Ubume kunye neentlobo avareji manani kunye neendlela ukubala kwabo. Iintlobo avareji-manani ezishwankathelweyo: imizekelo Table

Ukususela isifundo kwale nzululwazi, amanani, kufuneka kuqondwe ukuba iqulathe (kwakunye nayiphi na inzululwazi), uninzi amagama ukuba kufuneka ukwazi nokuqonda. Namhlanje siza kujonga into enjalo njengoko ixabiso avareji, uze ufumanise ukuba iintlobo awabelana ukuze ubale njani. Kodwa ngaphambi kokuba siqale, makhe sithethe kancinane ngembali malunga nendlela yaye kutheni kukho lesayensi, njengoko amanani.

indaba

Igama elithi "statistics" uqhuba linentsusa yalo ulwimi Latin. It livela elithi "status" yaye lithetha "izinto" okanye "imeko". Le nkcazelo emifutshane ibonisa, enyanisweni, into yonke kunye nenjongo-manani. It iqokelela iinkcukacha malunga nemeko izinto kwaye ivumela ukuba ukuhlalutya nayiphi na imeko. Sebenza kunye manani ababandakanyekayo eRoma Ancient. lwaqhutywa khona ingxelo abemi simahla, impahla kunye nempahla yabo. Ngokubanzi ekuqaleni manani zasetyenziswa ukufumana idata kwi inani labantu kunye nempahla yabo. Umzekelo, eNgilani, kubalo yokuqala ehlabathini lwaqhutywa ngo-1061. Khans ababelawula eRashiya ngenkulungwane ye-13, naye wayeqhuba ubalo ukuthatha irhafu evela emazweni.

Ngasinye sebenzisa izibalo iinjongo zabo, kwaye kwiimeko ezininzi isifake isiphumo elindelweyo. Xa abantu bebona ukuba oku zezibalo nje nenzululwazi eyahlukileyo, ekufuneka ifundwe kakuhle, saqalisa ukuvela izazinzulu yokuqala abanomdla lwalo lokukhawulelana nophuhliso. Abantu kuqala waba nomdla kule ndawo waza ukuqonda ngenkuthalo kuyo, beseka ezikolo ezimbini eziphambili: isikolo British yenzululwazi izibalo zezopolitiko eyimbali German yesikolo. Okokuqala ukuvela ngenkulungwane ye-17 yaye ijolise ukuba niyinikele ngezenzeko loluntu ngokusebenzisa izalathisi ngamanani. Babefuna ukubona iipateni kwi nesenzeko nezentlalo isifundo sezibalo. Abaxhasi yesikolo ezichazayo Wachaza iinkqubo zentlalo, kodwa kusetyenziswa amagama kuphela. Babengenako yexa Dynamics iziganeko, ukuze baqonde ngcono oko.

Kwisiqingatha sokuqala kwenkulungwane ye-19, kodwa omnye kwakukho, kwicala lesithathu kwale nzululwazi: manani nemathematika. igalelo elikhulu kuphuhliso kule ndawo wenza sisazinzulu ezaziwayo-kakuhle, eThintelweyo Adolf Ketle e Belgium. Yaba nguye owathi iintlobo amaxabiso avareji kwi-manani, kunye ngeenkongolo bamazwe ukuba kubanjwa ngokwakhe, elingcwele ngenzululwazi. Ukususela ekuqaleni kwenkulungwane yama-20 kwi-manani baqalisa ukuba kusetyenziswa iindlela nobunzima zemathematika, ezifana kwithiyori lilonke.

Namhlanje, inzululwazi amanani iqhutywa computerization. Ukusebenzisa nganye kwiinkqubo ezahlukeneyo Oku igrafu ngokususela kwidatha ecebisa. Kwi-Internet mininzi kananjalo izibonelelo ezinika naziphi na iinkcukacha-manani inani labemi hayi kuphela.

Kwicandelo elilandelayo siza kujonga oko kuthethwa amagama afana manani, iintlobo-avareji kunye lilonke. Okulandelayo, sifikelela kwi umbuzo njani yaye phi njani ukusebenzisa olu lwazi.

Yintoni na izibalo?

It is a inzululwazi injongo yakhe ephambili kukuba ukwenza ulwazi ekufundweni imithetho iinkqubo ezenzekayo eluntwini. Ngenxa yoko, nathi kuqulunqa kwisigqibo sokuba amanani ufunda uluntu kunye nesenzeko ezithi zenzeke kuyo.

Kukho ezininzi iinkalo nenzululwazi lwamanani:

1) Jikelele Theory of Statistics. Ukuphuhlisa iindlela ukulungiselela ukuqokelelwa kweenkcukacha-manani sisiseko zonke ezinye iindawo.

2) Social kunye manani kwezoqoqosho. It ufunda nesenzeko zoqoqosho ngokwemiqathango kwingqeqesho yangaphambili kufunyaniswe iinkqubo zentlalo.

3) Statistics Mathematical. Ayikho into kweli hlabathi ingahlolwa. Into iqala. Iinkcukacha-manani Mathematical ukufunda izinto random kunye nemithetho ukusasazwa lilonke ku manani.

4) Industry kunye showgirl ngamazwe. Le intsimi emxinwa abahlola inkalo ubungakanani ngezenzeko kumazwe okanye amacandelo oluntu athile.

Ngoku siza kujonga iintlobo amaxabiso avareji kwi-manani, sicinga ngokufutshane izicelo zabo kwezinye iindawo, ngaphantsi engenamsebenzi njengoko manani.

Iintlobo avareji manani

Apha ukuba eyona nto ibalulekileyo, enyanisweni, isihloko wenqaku. Kakade ke, ukuze uphuhliso iingqiqo eziphathekayo zokufunda ezifana uhlobo kunye neentlobo avareji-manani efunekayo ulwazi oluthile lwemathematika. Okokuqala, makhe khumbula ukuba le izibalo kuthetha, harmonic, nezejometri equation '.

I izibalo ukuthini, ukuba ndingaba esikolweni. Oku kubalwa kakhulu nje: sithatha a amanani ezimbalwa phakathi kuloo imfuneko ukufumana. Dibanisa abo amanani Uze uwahlule isixa ngenani. Ngokwezibalo, oku kumelwa ngolu hlobo. Thina uthotho amanani, umzekelo, inani elula njengokuba: 1,2,3,4. Xa iyonke esinayo ezinamanani ama-4. Sifumana-avareji yawo ngolu hlobo lulandelayo: (1 + 2 + 3 + 4) / 4 = 2.5. Yinto elula. Siqala ngale, kuba kulula ukuqonda iimbono amaxabiso avareji kwi-manani.

Ngokufutshane atshele ye kwemin yemigca. Thatha uthotho kwamanani, njengoko bekunjalo kumzekelo wokuqala. Kodwa ngoku, ukuze ubale imin zejometri, kufuneka ukususa ingcambu apho lilingana nenani la manani, imisebenzi yabo. Ngenxa yoko, ukuba bafumane umzekelo lwangaphambili: (1 * 2 * 3 * 4 ) 1/4 ~ 2.21.

Kukubethelela ingqiqo kwemin harmonic. njani oqhele kwimathematika kwisikolo ukubala olu hlobo medium, kufuneka kuqala ukufumana inani, khangela inani thotho. Oko kukuthi, sisahlula iyunithi loo nombolo. Ngoko ukubuyela inani. Umlinganiselo imali yawo kwaye inani iya kuba imin harmonic. Thabatha umzekelo inani elifanayo-1, 2, 3, 4. inani Reverse ngabe unjani: 1, 1/2, 1/3, 1/4. Ke imin harmonic nga kubalwa ngolu hlobo lulandelayo: 4 / (1 + 1/2 + 1/3 + 1/4) ~ 1,92.

Zonke ezi ntlobo amaxabiso avareji kwi-manani, Imizekelo esifunde ngazo ukuba babe yinxalenye yeqela ekuthiwa amandla. Kukho kwakhona eliphakathi kwesakhiwo, apho siza kujonga kamva. Ngoku ingqalelo kwifom lokuqala.

amanani avareji Power

Sele sixubushe izibalo, zeijiyometri harmonic. Kukho kwakhona ifomu ezinobunzima, ebizwa RMS. Nangona yaye musani ukuya esikolweni, nto ilula ukubala. Kuyimfuneko kuphela ukuba walala phantsi inani zembutho amanani, wandule ukohlula isiphumo soko ngenani, yaye sinokufunda ntoni konke oku ingcambu. Kuba uthotho esizithandayo wayeza khangela ngolu hlobo: ((1 ² 2 ² 3 ² 4 ²⁾ / 4) = ^1/2 (30/4) ^1/2 ~ 2,74.

Enyanisweni, ukuba zonke iimeko nje ekhethekileyo kunamandla aqhelekileyo. Ngokubanzi, oku kuchazwe ngolu hlobo lulandelayo: ngesidanga ukuze isidanga n n-Nogo lilingana ingcambu wamcacisela inani amanani izidanga n-zehydrochloric lahlulwe ngenani la manani. Nangona nto ke ayithethi kunzima njengoko kubonakala.

Noko ke, nkqu iqondo umlinganiselo ityala ekhethekileyo uhlobo olunye - medium-Kolmogorov. Enyanisweni, zonke iindlela siyifumene amaxabiso ezahlukeneyo avareji ngaphambili, angamelwa njenge ^{ifomula: y -1 * ((y (} x ₁₎ + y (x ₂₎ + y (x ₃₎ + ... + _{y (x n)) / n} ). Apha zonke ezitshintshayo x - inani lemiqolo kunye y (x) - imisebenzi ethile, leyo siyakholwa -avareji. Kwimeko, yithini, kunye umlinganiselo umsebenzi equation y = x ^2, yaye safumana owona mndilili ka y = x. Yiloo nto thusa kuthi maxa wambi kuveza manani. Iintlobo avareji Asizanga okwangoku ezibekwe phambi kokuphela. Ukongeza, kukho kwakhona isakhiwo yesibini. Makhe sithethe ngabo.

ezomhlaba noshowo manani. fashion

Kuxhomekeke kancinane esintsonkothileyo. Ukuyiqhaqha ezi ndidi avareji manani kunye neendlela ukubala kwabo, kufuneka ucinge ngenyameko. Kukho iindidi ezimbini eziphambili zokusebenza imiyinge imo kunye udibaniso. Siza ukuqonda kuqala.

Fashion yeyona common kakhulu. Isetyenziswa kakhulu rhoqo ukuqinisekisa imfuno meko okanye loo nto. Ukuze ufumane ixabiso layo, kufuneka ufumane lokuphumla ethumayo kuqala. Yintoni na? Ethumayo uluhlu - uluhlu lwamaxabiso apho nakweliphi na ukuba zezantoni liphezulu. ukubonakala kudingeka ukuba uqonde ngcono iintlobo fashion kunye amaxabiso avareji kwi-manani. Le theyibhile, oko kuthetha ngezantsi, yinxalenye yengxaki, i imeko:

Ukumisela indlela angokokusebenza isityalo kwemveliso ngemihla.

Kwimeko yethu, uluhlu ethumayo - isalathiso icandelo imveliso ngemihla kunye nani likhulu labantu, okt 40-44. umda wayo asezantsi - 44.

Kwaye ngoku kuxoxa ukubala le efanayo. Ifomula ayikho inzima kakhulu kwaye angabhalwa ngolu hlobo: M = x _{1 + n * (f M -f M} -1) / ((f M -f M -1) + (f M -f M + _1)). Apha f _M - esiwubonayo ethumayo interval, f _M-1 - lokuphumla phambi frequency zizilabalabi (kulo mzekelo 36-40), f _{M + 1} - emva frequency ethumayo kwithuba lokuphumla (kuba thina - 44-48), n - ixabiso lokuphumla ( okt umahluko phakathi ezisezantsi wabopha eliphezulu)? x ₁ - ixabiso umda osezantsi (kulo mzekelo 40). Ukwazi yonke le datha, singakwazi lula ukubala befashoni kwinani kwemveliso imihla ngemihla: M = 40 + 4 * (24-20) / ((24-20) + (24-19)) = 40 + 16/9 = 41 ( 7).

Kwesakhiwo wesimo manani. udibaniso

Makhe sihlolisise ngakumbi olu hlobo ezahlukeneyo zezakhiwo, udibaniso. Iinkcukacha kuwo asiyi kuyeka, xelela ngomahluko nohlobo yangaphambili kuphela. Udibaniso geometry bisects-engile. Kungekho nto-manani olu hlobo naphakathi kangaka igama. Ukuba inombolo isikhundla (umzekelo, kwi elinabantu ubunzima elithile inyuka umyalelo inani), udibaniso lixabiso leyo yahlula manqaku ibe ngamaqela amabini alinganayo ngenani.

Ezinye iintlobo avareji manani

iintlobo zezakhiwo, kudityaniswa isivuno ngamandla ayikho yonke into efunekayo ukuze izibalo kwiindawo ezahlukeneyo. Ukubeka ezinye iindidi ze data. Ngoko ke, kukho ezomhlaba bemfuno. Olu hlobo kusetyenziswa xa kukho inani abe "ubunzima yokwenene" ezahlukeneyo. Oku kunokucaciswa umzekelo olula. Thatha imoto. Ihamba ngesantya ezahlukeneyo nggamathuba ngexesha ezahlukeneyo. Kule meko kwahluka enye kwenye yaye amaxabiso yezi ixesha ekhefu kunye sesiqhelo. Ngoku, le izikhewu kwaye iya kuba ubunzima wokwenene. Ukumiswa unokwenza naluphi na uhlobo imiyinge amandla.

Xa ubushushu bugcisa kwakhona kusetyenziswa esinye uhlobo avareji - avareji log. Lubonakaliswa ifomula kunokuba nzima, kuba nakanye.

yayisebenzisa Uphi na?

Amanani - inzululwazi ukuba akukho ebotshelelwe naliphi na icandelo elinye. Nangona wadalwa njengenxalenye yesigaba ezentlalo nezoqoqosho, kodwa namhlanje zisetyenziswe physics, chemistry, kunye eziphilayo iindlela zayo kunye nemithetho. Ukuba nolwazi kule ndawo, singakwazi lula ukubona iintsingiselo oluntu kunye nokuthintela le ngozi kwexesha. Rhoqo siva ibinzana elithi "esongela-manani", yaye le nto amazwi alambathayo. Le inzululwazi isixelela ntoni ngokwethu, yaye ukufunda ngenxa iyakwazi lokulumkisa ngento enokwenzeka.

Njani na iintlobo avareji-manani?

Ubudlelwane phakathi kwabo azisoloko apho, apha, umzekelo, iindidi noshowo akadibananga yi na fomyula. Kodwa ngamandla yonke umdla kakhulu ngakumbi. Umzekelo, kukho ipropati imin lokubala eliguqukayo amanani amabini liyakholisa ukuba ngaphezulu kune okanye ilingana imin lwabo yemigca. Ngokwezibalo ibhalwe ngolu hlobo: (a b +) / ^{2> = (a * b) 1/2} . Sisuke ukungalingani ukutshintshwa ilungelo eliCebisayo ngasekhohlo ngakumbi. Ngenxa yoko, nathi ukufumana iingcambu umahluko, zakhiwe kwindawo yembutho yesixeko. Ekubeni naliphi na inani kabini yi-HIV, ngokulandelelana, ukungalingani uba oyinyaniso.

Ukongeza kukho amaxabiso unxulumano jikelele. Kubonakala ukuba imin harmonic isoloko ngaphantsi kwe imin zejometri, nto leyo ngaphantsi kwemin arithmetic. Nevuthisayo na, ke, ngaphantsi yembutho abangenagama. Uyakwazi ngokuzimeleyo uqinisekise ezi esuka umzekelo amanani amabini - 10 no-6.

Yintoni kule umdla?

Kazi iintlobo avareji manani okwakubonakala ukubonisa avareji nje kwinqanaba elithile, ngaba eneneni uthi umntu owaziyo okuninzi. Xa ubukele iindaba, akukho bani ucinga ngayo intsingiselo yezi amanani, nendlela yokufumana kubo bonke.

Yiyiphi eyona, ungakwazi ukufunda?

Ukuze uphuhliso olusa phambili umxholo, sicebisa ukuba ufunde (okanye umamele) ikhosi ye-manani kunye nemathematika eziphezulu. Eneneni, kweli nqaku, sathetha kuphela isibi equlathe le inzululwazi, kwaye ngokwalo it umdla ngaphezu kubonakala xa efika kuqala.

Njengoko olu lwazi iya kundinceda?

Mhlawumbi luncedo kuwe ebomini. Kodwa ukuba unomdla yobume ngezenzeko zentlalo, indlela yabo nesiphumo ubomi bakho, ngoko ke manani kuya kukunceda ukuqonda nzulu le miba. Ngokubanzi, oku ukuchaza phantse zonke iinkalo zobomi bethu, xa e data zokulahla yayo ziyafumaneka. Kulungile, ngoko, ukuba ungafumana khona kunye nendlela ingcaciso ukwenzela uhlalutyo - ngesihloko omnye nqaku.

isiphelo

Ngoku siyazi ukuba kukho iintlobo ezahlukileyo avareji-manani: ubungakanani kunye kwesakhiwo. Siyakuqonda ndlela yokubala yabo, yaye oko kusetyenziswa phi, kanjani.