{"id":2676,"date":"2024-10-15T10:20:37","date_gmt":"2024-10-15T08:20:37","guid":{"rendered":"https:\/\/clooma.ai\/?post_type=ressource-pedagogiqu&#038;p=2676"},"modified":"2024-10-24T16:26:36","modified_gmt":"2024-10-24T14:26:36","slug":"kozponti-hatarertektetel","status":"publish","type":"ressource-pedagogiqu","link":"https:\/\/clooma.ai\/hu\/oktatasi-forras\/kozponti-hatarertektetel\/","title":{"rendered":"K\u00f6zponti hat\u00e1r\u00e9rt\u00e9kt\u00e9tel"},"content":{"rendered":"<p>A k\u00f6zponti hat\u00e1r\u00e9rt\u00e9kt\u00e9tel magyar\u00e1zat\u00e1hoz vegy\u00fck ezt a kiindul\u00f3pontot. Isten nem kock\u00e1zik\" - mondta egyszer. <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Albert_Einstein\">A.Einstein<\/a> a kvantummechanik\u00e1r\u00f3l, megk\u00e9rd\u0151jelezve a modern fizika egyik alapj\u00e1t. A 20. sz\u00e1zadban v\u00e9gzett k\u00eds\u00e9rletek azonban bebizony\u00edtott\u00e1k, hogy t\u00e9vedett, \u00e9s ma m\u00e1r elfogadott, hogy a vil\u00e1gban minden megfigyelhet\u0151 v\u00e1ltoz\u00f3t eloszl\u00e1si val\u00f3sz\u00edn\u0171s\u00e9gek szab\u00e1lyoznak, \u00e9s Heisenberg bizonytalans\u00e1gi elv\u00e9nek hat\u00e1lya al\u00e1 tartoznak. A vil\u00e1g v\u00e9letlenszer\u0171...\u00a0<\/p>\n\n\n\n<p>A v\u00e9letlen jelens\u00e9gek meg\u00e9rt\u00e9se alapvet\u0151 fontoss\u00e1g\u00fa a vil\u00e1g m\u0171k\u00f6d\u00e9s\u00e9nek meg\u00e9rt\u00e9s\u00e9hez. A statisztikai adatelemz\u00e9s egyik k\u00f6zponti t\u00e9tele matematikailag is kimutathat\u00f3: a k\u00f6zponti hat\u00e1r\u00e9rt\u00e9kt\u00e9tel.&nbsp;<\/p>\n\n\n\n<p>Minden olyan rendszer, amely sok, egym\u00e1st\u00f3l f\u00fcggetlen \u00e9s azonos nagys\u00e1grend\u0171 t\u00e9nyez\u0151 \u00f6sszeg\u00e9b\u0151l ad\u00f3dik, olyan eloszl\u00e1si t\u00f6rv\u00e9nyt hoz l\u00e9tre, amely a norm\u00e1lis eloszl\u00e1s fel\u00e9 hajlik.&nbsp;<\/p>\n\n\n\n<p>Ez a t\u00e9tel megmutatja a norm\u00e1leloszl\u00e1s fontoss\u00e1g\u00e1t egy megfigyelhet\u0151 v\u00e1ltoz\u00f3 elemz\u00e9se sor\u00e1n. Ennek illusztr\u00e1l\u00e1s\u00e1ra dobjunk egy kock\u00e1t 1000-szer egym\u00e1s ut\u00e1n, \u00e9s figyelj\u00fck meg az eredm\u00e9nyek eloszl\u00e1s\u00e1t:&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/image-14-1024x644.png\" alt=\"\" class=\"wp-image-2753\"\/><\/figure><\/div>\n\n\n<p>Az eloszl\u00e1s egyenletes eloszl\u00e1st k\u00f6vet, azaz egyenl\u0151 es\u00e9ly van arra, hogy a kocka 1, 2, 3, 4, 5 vagy 6-ra esik. Az eloszl\u00e1s nem hasonl\u00edt a norm\u00e1lis eloszl\u00e1sra.&nbsp;<\/p>\n\n\n\n<p>Dobjunk 10 kock\u00e1t 1000-szer egym\u00e1s ut\u00e1n, \u00e9s n\u00e9zz\u00fck meg, hogyan oszlik el ennek a 10 kock\u00e1nak az \u00f6sszege:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/clooma.ai\/wp-content\/uploads\/image-17-1024x803.png\" alt=\"\" class=\"wp-image-2757\"\/><\/figure>\n\n\n\n<p>B\u00e1r minden kocka egyenletes eloszl\u00e1st k\u00f6vet, a 10 kocka \u00f6sszeg\u00e9nek eloszl\u00e1sa harangg\u00f6rb\u00e9t k\u00f6vet. Ez az eloszl\u00e1s nagyon k\u00f6zel \u00e1ll a norm\u00e1lis eloszl\u00e1shoz.&nbsp;<\/p>\n\n\n\n<p>Val\u00f3ban, ha a k\u00f6zponti hat\u00e1r\u00e9rt\u00e9kt\u00e9telt k\u00f6vetj\u00fck :&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Van egy rendszer\u00fcnk&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sok t\u00e9nyez\u0151 \u00f6sszeg\u00e9b\u0151l ad\u00f3dik (ebben az esetben 10 kocka \u00f6sszeg\u00e9b\u0151l).&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>egym\u00e1st\u00f3l f\u00fcggetlenek (az egyik kocka eredm\u00e9nye nem befoly\u00e1solja a m\u00e1sik kocka eredm\u00e9ny\u00e9t).&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Az egyes kock\u00e1k nagys\u00e1grendje egyen\u00e9rt\u00e9k\u0171&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>Az e rendszer \u00e1ltal gener\u00e1lt eloszl\u00e1s a norm\u00e1lis eloszl\u00e1s fel\u00e9 hajlik. Mindent egybevetve, ez meglehet\u0151sen intuit\u00edv. Amikor 10 kock\u00e1t dobunk, csak egyetlen olyan kombin\u00e1ci\u00f3 van, amely 10-es eredm\u00e9nyt ad (az \u00f6sszes kocka 1-esre esik), m\u00edg t\u00f6bb ezer olyan kombin\u00e1ci\u00f3 van, amely 35-\u00f6s eredm\u00e9nyt ad. Ennek eredm\u00e9nyek\u00e9ppen a 35-\u00f6sh\u00f6z k\u00f6zeli eredm\u00e9nyek sokkal val\u00f3sz\u00edn\u0171bbek, mint az olyan sz\u00e9ls\u0151s\u00e9ges eredm\u00e9nyek, mint a 10 vagy a 60. A kapott eloszl\u00e1si t\u00f6rv\u00e9ny teh\u00e1t k\u00f6zel \u00e1ll a norm\u00e1lis eloszl\u00e1si t\u00f6rv\u00e9nyhez.&nbsp;<\/p>\n\n\n\n<p>Az \u00e1ltalunk \u00e1ltal\u00e1ban megfigyelt rendszerek ilyen t\u00edpus\u00fa eloszl\u00e1ssal rendelkeznek, mivel megfelelnek a k\u00f6zponti hat\u00e1r\u00e9rt\u00e9kt\u00e9tel felt\u00e9telez\u00e9seinek. Vegy\u00fck egy alkatr\u00e9sz megmunk\u00e1l\u00e1s\u00e1nak p\u00e9ld\u00e1j\u00e1t:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ez egy olyan rendszer, amely egy jellemz\u0151t hoz l\u00e9tre.&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A jellemz\u0151nek a c\u00e9lt\u00f3l val\u00f3 elt\u00e9r\u00e9se sz\u00e1mos t\u00e9nyez\u0151 (rezg\u00e9sek, az anyag kem\u00e9nys\u00e9ge, a szersz\u00e1m pozicion\u00e1l\u00e1si hib\u00e1ja stb. ....) \u00f6sszeg\u00e9b\u0151l ad\u00f3dik.&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A t\u00e9nyez\u0151k f\u00fcggetlenek egym\u00e1st\u00f3l (a g\u00e9p rezg\u00e9sei nem befoly\u00e1solj\u00e1k az anyag kem\u00e9nys\u00e9g\u00e9t).&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ezen elt\u00e9r\u00e9sek nagys\u00e1grendje a k\u00f6vetkez\u0151vel egyen\u00e9rt\u00e9k\u0171&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>Az alkatr\u00e9szek eloszl\u00e1sa teh\u00e1t a norm\u00e1lis eloszl\u00e1s fel\u00e9 tend\u00e1l, amit akkor figyelhet\u00fcnk meg, amikor alkatr\u00e9szek sorozat\u00e1t m\u00e9rj\u00fck.&nbsp;<\/p>","protected":false},"featured_media":0,"template":"","meta":{"_acf_changed":false},"menu-ressource-pedagogique":[27],"class_list":["post-2676","ressource-pedagogiqu","type-ressource-pedagogiqu","status-publish","hentry","menu-ressource-pedagogique-3-statistiques-descriptives"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - 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