{"id":2814,"date":"2023-07-20T14:16:08","date_gmt":"2023-07-20T14:16:08","guid":{"rendered":"https:\/\/statorials.org\/tr\/ortalamanin-onemi\/"},"modified":"2023-07-20T14:16:08","modified_gmt":"2023-07-20T14:16:08","slug":"ortalamanin-onemi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ortalamanin-onemi\/","title":{"rendered":"I\u0307statistiklerde ortalama neden \u00f6nemlidir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Bir veri k\u00fcmesinin <strong>ortalamas\u0131<\/strong> , veri k\u00fcmesinin ortalama de\u011ferini temsil eder. A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ortalama = \u03a3x <sub>i<\/sub> \/ n<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3:<\/strong> \u201ctoplam\u201d anlam\u0131na gelen bir sembol<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>i<\/sub> :<\/strong> Bir veri setindeki <sup>i&#8217;inci<\/sup> g\u00f6zlem<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> veri k\u00fcmesindeki toplam g\u00f6zlem say\u0131s\u0131<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, 11 g\u00f6zlem i\u00e7eren a\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Veri k\u00fcmesi:<\/strong> 3, 4, 4, 6, 7, 8, 12, 13, 15, 16, 17<\/span><\/p>\n<p> <span style=\"color: #000000;\">Veri setinin ortalamas\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ortalama = (3+4+4+6+7+8+12+13+15+16+17) \/ 11 = <strong>9,54<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130statistiklerde ortalama a\u015fa\u011f\u0131daki nedenlerden dolay\u0131 \u00f6nemlidir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> Ortalama bize bir veri k\u00fcmesinin \u201cmerkezinin\u201d nerede oldu\u011funa dair bir fikir verir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> Hesaplanma \u015fekli nedeniyle ortalama, bir veri setindeki <em>her<\/em> <a href=\"https:\/\/statorials.org\/tr\/istatistikte-gozlem\/\" target=\"_blank\" rel=\"noopener\">g\u00f6zlemden<\/a> elde edilen bilgileri i\u00e7erir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnek bu iki nedeni g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: Bir veri k\u00fcmesinin ortalamas\u0131n\u0131 hesaplama<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Diyelim ki elimizde belli bir \u015fehirdeki 10.000 farkl\u0131 evin sat\u0131\u015f fiyatlar\u0131n\u0131 i\u00e7eren bir veri setimiz var.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-18105 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/medianeimportance1.png\" alt=\"\" width=\"170\" height=\"255\" srcset=\"\" sizes=\"auto, \"><\/span><\/p>\n<p> <span style=\"color: #000000;\">Binlerce <a href=\"https:\/\/statorials.org\/tr\/islenmemis-veri\/\" target=\"_blank\" rel=\"noopener\">sat\u0131rl\u0131k ham veriye<\/a> bakmak yerine, o \u015fehirdeki evlerin ortalama sat\u0131\u015f fiyat\u0131n\u0131 h\u0131zl\u0131 bir \u015fekilde anlamak i\u00e7in ortalama de\u011feri hesaplayabiliriz.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-24710 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/importance-moyenne1.jpg\" alt=\"\" width=\"477\" height=\"278\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ortalama sat\u0131\u015f fiyat\u0131n\u0131n 297.000 dolar oldu\u011funu bilmek bize bu \u015fehirde \u201ctipik\u201d bir evin ne kadara sat\u0131ld\u0131\u011f\u0131 konusunda fikir veriyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ortalaman\u0131n bu tek de\u011ferini yorumlamak, t\u00fcm ham veri sat\u0131rlar\u0131na bakmaktan \u00e7ok daha kolayd\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ortalamay\u0131 hesaplamak i\u00e7in her ev sat\u0131\u015f fiyat\u0131 kullan\u0131ld\u0131\u011f\u0131ndan, o \u015fehirdeki t\u00fcm evlerin toplam sat\u0131\u015f fiyat\u0131n\u0131 bulmak i\u00e7in ortalama sat\u0131\u015f fiyat\u0131n\u0131 toplam ev say\u0131s\u0131yla \u00e7arpabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">T\u00fcm evlerin toplam sat\u0131\u015f fiyat\u0131 = Ortalama sat\u0131\u015f fiyat\u0131 * Ev say\u0131s\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">T\u00fcm evlerin toplam sat\u0131\u015f fiyat\u0131 = 297.000 $ * 10.000<\/span><\/li>\n<li> <span style=\"color: #000000;\">T\u00fcm evlerin toplam sat\u0131\u015f fiyat\u0131 = 2.970.000.000$<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu \u015fehirdeki t\u00fcm evlerin toplam sat\u0131\u015f fiyat\u0131n\u0131n 2,97 milyar dolar oldu\u011funu g\u00f6r\u00fcyoruz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ortalama ne zaman kullan\u0131l\u0131r?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Veri setlerini analiz ederken genellikle merkezi de\u011ferin nerede oldu\u011funu anlamak isteriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0130statistikte bir veri k\u00fcmesinin merkezini \u00f6l\u00e7mek i\u00e7in kulland\u0131\u011f\u0131m\u0131z iki ortak \u00f6l\u00e7\u00fcm vard\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Ortalama<\/strong> : Bir veri k\u00fcmesindeki ortalama de\u011fer<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Medyan<\/strong> : Bir veri k\u00fcmesindeki medyan de\u011feri<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ortalama, bir veri k\u00fcmesinin merkezini \u00f6l\u00e7menin en yayg\u0131n yoludur, ancak asl\u0131nda a\u015fa\u011f\u0131daki durumlarda yan\u0131lt\u0131c\u0131 olabilir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Da\u011f\u0131t\u0131m <a href=\"https:\/\/statorials.org\/tr\/sol-onyargi-ve-sag-onyargi\/\" target=\"_blank\" rel=\"noopener\">asimetrik<\/a> oldu\u011funda.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Da\u011f\u0131t\u0131m <a href=\"https:\/\/statorials.org\/tr\/aykiri-degerler-ortalamayi-nasil-etkiler\/\" target=\"_blank\" rel=\"noopener\">ayk\u0131r\u0131 de\u011ferler<\/a> i\u00e7erdi\u011finde.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bunu a\u00e7\u0131klamak i\u00e7in a\u015fa\u011f\u0131daki iki \u00f6rne\u011fi inceleyin.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: \u00c7arp\u0131k bir da\u011f\u0131l\u0131m\u0131n ortalamas\u0131n\u0131 hesaplamak<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Belirli bir \u015fehrin sakinleri i\u00e7in a\u015fa\u011f\u0131daki maa\u015f da\u011f\u0131l\u0131m\u0131n\u0131 d\u00fc\u015f\u00fcn\u00fcn:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-4778 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/mediane_diste.jpg\" alt=\"\" width=\"473\" height=\"439\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Da\u011f\u0131l\u0131m\u0131n sa\u011f taraf\u0131ndaki y\u00fcksek \u00fccretler, ortalamay\u0131 da\u011f\u0131l\u0131m\u0131n merkezinden uzakla\u015ft\u0131r\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu nedenle, da\u011f\u0131l\u0131m sa\u011fa \u00e7arp\u0131k oldu\u011fundan medyan, bir sakinin \u201ctipik\u201d maa\u015f\u0131n\u0131 ortalamadan daha iyi yans\u0131t\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6zel \u00f6rnekte ortalama maa\u015f 47.000 Dolar, ortalama maa\u015f ise 32.000 Dolard\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Dolay\u0131s\u0131yla medyan o \u015fehirdeki tipik maa\u015f\u0131 \u00e7ok daha iyi temsil ediyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Ayk\u0131r\u0131 de\u011ferlerin varl\u0131\u011f\u0131nda ortalaman\u0131n hesaplanmas\u0131<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Belirli bir caddedeki evlerin metrekaresini g\u00f6steren a\u015fa\u011f\u0131daki grafi\u011fi d\u00fc\u015f\u00fcn\u00fcn:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-4779\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyenne_dist3.jpg\" alt=\"Ortalama ve medyan ne zaman kullan\u0131lmal\u0131?\" width=\"434\" height=\"378\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ortalama, birka\u00e7 a\u015f\u0131r\u0131 b\u00fcy\u00fck evden b\u00fcy\u00fck \u00f6l\u00e7\u00fcde etkilenirken, medyan etkilenmemektedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ortancan\u0131n o sokaktaki bir evin &#8220;tipik&#8221; metrekaresini ortalamadan daha iyi yakalad\u0131\u011f\u0131n\u0131 g\u00f6rebiliriz \u00e7\u00fcnk\u00fc ayk\u0131r\u0131 de\u011ferlerden etkilenmez.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6zet<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0130\u015fte bu makaleden \u00e7\u0131kan ana \u00e7\u0131kar\u0131mlar\u0131n k\u0131sa bir \u00f6zeti:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Ortalama, bir veri k\u00fcmesindeki ortalama de\u011feri temsil eder.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama \u00f6nemlidir \u00e7\u00fcnk\u00fc bize bir veri setinde merkezi de\u011ferin nerede oldu\u011funa dair bir fikir verir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama ayn\u0131 zamanda \u00f6nemlidir \u00e7\u00fcnk\u00fc bir veri setindeki <em>her<\/em> g\u00f6zlemden elde edilen bilgileri i\u00e7erir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bir veri seti \u00e7arp\u0131k oldu\u011funda veya ayk\u0131r\u0131 de\u011ferler i\u00e7erdi\u011finde ortalama yan\u0131lt\u0131c\u0131 olabilir. Bu senaryolarda medyan, bir veri k\u00fcmesinin &#8220;merkezinin&#8221; nerede oldu\u011funa dair daha kesin bir fikir verir.<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler di\u011fer tan\u0131mlay\u0131c\u0131 istatistikler hakk\u0131nda ek bilgi sa\u011flar:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/medyanin-onemi\/\" target=\"_blank\" rel=\"noopener\">Medyan istatistikte neden \u00f6nemlidir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/standart-sapma-neden-onemlidir\/\" target=\"_blank\" rel=\"noopener\">\u0130statistikte standart sapma neden \u00f6nemlidir?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/ortalama-ve-medyan-ne-zaman-kullanilir\/\" target=\"_blank\" rel=\"noopener\">Ortalama ve medyan ne zaman kullan\u0131lmal\u0131?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bir veri k\u00fcmesinin ortalamas\u0131 , veri k\u00fcmesinin ortalama de\u011ferini temsil eder. A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r: Ortalama = \u03a3x i \/ n Alt\u0131n: \u03a3: \u201ctoplam\u201d anlam\u0131na gelen bir sembol x i : Bir veri setindeki i&#8217;inci g\u00f6zlem n: veri k\u00fcmesindeki toplam g\u00f6zlem say\u0131s\u0131 \u00d6rne\u011fin, 11 g\u00f6zlem i\u00e7eren a\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m: Veri k\u00fcmesi: 3, 4, [&hellip;]<\/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-2814","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0130statistiklerde ortalama neden \u00f6nemlidir? - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde istatistikte ortalaman\u0131n \u00f6nemi bir tan\u0131m ve birka\u00e7 \u00f6rnekle a\u00e7\u0131klanmaktad\u0131r.\" \/>\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\/ortalamanin-onemi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0130statistiklerde ortalama neden \u00f6nemlidir? 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