Indlela Yokubala Ama-Quartiles, Ama-Deciles, nama-Percentiles ku-Statistical Data
Kuzibalo, sivame ukudinga ukunquma indawo yenani ngaphakathi kwesethi yedatha. Ukubala nje isilinganiso noma i-median akwanele, njengoba lezi zilinganiso zehluleka ukuchaza ukuthi idatha isatshalaliswa kanjani nokuthi ukubonwa kuqhathaniswa kanjani nezinye. Yilapho ama-quartiles, ama-deciles, nama-percentile eqala khona ukusebenza. Lezi zintathu ziyizilinganiso zesimo ezihlukanisa idatha ehlungiwe zibe izingxenye ezilinganayo. Lesi sihloko sixoxa ngezincazelo, izinyathelo ezijwayelekile, kanye nendlela yokubala ama-quartiles, ama-deciles, nama-percentile kokubili kumasethi edatha angawodwa namaqembu.
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1. Umqondo Oyisisekelo: Idatha Kumelwe Ihlungwe
Ngaphambi kokubala ama-quartile, ama-decile, noma ama-percentile, isinyathelo esibaluleke kakhulu ukuhlunga idatha kusukela kwencane kuya kwenkulu. Uma idatha isihlungiwe, singanquma indawo yama-quartile, ama-decile, noma ama-percentile ngokusekelwe ezikhundleni zawo zenkomba.
Ngenjwayelo:
– Ama-Quartiles ahlukanisa idatha ibe izingxenye ezine.
– Ama-Deciles ahlukanisa idatha ibe izingxenye eziyi-10.
– Ama-Percentile ahlukanisa idatha ibe yizingxenye eziyi-100.
Empeleni, ama-quartile, ama-deciles, nama-percentile avame ukusetshenziswa ekuhlaziyeni amaphuzu okuhlolwa, idatha yemali engenayo, izilinganiso ze-anthropometric (ukuphakama/isisindo), kanye nokuhlolwa kokusebenza.
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2. Indlela Yokubala Ama-Quartiles (Q1, Q2, Q3)
A. Ama-Quartiles kuDatha Eyodwa (Awaqoqwanga)
Ama-Quartiles aqukethe:
– Q1: ikota ephansi (25% yedatha ingaphansi kwayo)
– Q2: isilinganiso (50%)
– Q3: ikota ephezulu (75%)
Izinyathelo zokubala ama-quartiles edatha eyodwa:
1. Hlela idatha.
2. Bala isikhundla sekota usebenzisa ifomula yesikhundla:
– Isikhundla Q1 = \((n+1)/4\)
– Isikhundla Q2 = \(2(n+1)/4\) noma \((n+1)/2\)
– Isikhundla Q3 = \(3(n+1)/4\)
Uma isikhundla siyinombolo ephelele, thatha inani elikuleso sikhundla. Uma isikhundla siyinombolo encane, faka phakathi (thatha inani eliphakathi kwamaphuzu amabili edatha aseduze).
Isibonelo esisheshayo:
Idatha ehleliwe: 4, 6, 7, 8, 10, 12, 13, 15 (n = 8)
Isikhundla Q1 = (8+1)/4 = 2,25 → siphakathi kwedatha yesibili neyesithathu.
Ngakho-ke i-Q1 iphakathi kuka-6 no-7.
Q1 = 6 + 0,25(7−6) = 6,25.
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B. Ama-Quartile kuDatha Eqoqwe (Ukusatshalaliswa Kwemvamisa)
Kudatha eqoqwe ngamaqoqo (isb. izikhawu zeklasi), ama-quartile abalwa kusetshenziswa ifomula:
\[
Q_k = L + \kwesobunxele( \frac{\kwesobunxele(\frac{k}{4}n – F\kwesokudla)}{f} \kwesokudla) \izikhathi c
\]
Imininingwane:
– \(Q_k\): kth ikota (k = 1,2,3)
– \(L\): umkhawulo ongezansi wekilasi lekota
– \(n\): inani ledatha (imvamisa iyonke)
– \(F\): imvamisa ehlanganisiwe ngaphambi kwekilasi lekota
– \(f\): imvamisa ekilasini lama-quartile
– \(c\): ubude beklasi
Izinyathelo ezijwayelekile:
1. Dala imvamisa ehlanganisiwe.
2. Nquma indawo yekota: \(k/4 \times n\).
3. Thola ikilasi eliqukethe leso sikhundla.
4. Faka ifomula.
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3. Indlela Yokubala Ama-Deciles (D1 kuya ku-D9)
Ama-Deciles ahlukanisa idatha ibe izingxenye eziyi-10, ukuze:
– \(D_1\) ikhombisa umkhawulo ophansi wedatha ongu-10%,
– \(D_5\) ilingana ne-median,
– \(D_9\) ikhombisa umkhawulo wedatha ongu-90%.
A. Ama-Deciles kudatha eyodwa
Ifomula yesikhundla se-Decile:
\[
\text{Isikhundla} D_k = \frac{k(n+1)}{10}
\]
nge \(k = 1,2,\amachashazi,9\).
Uma isikhundla sesitholiwe, indlela yokuthatha inani iyafana neye-quartile: uma iphelele, yithathe ngqo, uma iyi-fractional, yi-interpolate.
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B. Ama-Deciles kudatha eqoqwe ngamaqoqo
Ifomula yokuhlukanisa idatha eqoqwe ngamaqoqo:
\[
D_k = L + \left( \frac{\left(\frac{k}{10}n – F\right)}{f} \right) \times c
\]
Incazelo ifana ne-quartile, kuphela i-divisor engu-10.
Isinyathelo:
1. Bala \(k/10 \times n\).
2. Nquma ikilasi le-decile ngokusekelwe emvamisa eqongelelekayo.
3. Faka esikhundleni sefomula.
Ama-deciles avame ukusetshenziswa ekuhlaziyweni kwezomnotho, isibonelo ukuhlukanisa imali engenayo yabantu ibe ngamaqembu ayi-10 (i-decile 1 iyisicebi kakhulu kune-decile 10).
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4. Indlela Yokubala Ama-Percentile (P1 kuya ku-P99)
Ama-percentile anemininingwane eminingi ngoba ahlukanisa idatha ibe yizingxenye eziyi-100. Inani P25 = Q1, P50 = i-median, kanye ne-P75 = Q3. Lokhu kusho ukuthi ama-quartile empeleni ayisibonelo esikhethekile sama-percentile.
A. Amaphesenti kudatha eyodwa
Ifomula yesikhundla sephesenti:
\[
\text{Isikhundla} P_k = \frac{k(n+1)}{100}
\]
nge \(k = 1,2,\amachashazi,99\).
Inqubo iyafana: hlela idatha, ubale indawo, bese uthatha inani noma uhlanganise.
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B. Amaphesenti kudatha eqoqwe
Ifomula yephesenti yedatha eqoqwe ndawonye:
\[
P_k = L + \left( \frac{\left(\frac{k}{100}n – F\right)}{f} \right) \times c
\]
Izinyathelo zifana nama-deciles/ama-quartiles:
1. Nquma indawo \(k/100 \times n\).
2. Thola isigaba sephesenti semvamisa eqongelelekayo.
3. Sebenzisa ifomula.
Ama-percentile avame ukusetshenziswa ekuhlolweni kwezemfundo kanye nezempilo. Isibonelo, ukuphakama kwengane ku-percentile engama-80 kusho ukuthi ingane iphakeme kune-80% yezingane ezineminyaka yayo.
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5. Amathiphu Abalulekile Namaphutha Avamile
1. Idatha kumele ihlungwe (ikakhulukazi ngedatha eyodwa). Ngaphandle kokuhlunga, ama-quartile/ama-deciles/ama-percentile awasho lutho.
2. Qiniseka ukuthi usebenzisa imiphetho yeklasi kudatha eqoqwe ngamaqoqo (hhayi imingcele yeklasi) uma usebenzisa imiqondo eqhubekayo.
3. Imvamisa eqongelelekayo kumele ibe yiyo, ngoba ikilasi le-quartile/decile/percentile linqunywa kusukela kumvamisa eqongelelekayo.
4. Naka ubude beklasi (c). Ubude beklasi akumelwe bube nephutha, ngoba buthinta imiphumela yokubala.
5. Ukuhunyushwa kubalulekile uma izikhundla zingakajikeleziswa. Abafundi abaningi basheshe bazungeze izikhundla, yize lokhu kunganciphisa ukunemba.
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6. Isiphetho
Ama-Quartiles, ama-deciles, nama-percentile amathuluzi abalulekile ezibalo okuqonda ukusatshalaliswa kwedatha. Ama-Quartiles afanelekela izifinyezo ezilula (isb., ku-boxplot), ama-deciles awusizo ekuqoqweni okunemininingwane eminingi njengokuhlaziywa kwemali engenayo, kuyilapho ama-percentile esiza ukuhlola isikhundla somuntu othize kakhulu ngaphakathi kwesibalo sabantu. Ngokuqonda izinyathelo eziyisisekelo—ukuhlela idatha, ukunquma isikhundla, nokusebenzisa amafomula afanele edatha eyodwa noma eqoqwe—ungabala ama-quartile, ama-deciles, nama-percentile ngokunemba okukhulu nokuzethemba.
Uma uthanda, ngingangeza isibonelo esiphelele sethebula ledatha eliqoqiwe (isikhawu, imvamisa, imvamisa eqoqiwe) bese ngibala i-Q1, i-D7, kanye ne-P85 ngokuningiliziwe ukuze kube lula ukuzijwayeza.
