{"id":415,"date":"2023-07-30T07:37:23","date_gmt":"2023-07-30T07:37:23","guid":{"rendered":"https:\/\/statorials.org\/tr\/ornekleme-dagilimi\/"},"modified":"2023-07-30T07:37:23","modified_gmt":"2023-07-30T07:37:23","slug":"ornekleme-dagilimi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ornekleme-dagilimi\/","title":{"rendered":"\u00d6rnekleme da\u011f\u0131l\u0131m\u0131 nedir?"},"content":{"rendered":"
\n

10.000 yunus pop\u00fclasyonu oldu\u011funu ve bu pop\u00fclasyondaki bir yunusun ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 300 pound oldu\u011funu d\u00fc\u015f\u00fcn\u00fcn.<\/span><\/p>\n

Bu pop\u00fclasyondan 50 yunustan olu\u015fanbasit rastgele bir \u00f6rnek<\/a> al\u0131rsak, bu \u00f6rnekteki yunuslar\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 305 pound oldu\u011funu bulabiliriz.<\/span><\/p>\n

Daha sonra, 50 yunustan olu\u015fan ba\u015fka bir basit rastgele \u00f6rnek al\u0131rsak, bu \u00f6rnekteki yunuslar\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 295 pound oldu\u011funu bulabiliriz.<\/span><\/p>\n

Ne zaman 50 yunustan olu\u015fan rastgele bir \u00f6rnek alsak, \u00f6rnekteki yunuslar\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n pop\u00fclasyon ortalamas\u0131 olan 300 pound’a yak\u0131n olmas\u0131 muhtemeldir, ancak tam olarak 300 pound de\u011fildir.<\/span><\/p>\n

Bu pop\u00fclasyondan 50 yunustan 200 basit rastgele \u00f6rnek ald\u0131\u011f\u0131m\u0131z\u0131 ve her \u00f6rne\u011fin ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n bir histogram\u0131n\u0131 olu\u015fturdu\u011fumuzu hayal edelim:<\/span> <\/p>\n

\"\"<\/p>\n

\u00c7o\u011fu numunede ortalama a\u011f\u0131rl\u0131k 300 pound’a yak\u0131n olacakt\u0131r. Nadir durumlarda, ortalama a\u011f\u0131rl\u0131\u011f\u0131 yaln\u0131zca 250 pound olan k\u00fc\u00e7\u00fck yunuslarla dolu bir \u00f6rnek alabiliriz. Veya ortalama 350 kiloluk \u015fi\u015fe burunlu yunuslarla dolu bir \u00f6rnek alabiliriz. Genel olarak, \u00f6rneklem ortalamalar\u0131n\u0131n da\u011f\u0131l\u0131m\u0131<\/em> yakla\u015f\u0131k olarak normal olacakt\u0131r ve da\u011f\u0131l\u0131m\u0131n merkezi pop\u00fclasyonun ger\u00e7ek merkezinde yer alacakt\u0131r.<\/span><\/p>\n

\u00d6rnek ortalamalar\u0131n\u0131n bu da\u011f\u0131l\u0131m\u0131 , ortalaman\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<\/strong> olarak bilinir ve a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/span><\/p>\n

\u00b5x<\/span><\/sub><\/strong> = \u00b5<\/span><\/p>\n

burada \u03bc x<\/span><\/sub> \u00f6rnek ortalamas\u0131d\u0131r ve \u03bc pop\u00fclasyon ortalamas\u0131d\u0131r.<\/span><\/p>\n

\u03c3x<\/span><\/sub><\/strong> = \u03c3\/\u221an<\/span><\/p>\n

burada \u03c3 x<\/span><\/sub> \u00f6rneklem standart sapmas\u0131, \u03c3 pop\u00fclasyon standart sapmas\u0131 ve n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr.<\/span><\/p>\n

\u00d6rne\u011fin, bu yunus pop\u00fclasyonunda ortalama a\u011f\u0131rl\u0131\u011f\u0131n \u03bc = 300 oldu\u011funu biliyoruz. Yani \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131 \u03bc x<\/span><\/sub><\/strong> = 300<\/strong> olur.<\/span><\/p>\n

Ayr\u0131ca pop\u00fclasyon standart sapmas\u0131n\u0131n 18 pound oldu\u011funu bildi\u011fimizi varsayal\u0131m. Dolay\u0131s\u0131yla numunenin standart sapmas\u0131 \u03c3 x<\/span><\/sub><\/strong> = 18\/ \u221a50 = 2,546’d\u0131r<\/strong> .<\/span><\/p>\n

Oran\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<\/strong><\/span><\/h2>\n

Ayn\u0131 10.000 yunus pop\u00fclasyonunu d\u00fc\u015f\u00fcn\u00fcn. Yunuslar\u0131n %10’unun siyah, geri kalan\u0131n\u0131n gri oldu\u011funu varsayal\u0131m. 50 yunustan olu\u015fanbasit rastgele bir \u00f6rnek<\/a> ald\u0131\u011f\u0131m\u0131z\u0131 ve bu \u00f6rnekteki yunuslar\u0131n %14’\u00fcn\u00fcn siyah oldu\u011funu buldu\u011fumuzu varsayal\u0131m. Daha sonra, 50 yunustan olu\u015fan ba\u015fka bir basit rastgele \u00f6rnek al\u0131yoruz ve bu \u00f6rnekteki yunuslar\u0131n %8’inin siyah oldu\u011funu buluyoruz.<\/span><\/p>\n

Bu pop\u00fclasyondan 50 yunustan olu\u015fan 200 basit rastgele \u00f6rnek ald\u0131\u011f\u0131m\u0131z\u0131 ve her \u00f6rnekteki siyah yunuslar\u0131n oran\u0131n\u0131n histogram\u0131n\u0131 olu\u015fturdu\u011fumuzu d\u00fc\u015f\u00fcn\u00fcn:<\/span> <\/p>\n

\"\"<\/p>\n

\u00d6rneklerin \u00e7o\u011funda siyah yunuslar\u0131n oran\u0131 ger\u00e7ek pop\u00fclasyon olan %10’a yak\u0131n olacakt\u0131r. Siyah yunuslar\u0131n \u00f6rnek oran\u0131n\u0131n da\u011f\u0131l\u0131m\u0131<\/em> yakla\u015f\u0131k olarak normal olacakt\u0131r ve da\u011f\u0131l\u0131m\u0131n merkezi pop\u00fclasyonun ger\u00e7ek merkezinde yer alacakt\u0131r.<\/span><\/p>\n

\u00d6rnek oranlar\u0131n\u0131n bu da\u011f\u0131l\u0131m\u0131, orant\u0131 \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<\/strong> olarak bilinir ve a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/span><\/p>\n

\u00b5p<\/sub><\/strong> = P<\/span><\/p>\n

burada p<\/em> \u00f6rnek oran\u0131 ve P<\/em> pop\u00fclasyon oran\u0131d\u0131r.<\/span><\/p>\n

\u03c3 p<\/sub><\/strong> = \u221a (P)(1-P) \/ n<\/span><\/span><\/p>\n

burada P n\u00fcfus oran\u0131 ve n \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr.<\/span><\/p>\n

\u00d6rne\u011fin, bu yunus pop\u00fclasyonunda siyah yunuslar\u0131n ger\u00e7ek oran\u0131n\u0131n %10 = 0,1 oldu\u011funu biliyoruz. Dolay\u0131s\u0131yla orant\u0131sal \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131 \u03bc p<\/sub><\/strong> = 0,1’dir<\/strong> .<\/span><\/p>\n

Ayr\u0131ca pop\u00fclasyon standart sapmas\u0131n\u0131n 18 pound oldu\u011funu bildi\u011fimizi varsayal\u0131m. B\u00f6ylece \u00f6rneklemin standart sapmas\u0131 \u03c3 p<\/sub><\/strong> = \u221a (P)(1-P) \/ n<\/span> = \u221a (.1)(1-.1) \/ 50<\/span> = .042<\/strong> olur.<\/span><\/p>\n

Normalli\u011fi tesis edin<\/strong><\/span><\/h2>\n

Yukar\u0131daki form\u00fclleri kullanabilmek i\u00e7in \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n normal olmas\u0131 gerekir.<\/span><\/p>\n

Merkezi limit teoremine<\/strong> g\u00f6re, pop\u00fclasyon da\u011f\u0131l\u0131m\u0131 normal olmasa bile, \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc yeterince b\u00fcy\u00fckse, bir \u00f6rneklem ortalamas\u0131n\u0131n \u00f6rnekleme<\/em> da\u011f\u0131l\u0131m\u0131 yakla\u015f\u0131k olarak normaldir. \u00c7o\u011fu durumda, 30 veya daha fazla \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn yeterince b\u00fcy\u00fck oldu\u011funu d\u00fc\u015f\u00fcn\u00fcyoruz.<\/span><\/p>\n

Beklenen ba\u015far\u0131 ve ba\u015far\u0131s\u0131zl\u0131k say\u0131s\u0131 en az 10 ise, bir numune oran\u0131n\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131 yakla\u015f\u0131k olarak normaldir.<\/span><\/p>\n

\u00d6rnekler<\/strong><\/span><\/h2>\n

Olas\u0131l\u0131klar\u0131 hesaplamak i\u00e7in \u00f6rnekleme da\u011f\u0131l\u0131mlar\u0131n\u0131 kullanabiliriz.<\/span><\/p>\n

\u00d6rnek 1:<\/strong> Belirli bir makine \u00e7erezler olu\u015fturur. Bu kurabiyelerin a\u011f\u0131rl\u0131k da\u011f\u0131l\u0131m\u0131, ortalama 10 ons ve standart sapma 2 ons olacak \u015fekilde sa\u011fa \u00e7arp\u0131kt\u0131r. Bu makine taraf\u0131ndan \u00fcretilen 100 kurabiyeden olu\u015fan basit rastgele bir \u00f6rnek al\u0131rsak, bu \u00f6rnekteki kurabiyelerin ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 9,8 onstan az olma olas\u0131l\u0131\u011f\u0131 nedir?<\/strong><\/em><\/span><\/p>\n

Ad\u0131m 1: Normalli\u011fi sa\u011flay\u0131n.<\/span><\/strong><\/p>\n

\u00d6rnek ortalamalar\u0131n\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n normal oldu\u011fundan emin olmam\u0131z gerekir. \u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcm\u00fcz 30’dan b\u00fcy\u00fck veya 30’a e\u015fit oldu\u011fundan, merkezi limit teoremine g\u00f6re \u00f6rnek ortalamalar\u0131n\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n normal oldu\u011funu varsayabiliriz.<\/span><\/p>\n

Ad\u0131m 2: \u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131n\u0131 ve standart sapmas\u0131n\u0131 bulun.<\/span><\/strong><\/p>\n

\u00b5x<\/span><\/sub><\/strong> = \u00b5<\/span><\/p>\n

\u03c3x<\/span><\/sub><\/strong> = \u03c3\/\u221an<\/span><\/p>\n

\u03bc x<\/span><\/sub><\/strong> = 10 ons<\/strong><\/span><\/p>\n

\u03c3 x<\/span><\/sub><\/strong> = 2\/ \u221a100 = 2\/10 = 0,2 ons<\/strong><\/span><\/p>\n

Ad\u0131m 3:<\/strong> Bu \u00f6rnekteki ortalama kurabiye a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 9,8 onstan az olma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Z-Score Alan Hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kullan\u0131n.<\/strong><\/span><\/p>\n

A\u015fa\u011f\u0131daki say\u0131lar\u0131 Z Puan\u0131 Alan\u0131 Hesaplay\u0131c\u0131s\u0131na girin.<\/a> Bu \u00f6rnekte yaln\u0131zca bir say\u0131 buldu\u011fumuz i\u00e7in “Ham Skor 2″yi bo\u015f b\u0131rakabilirsiniz.<\/span> <\/p>\n

\"\"
Bu \u00f6rnekteki kurabiyelerin ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 9,8 onstan az<\/em> olma olas\u0131l\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimiz i\u00e7in soldaki<\/em> 9,8 onsluk alanla ilgileniyoruz. Hesap makinesi bize bu olas\u0131l\u0131\u011f\u0131n 0,15866<\/strong> oldu\u011funu s\u00f6yl\u00fcyor.<\/span><\/p>\n

\u00d6rnek 2:<\/strong> Okul \u00e7ap\u0131nda yap\u0131lan bir ara\u015ft\u0131rmaya g\u00f6re, belirli bir okuldaki \u00f6\u011frencilerin %87’si pizzay\u0131 dondurmaya tercih ediyor. 200 \u00f6\u011frenciden olu\u015fan basit rastgele bir \u00f6rnek ald\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. Pizza tercih eden \u00f6\u011frencilerin oran\u0131n\u0131n %85’ten az olma olas\u0131l\u0131\u011f\u0131 nedir?<\/strong><\/em><\/span><\/p>\n

Ad\u0131m 1: Normalli\u011fi sa\u011flay\u0131n.<\/span><\/strong><\/p>\n

Beklenen “ba\u015far\u0131” ve “ba\u015far\u0131s\u0131zl\u0131k” say\u0131s\u0131 en az 10 ise, bir numune oran\u0131n\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n yakla\u015f\u0131k olarak normal oldu\u011funu hat\u0131rlay\u0131n.<\/span><\/p>\n

Bu durumda pizzay\u0131 tercih etmesi beklenen \u00f6\u011frenci say\u0131s\u0131 %87 * 200 \u00f6\u011frenci = 174 \u00f6\u011frencidir. Pizza tercih etmeyecek \u00f6\u011frenci say\u0131s\u0131 ise %13 * 200 \u00f6\u011frenci = 26 \u00f6\u011frencidir. Bu say\u0131lar\u0131n her ikisi de en az 10 oldu\u011fundan pizzay\u0131 tercih edecek \u00f6\u011frenci oran\u0131n\u0131n \u00f6rneklem da\u011f\u0131l\u0131m\u0131n\u0131n yakla\u015f\u0131k olarak normal oldu\u011funu varsayabiliriz.<\/span><\/p>\n

Ad\u0131m 2: \u00d6rnekleme da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131n\u0131 ve standart sapmas\u0131n\u0131 bulun.<\/span><\/strong><\/p>\n

\u00b5p<\/sub><\/strong> = P<\/span><\/p>\n

\u03c3 p<\/sub><\/strong> = \u221a (P)(1-P) \/ n<\/span><\/span><\/p>\n

\u00b5p<\/sub><\/strong> = 0,87<\/strong><\/span><\/p>\n

\u03c3 p<\/sub><\/strong> = \u221a (0,87)(1-0,87) \/ 200<\/span> = 0,024<\/strong><\/span><\/p>\n

Ad\u0131m 3:<\/strong> Pizza tercih eden \u00f6\u011frencilerin oran\u0131n\u0131n %85’ten az olma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Z-Score Alan Hesaplay\u0131c\u0131s\u0131n\u0131<\/a> kullan\u0131n.<\/strong><\/span><\/p>\n

A\u015fa\u011f\u0131daki say\u0131lar\u0131 Z Puan\u0131 Alan\u0131 Hesaplay\u0131c\u0131s\u0131na girin.<\/a> Bu \u00f6rnekte yaln\u0131zca bir say\u0131 buldu\u011fumuz i\u00e7in “Ham Skor 2″yi bo\u015f b\u0131rakabilirsiniz.<\/span> <\/p>\n

\"\"<\/p>\n

Pizza tercih eden \u00f6\u011frencilerin oran\u0131n\u0131n %85’ten az olma olas\u0131l\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimiz i\u00e7in 0,85’in solundaki<\/em> alanla ilgileniyoruz. Hesap makinesi bize bu olas\u0131l\u0131\u011f\u0131n 0,20233<\/strong> oldu\u011funu s\u00f6yl\u00fcyor.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

10.000 yunus pop\u00fclasyonu oldu\u011funu ve bu pop\u00fclasyondaki bir yunusun ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 300 pound oldu\u011funu d\u00fc\u015f\u00fcn\u00fcn. Bu pop\u00fclasyondan 50 yunustan olu\u015fanbasit rastgele bir \u00f6rnek al\u0131rsak, bu \u00f6rnekteki yunuslar\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 305 pound oldu\u011funu bulabiliriz. Daha sonra, 50 yunustan olu\u015fan ba\u015fka bir basit rastgele \u00f6rnek al\u0131rsak, bu \u00f6rnekteki yunuslar\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 295 pound oldu\u011funu bulabiliriz. Ne zaman […]<\/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-415","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\n\u00d6rnekleme da\u011f\u0131l\u0131m\u0131 nedir? - Statoryaller<\/title>\n<meta name=\"description\" content=\"\u0130statistikte \u00f6nemli bir kavram olan \u00f6rnekleme da\u011f\u0131l\u0131mlar\u0131na basit bir giri\u015f.\" \/>\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\/ornekleme-dagilimi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u00d6rnekleme da\u011f\u0131l\u0131m\u0131 nedir? - Statoryaller\" \/>\n<meta property=\"og:description\" content=\"\u0130statistikte \u00f6nemli bir kavram olan \u00f6rnekleme da\u011f\u0131l\u0131mlar\u0131na basit bir giri\u015f.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/ornekleme-dagilimi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-30T07:37:23+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/echantillonnagedist1.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=\"6 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/ornekleme-dagilimi\/\",\"url\":\"https:\/\/statorials.org\/tr\/ornekleme-dagilimi\/\",\"name\":\"\u00d6rnekleme da\u011f\u0131l\u0131m\u0131 nedir? - Statoryaller\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-30T07:37:23+00:00\",\"dateModified\":\"2023-07-30T07:37:23+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"\u0130statistikte \u00f6nemli bir kavram olan \u00f6rnekleme da\u011f\u0131l\u0131mlar\u0131na basit bir giri\u015f.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/ornekleme-dagilimi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/ornekleme-dagilimi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/ornekleme-dagilimi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u00d6rnekleme da\u011f\u0131l\u0131m\u0131 nedir?\"}]},{\"@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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