{"id":598,"date":"2023-07-29T09:23:58","date_gmt":"2023-07-29T09:23:58","guid":{"rendered":"https:\/\/statorials.org\/tr\/sureklilik-duzeltmesi\/"},"modified":"2023-07-29T09:23:58","modified_gmt":"2023-07-29T09:23:58","slug":"sureklilik-duzeltmesi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/sureklilik-duzeltmesi\/","title":{"rendered":"I\u0307statistikte s\u00fcreklilik d\u00fczeltmesinin basit bir a\u00e7\u0131klamas\u0131"},"content":{"rendered":"

<\/p>\n

\n

S\u00fcreklilik d\u00fczeltmesi,<\/strong> ayr\u0131k bir da\u011f\u0131l\u0131ma yakla\u015fmak i\u00e7in s\u00fcrekli bir da\u011f\u0131l\u0131m kullanmak istedi\u011finizde uygulan\u0131r.<\/span> Genellikle, binom da\u011f\u0131l\u0131m\u0131na<\/a> yakla\u015fmak i\u00e7in normal da\u011f\u0131l\u0131m kullanmak istedi\u011finizde kullan\u0131l\u0131r.<\/span><\/p>\n

Tek bir denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131n p<\/em> oldu\u011fu g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, binom da\u011f\u0131l\u0131m\u0131n\u0131n bize n<\/em> denemede x<\/em> ba\u015far\u0131ya ula\u015fma olas\u0131l\u0131\u011f\u0131n\u0131 s\u00f6yledi\u011fini hat\u0131rlay\u0131n.<\/span> Olas\u0131l\u0131kla ilgili sorular\u0131 bir binom da\u011f\u0131l\u0131m\u0131yla yan\u0131tlamak i\u00e7in, basit\u00e7e bir binom da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131<\/a> kullanabiliriz, ancak ayn\u0131 zamanda s\u00fcreklilik d\u00fczeltmeli bir normal da\u011f\u0131l\u0131m kullanarak da olas\u0131l\u0131\u011f\u0131 yakla\u015f\u0131k olarak tahmin<\/em> edebiliriz.<\/span><\/p>\n

S\u00fcreklilik d\u00fczeltmesi, ayr\u0131k bir x de\u011ferine<\/strong> 0,5 ekleme veya \u00e7\u0131karma i\u015flemine<\/strong> verilen add\u0131r.<\/span><\/p>\n

\u00d6rne\u011fin, bir paran\u0131n 100 at\u0131\u015fta 45 kereden az veya buna e\u015fit tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 bulmak istedi\u011fimizi varsayal\u0131m. Yani P(X \u2264 45)’i bulmak istiyoruz. Binom da\u011f\u0131l\u0131m\u0131na yakla\u015fmak amac\u0131yla normal da\u011f\u0131l\u0131m\u0131 kullanmak i\u00e7in bunun yerine P(X \u2264 45,5) buluruz.<\/span><\/p>\n

A\u015fa\u011f\u0131daki tablo, bulmaya \u00e7al\u0131\u015ft\u0131\u011f\u0131n\u0131z olas\u0131l\u0131k t\u00fcr\u00fcne ba\u011fl\u0131 olarak ne zaman 0,5 eklemeniz veya \u00e7\u0131karman\u0131z gerekti\u011fini g\u00f6sterir:<\/span><\/p>\n\n\n\n\n\n\n\n\n
Binom da\u011f\u0131l\u0131m\u0131n\u0131 kullan\u0131n<\/strong><\/span><\/th>\n S\u00fcreklilik d\u00fczeltmesiyle normal da\u011f\u0131l\u0131m\u0131n kullan\u0131lmas\u0131<\/strong><\/span><\/th>\n<\/tr>\n
X = 45<\/span><\/td>\n 44,5 < X < 45,5<\/span><\/td>\n<\/tr>\n
X \u2264 45<\/span><\/td>\n X < 45,5<\/span><\/td>\n<\/tr>\n
X < 45<\/span><\/td>\n X < 44,5<\/span><\/td>\n<\/tr>\n
X \u2265 45<\/span><\/td>\n X > 44,5<\/span><\/td>\n<\/tr>\n
X > 45<\/span><\/td>\n X > 45,5<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

Not:<\/strong><\/span><\/p>\n

Sadece n*p ve n*(1-p)’nin her ikisi de en az 5 oldu\u011funda binom da\u011f\u0131l\u0131m\u0131na yakla\u015fmak i\u00e7in normal da\u011f\u0131l\u0131ma bir s\u00fcreklilik d\u00fczeltmesi uygulamak uygundur.<\/span><\/p>\n

\u00d6rne\u011fin, n = 15 ve p = 0,6 oldu\u011funu varsayal\u0131m. Bu durumda:<\/span><\/p>\n

n*p = 15 * 0,6 = 9<\/span><\/p>\n

n*(1-p) = 15 * (1 \u2013 0,6) = 15 * (0,4) = 6<\/span><\/p>\n

Bu say\u0131lar\u0131n her ikisi de 5’ten b\u00fcy\u00fck veya ona e\u015fit oldu\u011fundan, bu senaryoda s\u00fcreklilik d\u00fczeltmesinin uygulanmas\u0131 kabul edilebilir olacakt\u0131r.<\/span><\/p>\n<\/blockquote>\n

A\u015fa\u011f\u0131daki \u00f6rnek, binom da\u011f\u0131l\u0131m\u0131na yakla\u015fmak i\u00e7in normal da\u011f\u0131l\u0131ma s\u00fcreklilik d\u00fczeltmesinin nas\u0131l uygulanaca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n

S\u00fcreklilik d\u00fczeltmesinin uygulama \u00f6rne\u011fi<\/strong><\/span><\/h2>\n

Bir madeni paran\u0131n 100 at\u0131\u015fta 43 veya daha az kez tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. Bu durumda:<\/span><\/p>\n

n = deneme say\u0131s\u0131 = 100<\/span><\/p>\n

X = ba\u015far\u0131 say\u0131s\u0131 = 43<\/span><\/p>\n

p = belirli bir denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 = 0,50<\/span><\/p>\n

Bu say\u0131lar\u0131 binom da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131na<\/a> yerle\u015ftirip madalyonun 43 kat\u0131 veya daha az tura gelme olas\u0131l\u0131\u011f\u0131n\u0131n 0,09667<\/strong> oldu\u011funu g\u00f6rebiliriz.<\/span> <\/p>\n

\"S\u00fcreklilik<\/p>\n

Normal da\u011f\u0131l\u0131ma s\u00fcreklilik d\u00fczeltmesi uygulayarak binom da\u011f\u0131l\u0131m\u0131na yakla\u015fmak i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 kullanabiliriz:<\/span><\/p>\n

Ad\u0131m 1: n*p ve n*(1-p) \u00f6\u011felerinin her ikisinin de en az 5 oldu\u011funu do\u011frulay\u0131n<\/strong> .<\/span><\/p>\n

n*p = 100*0,5 = 50<\/p>\n

n*(1-p) = 100*(1 \u2013 0,5) = 100*0,5 = 50<\/p>\n

Her iki say\u0131 da 5’ten b\u00fcy\u00fck veya e\u015fittir, dolay\u0131s\u0131yla devam edebiliriz.<\/span><\/p>\n

Ad\u0131m 2: 0,5’in eklenip \u00e7\u0131kar\u0131lmayaca\u011f\u0131n\u0131 belirleyin<\/strong><\/span><\/p>\n

Yukar\u0131daki tabloya bak\u0131ld\u0131\u011f\u0131nda X \u2264 43 \u015feklinde olas\u0131l\u0131k ile \u00e7al\u0131\u015ft\u0131\u011f\u0131m\u0131zda 0,5<\/strong> eklememiz<\/strong> gerekti\u011fini g\u00f6r\u00fcyoruz. B\u00f6ylece P(X< 43,5) bulaca\u011f\u0131z.<\/span><\/p>\n

Ad\u0131m 3: Binom da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131n\u0131 (\u03bc) ve standart sapmas\u0131n\u0131 (\u03c3) bulun.<\/strong><\/span><\/p>\n

\u00b5<\/strong> = n*p = 100*0,5 = 50<\/span><\/p>\n

\u03c3<\/strong> = \u221a n*p*(1-p)<\/span> = \u221a 100*.5*(1-.5)<\/span> = \u221a 25<\/span> = 5<\/span><\/p>\n

Ad\u0131m 4: \u00d6nceki ad\u0131mda bulunan ortalama ve standart sapmay\u0131 kullanarak z-puan\u0131n\u0131 bulun.<\/strong><\/span><\/p>\n

z<\/strong> = (x \u2013 \u03bc) \/ \u03c3 = (43,5 \u2013 50) \/ 5 = -6,5 \/ 5 = -1,3.<\/span><\/p>\n

Ad\u0131m 5: Z puan\u0131yla ili\u015fkili olas\u0131l\u0131\u011f\u0131 bulmak i\u00e7in Z tablosunu kullan\u0131n.<\/strong><\/span><\/p>\n

Tablo Z’ye g\u00f6re z = -1,3 ile ili\u015fkili olas\u0131l\u0131k 0,0968’dir<\/strong> .<\/span> <\/p>\n

\"S\u00fcreklilik<\/p>\n

Yani binom da\u011f\u0131l\u0131m\u0131n\u0131 kullanarak buldu\u011fumuz kesin olas\u0131l\u0131k 0,09667<\/strong> iken, normal da\u011f\u0131l\u0131mla s\u00fcreklilik d\u00fczeltmesini kullanarak buldu\u011fumuz yakla\u015f\u0131k olas\u0131l\u0131k 0,0968’di<\/strong> . Bu iki de\u011fer birbirine olduk\u00e7a yak\u0131nd\u0131r.<\/span><\/p>\n

S\u00fcreklilik d\u00fczeltmesi ne zaman kullan\u0131l\u0131r?<\/strong><\/span><\/h2>\n

Modern istatistiksel yaz\u0131l\u0131mlar mevcut olmadan ve hesaplamalar\u0131n manuel olarak yap\u0131lmas\u0131 gerekmeden \u00f6nce, kesikli da\u011f\u0131l\u0131mlar\u0131 i\u00e7eren olas\u0131l\u0131klar\u0131 bulmak i\u00e7in s\u00fcreklilik d\u00fczeltmeleri s\u0131kl\u0131kla kullan\u0131l\u0131yordu.<\/span> G\u00fcn\u00fcm\u00fczde s\u00fcreklilik d\u00fczeltmeleri olas\u0131l\u0131klar\u0131n hesaplanmas\u0131nda daha az rol oynuyor \u00e7\u00fcnk\u00fc olas\u0131l\u0131klar\u0131 bizim i\u00e7in hesaplamak i\u00e7in genellikle yaz\u0131l\u0131mlara veya hesap makinelerine g\u00fcvenebiliyoruz.<\/span><\/p>\n

Bunun yerine, bir binom da\u011f\u0131l\u0131m\u0131 ile normal bir da\u011f\u0131l\u0131m aras\u0131ndaki ili\u015fkiyi g\u00f6stermek ve normal bir da\u011f\u0131l\u0131m\u0131n bir s\u00fcreklilik d\u00fczeltmesi uygulayarak bir binom da\u011f\u0131l\u0131m\u0131na yakla\u015fmas\u0131n\u0131n m\u00fcmk\u00fcn oldu\u011funu g\u00f6stermek, istatistik derslerinde ele al\u0131nan bir konudur.<\/span><\/p>\n

S\u00fcreklilik d\u00fczeltme hesaplay\u0131c\u0131s\u0131<\/strong><\/span><\/h2>\n

Binom olas\u0131l\u0131klar\u0131n\u0131 yakla\u015f\u0131k olarak normal da\u011f\u0131l\u0131ma otomatik olarak bir s\u00fcreklilik d\u00fczeltmesi uygulamak i\u00e7in s\u00fcreklilik d\u00fczeltme hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kullan\u0131n.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

S\u00fcreklilik d\u00fczeltmesi, ayr\u0131k bir da\u011f\u0131l\u0131ma yakla\u015fmak i\u00e7in s\u00fcrekli bir da\u011f\u0131l\u0131m kullanmak istedi\u011finizde uygulan\u0131r. Genellikle, binom da\u011f\u0131l\u0131m\u0131na yakla\u015fmak i\u00e7in normal da\u011f\u0131l\u0131m kullanmak istedi\u011finizde kullan\u0131l\u0131r. Tek bir denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131n p oldu\u011fu g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, binom da\u011f\u0131l\u0131m\u0131n\u0131n bize n denemede x ba\u015far\u0131ya ula\u015fma olas\u0131l\u0131\u011f\u0131n\u0131 s\u00f6yledi\u011fini hat\u0131rlay\u0131n. Olas\u0131l\u0131kla ilgili sorular\u0131 bir binom da\u011f\u0131l\u0131m\u0131yla yan\u0131tlamak i\u00e7in, basit\u00e7e bir binom […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-598","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\n\u0130statistikte s\u00fcreklilik d\u00fczeltmesinin basit bir a\u00e7\u0131klamas\u0131 - Statorials<\/title>\n<meta name=\"description\" content=\"\u0130statistikte s\u00fcreklilik d\u00fczeltmesi kavram\u0131n\u0131n bir \u00f6rnekle basit a\u00e7\u0131klamas\u0131.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/sureklilik-duzeltmesi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0130statistikte s\u00fcreklilik d\u00fczeltmesinin basit bir a\u00e7\u0131klamas\u0131 - Statorials\" \/>\n<meta property=\"og:description\" content=\"\u0130statistikte s\u00fcreklilik d\u00fczeltmesi kavram\u0131n\u0131n bir \u00f6rnekle basit a\u00e7\u0131klamas\u0131.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/sureklilik-duzeltmesi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T09:23:58+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/suitecorrection2.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/sureklilik-duzeltmesi\/\",\"url\":\"https:\/\/statorials.org\/tr\/sureklilik-duzeltmesi\/\",\"name\":\"\u0130statistikte s\u00fcreklilik d\u00fczeltmesinin basit bir a\u00e7\u0131klamas\u0131 - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-29T09:23:58+00:00\",\"dateModified\":\"2023-07-29T09:23:58+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"\u0130statistikte s\u00fcreklilik d\u00fczeltmesi kavram\u0131n\u0131n bir \u00f6rnekle basit a\u00e7\u0131klamas\u0131.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/sureklilik-duzeltmesi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/sureklilik-duzeltmesi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/sureklilik-duzeltmesi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"I\u0307statistikte s\u00fcreklilik d\u00fczeltmesinin basit bir a\u00e7\u0131klamas\u0131\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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