kwa kalasi
Masitepe onse:
1. Pangani kuchuluka kwa nthawi yowerengera.
2. Dziwani komwe kuli gawo la magawo anayi: \(k/4 \times n\).
3. Pezani kalasi yomwe ili ndi malo amenewo.
4. Lowani mu fomula.
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3. Momwe Mungawerengere Ma Deciles (D1 mpaka D9)
Ma deciles amagawa deta m'magawo 10, kotero kuti:
– \(D_1\) imasonyeza malire otsika a 10% a deta,
– \(D_5\) ndi ofanana ndi apakati,
– \(D_9\) imasonyeza malire a 90% a deta.
A. Ma Deciles mu Deta Imodzi
Fomula yosinthira malo:
\[
\text{Position} D_k = \frac{k(n+1)}{10}
\]
ndi \(k = 1,2,\madontho,9\).
Malo akapezeka, njira yotengera mtengowo ndi yofanana ndi ya quartile: ngati ndi yonse, itengeni mwachindunji, ngati ndi ya fractional, interpolate.
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B. Ma Deciles mu Deta Yogawidwa
Fomula yosinthira deta yamagulu:
\[
D_k = L + \left( \frac{\left(\frac{k}{10}n – F\right)}{f} \right) \times c
\]
Kufotokozera kwake kuli kofanana ndi kwa quartile, wogawa yekha ndiye 10.
Gawo:
1. Werengerani \(k/10 \times n\).
2. Dziwani kalasi ya decile kutengera kuchuluka kwa ma cumulative.
3. Lowetsani mu fomula.
Ma deciles nthawi zambiri amagwiritsidwa ntchito pofufuza zachuma, mwachitsanzo kugawa ndalama za anthu m'magulu 10 (decile 1 kukhala wosauka kwambiri kuposa decile 10 kukhala wolemera kwambiri).
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4. Momwe Mungawerengere Ma Percentiles (P1 mpaka P99)
Ma percentiles ali ndi tsatanetsatane wambiri chifukwa amagawa deta m'magawo 100. Mtengo P25 = Q1, P50 = wapakati, ndipo P75 = Q3. Izi zikutanthauza kuti ma quartiles kwenikweni ndi chitsanzo chapadera cha ma percentiles.
A. Maperesenti pa Deta Imodzi
Fomula ya malo a peresenti:
\[
\text{Position} P_k = \frac{k(n+1)}{100}
\]
ndi \(k = 1,2,\madontho,99\).
Njirayi ndi yofanana: sankhani deta, werengerani malo, kenako tengani mtengo kapena interpolate.
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B. Maperesenti mu Deta Yogawidwa
Fomula ya data ya percentile yogawidwa m'magulu:
\[
P_k = L + \left( \frac{\left(\frac{k}{100}n – F\right)}{f} \right) \times c
\]
Masitepewo ndi ofanana ndi ma deciles/quartiles:
1. Dziwani malo \(k/100 \times n\).
2. Pezani kalasi ya percentile ya ma cumulative frequency.
3. Gwiritsani ntchito fomula.
Ma percentiles nthawi zambiri amagwiritsidwa ntchito poyesa maphunziro ndi thanzi. Mwachitsanzo, kutalika kwa mwana pa percentiles 80 kumatanthauza kuti mwanayo ndi wamtali kuposa 80% ya ana azaka zake.
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5. Malangizo Ofunika ndi Zolakwa Zofala
1. Deta iyenera kusankhidwa (makamaka pa deta imodzi). Popanda kusankhidwa, ma quartiles/deciles/percentiles alibe tanthauzo.
2. Onetsetsani kuti mukugwiritsa ntchito m'mphepete mwa kalasi pa deta yamagulu (osati malire a kalasi) ngati mukugwiritsa ntchito mfundo zopitilira.
3. Kuchuluka kwa ma cumulative kuyenera kukhala kolondola, chifukwa kalasi ya quartile/decile/percentile imatsimikiziridwa kuchokera ku kuchuluka kwa ma cumulative.
4. Samalani kutalika kwa kalasi (c). Kutalika kwa kalasi sikuyenera kukhala kolakwika, chifukwa kumakhudza zotsatira za kuwerengera.
5. Kusinthasintha ndikofunikira ngati malo sanazunguliridwe. Ophunzira ambiri nthawi yomweyo amazungulira malo, ngakhale izi zitha kuchepetsa kulondola.
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6. Mapeto
Ma Quartile, ma decile, ndi ma percentile ndi zida zofunika kwambiri zowerengera kuti mumvetsetse kufalikira kwa deta. Ma Quartile ndi oyenera kufotokozera mwachidule (monga, mu bokosi), ma decile ndi othandiza pamagulu atsatanetsatane monga kusanthula ndalama, pomwe ma percentile amathandiza kuwunika malo enieni a munthu mkati mwa anthu. Mwa kumvetsetsa masitepe oyambira—kukonza deta, kudziwa malo, ndi kugwiritsa ntchito njira zoyenera za deta imodzi kapena yamagulu—mutha kuwerengera ma quartile, ma decile, ndi ma percentile molondola komanso modalirika.
Ngati mukufuna, nditha kuwonjezera chitsanzo chonse cha tebulo la deta logawidwa m'magulu (nthawi, kuchuluka, kuchuluka kwa nthawi) kenako ndikuwerengera Q1, D7, ndi P85 mwatsatanetsatane kuti zikhale zosavuta kuchita.
