Fomura yePensile muStatistics
Percentile ipfungwa huru muhuwandu hwemanhamba, inowanzoshandiswa kunzwisisa kugoverwa kwedata uye kuenzanisa kukosha kwemunhu mumwe nemumwe mukati medata rakakura. Chinyorwa chino chichaongorora zvakadzama pfungwa yemapercentile, maitiro ekuaverenga, uye mashandisirwo awo muminda yakasiyana-siyana.
Kunzwisisa Percentile
Percentile chiyero chenhamba chinoratidza nzvimbo kana chinzvimbo chemutengo mu data set. Kana data rakarongwa kubva pakaderera kusvika pakakwirira, nth percentile (Pn) ndiyo kukosha uko n muzana yedata inowira pasi pemutengo iwoyo uye (100-n) muzana yedata inowira pamusoro pemutengo iwoyo. Semuenzaniso, P50, kana kuti 50th percentile, inozivikanwawo se median, ndiyo kukosha kunoparadzanisa data rakaiswa kuita zvikamu zviviri zvakaenzana.
Kukosha kwePentilenti
Percentile ine mashandisirwo akasiyana-siyana anoshanda muminda yakawanda, kusanganisira:
– Dzidzo: Maperesenti anowanzo shandiswa kushuma mamakisi ebvunzo, semuenzaniso, mudzidzi ari mu90th percentile zvinoreva kuti akakwira kupfuura 90% yevamwe vadzidzi.
– Hutano: Kukura kwevana kunoyerwa uchishandisa makomba ekukura zvichibva pahuwandu hwevana, zvichibatsira vanachiremba nevabereki kutarisa kukura kwemuviri wemwana wavo.
– Zvehupfumi: Kuongorora mari inowanikwa kunowanzo shandisa ma percentiles kuyera kugoverwa kwemari inowanikwa uye kusaenzana kwehupfumi.
Maitiro Ekuverenga Percentile
Pane matanho akati wandei ekuverenga percentile yedata set. Ngatitii tinoda kuverenga percentile nth yedata set \( X \) ine \( N \) elements. Maitiro ekuverenga ndeekuti:
1. Ronga Data: Ronga data \( X \) kubva padiki kusvika pahukuru.
2. Nhamba yePesenti: Verengai nhamba yePesenti uchishandisa fomura inotevera:
\[
L = \frac{n}{100} \nguva (N + 1)
\]
Apo \( L \) iri nzvimbo yepercentile, \( n \) ndiyo kukosha kwepercentile kunodiwa, uye \( N \) ndiyo huwandu hwese hwezvinhu zviri mudataset.
3. Kupindirana (Kana Zvichidikanwa): Kana \(L \) isiri nhamba yakakwana, pindirana pakati pezvinhu zviri pedyo.
Heino muenzaniso wekuverenga wakadzama:
Muenzaniso weKuverenga kwePesenti
Ngatitii tine data rinotevera: [15, 20, 35, 40, 50]. Tinoda kuwana chikamu che40 muzana.
1. Kuronga Data: Data rakarongwa kubva padiki kusvika pahukuru: [15, 20, 35, 40, 50].
2. Nhamba yePensenti: Shandisa fomura iyi:
\[
L = \frac{40}{100} \nguva (5 + 1) = 2.4
\]
3. Kupindirana: Sezvo \( L \) isiri nhamba yakakwana (2.4), pindirana pakati pezvinhu zviri panzvimbo yechipiri neyechitatu.
\[
P_{40} = X_2 + 0.4 \nguva (X_3 – X_2)
\]
\[
P_{40} = 20 + 0.4 \nguva (35 - 20) = 20 + 0.4 \nguva 15 = 20 + 6 = 26
\]
Saka, chikamu che40 muzana chedata iri pa26.
Mhando dzeMaperesenti
Kunze kwe50th percentile kana kuti median, kune mamwe mapercentile akasiyana-siyana anowanzoshandiswa:
– P25 (25th Percentile kana First Quartile): Inoratidza kukosha kuri pasi apa uko 25% yedata iri.
– P75 (75th Percentile kana Third Quartile): Inoratidza kukosha kuri pasi apa uko 75% yedata iri.
– P90 (90th Percentile): Inoratidza kukosha kuri pasi apa uko 90% yedata inowira.
Percentile yega yega inopa ruzivo rwakasiyana nezvekugoverwa kwedata. Semuenzaniso, interquartile range (IQR) ndiyo musiyano uripo pakati pe third quartile (P75) ne first quartile (P25), iyo inoshandiswa kuyera kusiyana kana kupararira kwedata.
Percentile muKugoverwa Kwakajairika
Mukugoverwa kwakajairika, mamwe ma percentile values ane chirevo chakafanana. Nekuti kugoverwa kwakajairika kwakaenzana uye kwakaumbwa sebhero, avhareji, median, uye mode zvese zvakaenzana. Mamwe ma percentile mukugoverwa kwakajairika ane hukama hwakakosha:
– P50 (Pakati): Zvakare avhareji yekugoverwa.
– P16 na P84: Aya ndiwo mavalues anogamuchira ±1 standard deviation kubva paavhareji.
– P2.5 na P97.5: Aya ndiwo mavalues anogamuchira ±2 standard deviation kubva paavhareji.
Mashandisirwo ePercentile mune Dzimwe Minda
Kunze kweizvo zvatotaurwa, ma percentile ane mashandisirwo akawanda muminda yakasiyana-siyana:
1. Mari: Inoshandiswa mukutarisira njodzi kuona kukosha kuri panjodzi (VaR) inova chikamu chehuwandu hwekugoverwa kwekurasikirwa kwepotefolio.
2. Sociology: Kuongorora kupararira kwezvinhu zvakasiyana-siyana zvakaita sezera, mari inowanikwa, mukana wekuwana dzidzo, nezvimwewo.
3. Kugadzira uye Hunhu: Inoshandiswa kudzora hunhu uye kuongorora kugoverwa kwemhedzisiro yekugadzirwa.
Mhedziso
Mapercentile chishandiso chine simba muhuwandu hwemashoko ekunzwisisa kugoverwa kwedata uye kuita zviyero zvinonzwisisika zvakananga. Kubva kudzidzo kusvika kumari nehutano, mashandisirwo anoshanda emapercentile anogonesa nyanzvi kuita sarudzo dziri nani, dzinotungamirirwa nedata.
Mapercentiles anopawo kushanduka-shanduka kwekuongorora kupfuura mamwe manhamba anotsanangura zvakaita se mean kana standard deviation, sezvo achigona kuratidza chinzvimbo chehunhu hwemunhu uye kupa maonero akajeka ekusiyana kwedata. Nekunzwisisa nekushandisa mapercentiles zvinobudirira, tinogona kuchera zvakadzama mudata, kuwana maitiro akavanzika, uye kuita sarudzo dzine ruzivo rwakawanda.
