{"id":224,"date":"2023-08-04T00:09:06","date_gmt":"2023-08-04T00:09:06","guid":{"rendered":"https:\/\/statorials.org\/tr\/normal-standart-dagilim\/"},"modified":"2023-08-04T00:09:06","modified_gmt":"2023-08-04T00:09:06","slug":"normal-standart-dagilim","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/normal-standart-dagilim\/","title":{"rendered":"Standart normal da\u011f\u0131l\u0131m"},"content":{"rendered":"
Bu makalede standart normal da\u011f\u0131l\u0131m\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Ayr\u0131ca standart normal da\u011f\u0131l\u0131m\u0131n \u00f6zelliklerini, karakteristik de\u011ferlerini i\u00e7eren tabloyu ve ayr\u0131ca \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 bulacaks\u0131n\u0131z. <\/p>\n
<\/span> Standart normal da\u011f\u0131l\u0131m nedir?<\/span><\/h2>\n
Birim normal da\u011f\u0131l\u0131m<\/strong> olarak da adland\u0131r\u0131lan standart normal da\u011f\u0131l\u0131m<\/strong> , normal da\u011f\u0131l\u0131m\u0131n en basit halidir. Daha do\u011frusu standart normal da\u011f\u0131l\u0131m, ortalama ve standart sapma de\u011ferleri s\u0131ras\u0131yla 0 ve 1’e e\u015fit olan bir normal da\u011f\u0131l\u0131md\u0131r.<\/p>\n
Bu nedenle standart normal da\u011f\u0131l\u0131m N(0,1) olarak tan\u0131mlan\u0131r; burada birinci parametre da\u011f\u0131l\u0131m\u0131n ortalamas\u0131, ikinci parametre ise standart sapmas\u0131d\u0131r (veya SD).<\/p>\n<\/p>\n
<\/p>\n<\/p>\n
Standart normal da\u011f\u0131l\u0131m\u0131n grafi\u011fi bu nedenle a\u015fa\u011f\u0131daki gibidir: <\/p>\n<\/figure>\n
<\/span> Standart normal da\u011f\u0131l\u0131m form\u00fcl\u00fc<\/span><\/h2>\n
Herhangi bir normal da\u011f\u0131l\u0131m\u0131 standart normal da\u011f\u0131l\u0131ma d\u00f6n\u00fc\u015ft\u00fcrmek i\u00e7in normal da\u011f\u0131l\u0131m\u0131n ortalamas\u0131n\u0131 t\u00fcm de\u011ferlerinden \u00e7\u0131karman\u0131z ve ard\u0131ndan normal da\u011f\u0131l\u0131m\u0131n standart sapmas\u0131na b\u00f6lmeniz gerekir.<\/p>\n
Standart normal da\u011f\u0131l\u0131m form\u00fcl\u00fc<\/strong> bu nedenle a\u015fa\u011f\u0131daki gibidir: <\/p>\n<\/figure>\n
Bu sayede yeni de\u011fi\u015fkenin aritmetik ortalamas\u0131 ve standart sapmas\u0131 s\u0131ras\u0131yla 0 ve 1 olaca\u011f\u0131ndan standart normal da\u011f\u0131l\u0131m elde etmi\u015f oluruz. Bu i\u015fleme ayn\u0131 zamanda tek de\u011fi\u015fkenli normalizasyon<\/strong> veya tek de\u011fi\u015fkenli normalizasyon<\/strong> da denir. <\/p>\n
<\/span> Standart normal da\u011f\u0131l\u0131m tablosu<\/span><\/h2>\n
Standart normal da\u011f\u0131l\u0131m tablosu, g\u00f6zlemlenen bir de\u011ferin standart normal da\u011f\u0131l\u0131m\u0131n belirli bir de\u011ferinden k\u00fc\u00e7\u00fck olma olas\u0131l\u0131klar\u0131n\u0131 i\u00e7eren bir tablodur.<\/p>\n
Ek olarak, normal da\u011f\u0131l\u0131m\u0131n i\u015flevi ortalamas\u0131na ve standart sapmas\u0131na ba\u011fl\u0131 oldu\u011fundan, herhangi bir normal da\u011f\u0131l\u0131m\u0131n olas\u0131l\u0131klar\u0131n\u0131 belirlemek i\u00e7in standart normal da\u011f\u0131l\u0131m tablosu da kullan\u0131l\u0131r. Bunu yapmak i\u00e7in normal da\u011f\u0131l\u0131m standart normal da\u011f\u0131l\u0131ma yaz\u0131l\u0131r ve ard\u0131ndan tabloya hangi olas\u0131l\u0131\u011f\u0131n buna kar\u015f\u0131l\u0131k geldi\u011fine bakar\u0131z.<\/p>\n
Yani standart normal da\u011f\u0131l\u0131m tablosundaki de\u011ferler \u015fu \u015fekildedir: <\/p>\n<\/figure>\n
<\/span> Standart Normal Da\u011f\u0131l\u0131m \u00d6rne\u011fi<\/span><\/h2>\n
Art\u0131k standart normal da\u011f\u0131l\u0131m\u0131n tan\u0131m\u0131n\u0131 ve form\u00fcl\u00fcn\u00fc bildi\u011fimize g\u00f6re, kavram\u0131 daha iyi anlamak i\u00e7in a\u015fa\u011f\u0131da somut bir \u00f6rnek verece\u011fiz.<\/p>\n
\n
S\u00fcrekli bir rastgele de\u011fi\u015fken, ortalamas\u0131 45 ve standart sapmas\u0131 15 olan normal bir da\u011f\u0131l\u0131m izlemektedir; 58’den k\u00fc\u00e7\u00fck veya buna e\u015fit bir de\u011fer elde etme olas\u0131l\u0131\u011f\u0131 nedir?<\/li>\n<\/ul>\n
<\/p>\n<\/p>\n
Normal da\u011f\u0131l\u0131m olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in \u00f6zellik tablosunu kullanmam\u0131z gerekir ancak bunu yapabilmek i\u00e7in \u00f6ncelikle standart normal da\u011f\u0131l\u0131m elde edecek \u015fekilde yazma i\u015flemini yapmam\u0131z gerekir. Bu nedenle standart normal da\u011f\u0131l\u0131m form\u00fcl\u00fcn\u00fc kullan\u0131yoruz:<\/p>\n<\/p>\n
<\/p>\n<\/p>\n
Yani ortalamay\u0131 olas\u0131l\u0131k de\u011ferinden \u00e7\u0131kar\u0131yoruz ve sonra standart sapmaya b\u00f6l\u00fcyoruz<\/p>\n<\/p>\n
<\/p>\n<\/p>\n
De\u011fi\u015fkeni standartla\u015ft\u0131rd\u0131ktan sonra, 0,87 de\u011ferinin hangi olas\u0131l\u0131\u011fa kar\u015f\u0131l\u0131k geldi\u011fini g\u00f6rmek i\u00e7in standart normal da\u011f\u0131l\u0131m olas\u0131l\u0131k tablosuna gideriz (yukar\u0131ya bak\u0131n):<\/p>\n<\/p>\n
<\/p>\n<\/p>\n
Dolay\u0131s\u0131yla 58’e e\u015fit veya daha k\u00fc\u00e7\u00fck bir de\u011fer elde etme olas\u0131l\u0131\u011f\u0131 %80,78’dir. <\/p>\n
<\/span> Standart normal da\u011f\u0131l\u0131m\u0131n \u00f6zellikleri<\/span><\/h2>\n
Standart normal da\u011f\u0131l\u0131m a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/p>\n
\n
Standart normal da\u011f\u0131l\u0131m 0 merkezli simetrik bir da\u011f\u0131l\u0131md\u0131r.<\/span><\/li>\n
Normal da\u011f\u0131l\u0131m gibi, standart normal da\u011f\u0131l\u0131m grafi\u011fi de \u00e7an \u015feklindedir ve grafik alan\u0131n\u0131n \u00e7o\u011fu ortalaman\u0131n etraf\u0131nda d\u00fc\u015fer.<\/span><\/li>\n
Bu nedenle normal da\u011f\u0131l\u0131m\u0131n ortalamas\u0131, modu ve medyan\u0131 ayn\u0131 de\u011fere yani 0’a sahiptir.<\/span><\/li>\n
Standart normal da\u011f\u0131l\u0131m\u0131n maksimumu z=0’dad\u0131r.<\/span><\/li>\n
Benzer \u015fekilde, standart normal da\u011f\u0131l\u0131m\u0131n z=-1 ve z=+1 olmak \u00fczere iki d\u00f6n\u00fcm noktas\u0131 vard\u0131r.<\/span><\/li>\n
Temel kurala g\u00f6re, de\u011ferlerin %68’inin +1 ile -1 aras\u0131ndaki standart normal da\u011f\u0131l\u0131ma, %95’inin +2 ile -2 aras\u0131ndaki de\u011ferlerin ve %99,7’sinin +1 ile -2 aras\u0131ndaki standart normal da\u011f\u0131l\u0131ma d\u00fc\u015ft\u00fc\u011f\u00fcn\u00fc biliyoruz. 3 ve – 3.<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"
Bu makalede standart normal da\u011f\u0131l\u0131m\u0131n ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Ayr\u0131ca standart normal da\u011f\u0131l\u0131m\u0131n \u00f6zelliklerini, karakteristik de\u011ferlerini i\u00e7eren tabloyu ve ayr\u0131ca \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 bulacaks\u0131n\u0131z. Standart normal da\u011f\u0131l\u0131m nedir? Birim normal da\u011f\u0131l\u0131m olarak da adland\u0131r\u0131lan standart normal da\u011f\u0131l\u0131m , normal da\u011f\u0131l\u0131m\u0131n en basit halidir. Daha do\u011frusu standart normal da\u011f\u0131l\u0131m, ortalama ve standart sapma […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-224","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"\n
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