Isibonelo Semibuzo Exoxa Ngama-Percentile Edatha Yeqembu
Ama-percentile ayisilinganiso sesikhundla kuzibalo ezisetshenziswa ukuqonda ukusatshalaliswa kwedatha. Kulesi sihloko, sizoxoxa ngokuningiliziwe ngendlela yokunquma ama-percentile edatha eqoqwe ngamaqoqo. Sizofaka izinkinga eziningana zezibonelo kanye nezincazelo zazo ukuze sicacise lo mqondo. Ake siqale ngokuqonda okuyisisekelo kwama-percentile bese siqhubekela ezibonelweni kanye nezincazelo zawo.
Ukuqonda ama-Percentile
Iphesenti yinani elihlukanisa idatha ibe yizingxenye eziyi-100 ezilinganayo. Okusho ukuthi, iphesenti le-nth yinani elingaphansi kwalokho i-n% yedatha ekusakazweni iwela khona. Isibonelo, uma idatha inephesenti lama-25 (P25), kusho ukuthi ama-25% edatha awela ngaphansi kwalelo nani.
Kudatha eqoqwe ngamaqoqo, sivame ukusebenzisa amathebula okusabalalisa imvamisa ukuhlela idatha bese sinquma ama-percentile afanele. Lawa mathebula aveza idatha ngezikhawu ezithile zekilasi, okusivumela ukuthi siqonde ukusatshalaliswa kwedatha ngokuphelele.
Ifomula Yephesenti Kudatha Yeqembu
Ifomula evamile yokunquma i-nth percentile (Pn) kudatha yeqembu yile elandelayo:
\[
P_n = L + \left( \frac{nN – \sum f_{\text{before}}}{f_{k}} \right) \times c
\]
Di mana:
– \(P_n\) yiphesenti le-nth.
– \(L\) umkhawulo ongezansi wesikhawu sekilasi lephesenti.
– \(n\) yiphesenti elifunekayo (isb., le-P25, n = 25).
– \(N\) inani eliphelele lamafrikhwensi aqongelelekayo.
– \(\sum f_{\text{before}}\) imvamisa ehlanganisiwe ngaphambi kwesikhawu sekilasi lephesenti.
– \(f_{k}\) imvamisa yesikhawu sekilasi lephesenti.
– \(c\) ubude besikhawu sekilasi.
Isibonelo sezinkinga
Ukuze siqonde kangcono, ake sibheke isibonelo sombuzo olandelayo bese sixoxa ngawo ngokuningiliziwe.
Isibonelo Umbuzo 1
Kucwaningo, kutholakale idatha mayelana nokuphakama (ngamasentimitha) kwabafundi besikole samabanga aphezulu abayi-100 bebanga le-10 kanje:
| Isikhawu Sekilasi | Imvamisa |
|——————-|———–|
| 150 – 154 | 5 |
| 155 – 159 | 8 |
| 160 – 164 | 12 |
| 165 – 169 | 20 |
| 170 – 174 | 30 |
| 175 – 179 | 15 |
| 180 – 184 | 10 |
Bala i-40th percentile (P40) yedatha.
Izinyathelo Zokuxazulula
1. Nquma imvamisa ehlanganisiwe yekilasi ngalinye:
| Isikhawu Sekilasi | Imvamisa | Imvamisa Ehlanganisiwe |
|——————-|————–|————————|
| 150 – 154 | 5 | 5 |
| 155 – 159 | 8 | 13 |
| 160 – 164 | 12 | 25 |
| 165 – 169 | 20 | 45 |
| 170 – 174 | 30 | 75 |
| 175 – 179 | 15 | 90 |
| 180 – 184 | 10 | 100 |
2. Thola isikhawu sekilasi lephesenti (P40):
Njengoba sifuna i-P40, sidinga u-40% wabafundi abayi-100, okungabafundi abangu-40. Uma sibheka ithebula lemvamisa ehlanganisiwe, sithola ukuthi abafundi abangu-40 balele esikhaleni sekilasi esingu-165 - 169 cm ngoba u-45 uwumvamisa wokuqala ohlanganisiwe odlula u-40.
3. Thola amanani adingekayo kufomula:
– \(L = 164.5\)
– \(nN = 40\)
– \(\sum f_{\text{before}} = 25\)
– \(f_k = 20\)
– \(c = 5\)
4. Faka amanani kufomula:
\[
P_{40} = 164.5 + \kwesobunxele( \frac{40 – 25}{20} \kwesokudla) \izikhathi 5
\]
\[
P_{40} = 164.5 + \kwesobunxele( \frac{15}{20} \kwesokudla) \izikhathi 5
\]
\[
P_{40} = 164.5 + 0.75 \izikhathi 5
\]
\[
P_{40} = 164.5 + 3.75
\]
\[
P_{40} = 168.25
\]
Ngakho-ke, i-40th percentile (P40) yedatha ingu-168.25 cm.
Isibonelo Umbuzo 2
Ake sithi kukhona idatha yamaphuzu okuhlolwa kwezibalo evela eqenjini labafundi abangu-200:
| Isikhawu Sekilasi | Imvamisa |
|——————-|———–|
| 40 – 44 | 10 |
| 45 – 49 | 18 |
| 50 – 54 | 32 |
| 55 – 59 | 45 |
| 60 – 64 | 50 |
| 65 – 69 | 25 |
| 70 – 74 | 12 |
| 75 – 79 | 8 |
Bala i-75th percentile (P75) yedatha.
Izinyathelo Zokuxazulula
1. Nquma imvamisa ehlanganisiwe yekilasi ngalinye:
| Isikhawu Sekilasi | Imvamisa | Imvamisa Ehlanganisiwe |
|——————-|————–|————————|
| 40 – 44 | 10 | 10 |
| 45 – 49 | 18 | 28 |
| 50 – 54 | 32 | 60 |
| 55 – 59 | 45 | 105 |
| 60 – 64 | 50 | 155 |
| 65 – 69 | 25 | 180 |
| 70 – 74 | 12 | 192 |
| 75 – 79 | 8 | 200 |
2. Thola isikhawu sekilasi lephesenti (P75):
Njengoba sifuna i-P75, sidinga u-75% wabafundi abangu-200, okungabafundi abangu-150. Uma sibheka imvamisa ehlanganisiwe, sithola ukuthi abafundi abangu-150 bawela esikhawulweni sekilasi kusukela ku-60 kuya ku-64.
3. Thola amanani adingekayo:
– \(L = 59.5\)
– \(nN = 150\)
– \(\sum f_{\text{before}} = 105\)
– \(f_k = 50\)
– \(c = 5\)
4. Faka amanani kufomula:
\[
P_{75} = 59.5 + \kwesobunxele( \frac{150 – 105}{50} \kwesokudla) \izikhathi 5
\]
\[
P_{75} = 59.5 + \kwesobunxele( \frac{45}{50} \kwesokudla) \izikhathi 5
\]
\[
P_{75} = 59.5 + 0.9 \izikhathi 5
\]
\[
P_{75} = 59.5 + 4.5
\]
\[
P_{75} = 64
\]
Ngakho-ke, i-75th percentile (P75) yedatha ingu-64.
Isiphetho
Kulesi sihloko, sixoxe ngendlela yokuthola ama-percentile edatha eqoqwe kusetshenziswa amafomula kanye nezinkinga eziningana zezibonelo. Ama-percentile ayithuluzi eliwusizo kwizibalo zokuqonda ukusatshalaliswa kwedatha nokunquma indawo ehlobene yamanani edatha. Ngokuqonda ukuthi ungabala kanjani ama-percentile kudatha eqoqwe, singahlaziya idatha kabanzi. Sithemba ukuthi lezi zinkinga zezibonelo kanye nengxoxo zikusize ukuthi uqonde kangcono umqondo wama-percentile kudatha eqoqwe.
