{"id":200,"date":"2023-08-04T07:13:36","date_gmt":"2023-08-04T07:13:36","guid":{"rendered":"https:\/\/statorials.org\/tr\/sinif-araligi\/"},"modified":"2023-08-04T07:13:36","modified_gmt":"2023-08-04T07:13:36","slug":"sinif-araligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/sinif-araligi\/","title":{"rendered":"S\u0131n\u0131f aral\u0131\u011f\u0131"},"content":{"rendered":"

Bu yaz\u0131m\u0131zda istatistikte s\u0131n\u0131f aral\u0131klar\u0131n\u0131n ne oldu\u011funu, \u00f6zelliklerinin neler oldu\u011funu ve s\u0131n\u0131f aral\u0131klar\u0131n\u0131n \u00f6rneklerini \u00f6\u011freneceksiniz. <\/p>\n

<\/span> Ders aral\u0131\u011f\u0131 nedir?<\/span><\/h2>\n

\u0130statistikte, bir s\u0131n\u0131f aral\u0131\u011f\u0131<\/strong> (veya basit\u00e7e s\u0131n\u0131f<\/strong> ), g\u00f6zlemlenen de\u011ferlerin bir gruplamas\u0131d\u0131r. Yani s\u0131n\u0131f aral\u0131klar\u0131 bir \u00f6rneklemdeki verilerin b\u00f6l\u00fcnd\u00fc\u011f\u00fc gruplard\u0131r.<\/p>\n

\u00d6rne\u011fin, s\u0131n\u0131f aral\u0131\u011f\u0131 [50,55), 50 (dahil) ile 55 (dahil de\u011fil) aras\u0131ndaki t\u00fcm de\u011ferleri i\u00e7erir.<\/p>\n

S\u0131n\u0131f aral\u0131klar\u0131 \u00e7ok say\u0131da de\u011fere sahip bir \u00f6rne\u011fi incelemek i\u00e7in kullan\u0131l\u0131r. \u00dczerinde \u00e7al\u0131\u015f\u0131lacak veriler b\u00fcy\u00fckse, analizi kolayla\u015ft\u0131rmak i\u00e7in genellikle farkl\u0131 s\u0131n\u0131f aral\u0131klar\u0131nda grupland\u0131r\u0131l\u0131r. Bu genellikle s\u00fcrekli de\u011fi\u015fkenlerde olur.<\/p>\n

Bir veri \u00f6rne\u011finin b\u00f6l\u00fcnmesi gereken s\u0131n\u0131f aral\u0131\u011f\u0131 say\u0131s\u0131n\u0131 hesaplamak i\u00e7in \u00e7e\u015fitli y\u00f6ntemler vard\u0131r, ancak bunlar\u0131n aras\u0131nda Sturges kural\u0131<\/a> \u00f6ne \u00e7\u0131kmaktad\u0131r. <\/p>\n

<\/span> S\u0131n\u0131f aral\u0131\u011f\u0131n\u0131n \u00f6zellikleri<\/span><\/h2>\n

Bir s\u0131n\u0131f aral\u0131\u011f\u0131n\u0131n par\u00e7alar\u0131<\/strong> \u015funlard\u0131r: s\u0131n\u0131f s\u0131n\u0131rlar\u0131, s\u0131n\u0131f geni\u015fli\u011fi ve s\u0131n\u0131f i\u015fareti. Bu par\u00e7alar\u0131n her birinin bile\u015fimi a\u015fa\u011f\u0131da a\u00e7\u0131klanmaktad\u0131r. <\/p>\n

<\/span> Ders Aral\u0131\u011f\u0131 Limitleri<\/span><\/h3>\n

S\u0131n\u0131f aral\u0131\u011f\u0131n\u0131n s\u0131n\u0131rlar\u0131<\/strong> , grubu s\u0131n\u0131rlayan de\u011ferler yani s\u0131n\u0131f aral\u0131\u011f\u0131n\u0131 olu\u015fturan minimum de\u011fer ve maksimum de\u011ferdir. Bu nedenle her s\u0131n\u0131f aral\u0131\u011f\u0131n\u0131n bir \u00fcst s\u0131n\u0131r\u0131 ve bir alt s\u0131n\u0131r\u0131 vard\u0131r.<\/p>\n

\u00d6rne\u011fin [70,80] s\u0131n\u0131f aral\u0131\u011f\u0131 i\u00e7in alt s\u0131n\u0131r 70 (dahil) ve \u00fcst s\u0131n\u0131r 80’dir (dahil de\u011fil). <\/p>\n

<\/span> S\u0131n\u0131f aral\u0131\u011f\u0131 geni\u015fli\u011fi<\/span><\/h3>\n

S\u0131n\u0131f aral\u0131\u011f\u0131n\u0131n geni\u015fli\u011fi,<\/strong> s\u0131n\u0131f\u0131n \u00fcst s\u0131n\u0131r\u0131 ile alt s\u0131n\u0131r\u0131 aras\u0131ndaki farkt\u0131r. B\u00f6ylece bir s\u0131n\u0131f aral\u0131\u011f\u0131n\u0131n geni\u015fli\u011fi, \u00fcst s\u0131n\u0131rdan alt s\u0131n\u0131r \u00e7\u0131kar\u0131larak hesaplan\u0131r.<\/p>\n

\u00d6rne\u011fin, s\u0131n\u0131f aral\u0131\u011f\u0131n\u0131n geni\u015fli\u011fi [70,80), iki s\u0131n\u0131f s\u0131n\u0131r\u0131 aras\u0131ndaki fark oldu\u011fundan 10’a e\u015fittir: <\/p>\n<\/p>\n

\"[70,80)\\quad\\longrightarrow\\<\/p>\n<\/p>\n

<\/span> S\u0131n\u0131f aral\u0131\u011f\u0131 i\u015fareti<\/span><\/h3>\n

S\u0131n\u0131f aral\u0131\u011f\u0131 i\u015fareti<\/strong> , s\u0131n\u0131f aral\u0131\u011f\u0131n\u0131n orta noktas\u0131d\u0131r. Bu nedenle, bir aral\u0131\u011f\u0131n s\u0131n\u0131f puan\u0131n\u0131 elde etmek i\u00e7in aral\u0131\u011f\u0131n iki limitini toplay\u0131p ikiye b\u00f6lmeniz gerekir.<\/p>\n

\u00d6rne\u011fin s\u0131n\u0131f aral\u0131\u011f\u0131n\u0131n i\u015fareti [70,80) 75’tir, \u00e7\u00fcnk\u00fc bu iki s\u0131n\u0131f limiti aras\u0131nda ba\u011flant\u0131 kuran noktad\u0131r.<\/p>\n<\/p>\n

\"[70,80)\\quad\\longrightarrow\\<\/p>\n<\/p>\n

S\u0131n\u0131f i\u015fareti genellikle Ci<\/sub> veya Xi<\/sub> sembol\u00fcyle temsil edilir. <\/p>\n

<\/span>S\u0131n\u0131f Aral\u0131\u011f\u0131 \u00d6rne\u011fi<\/span><\/h2>\n

S\u0131n\u0131f aral\u0131\u011f\u0131n\u0131n tan\u0131m\u0131n\u0131n ne oldu\u011funu g\u00f6rd\u00fckten sonra, kavram\u0131 daha iyi anlayabilmeniz i\u00e7in, t\u00fcm farkl\u0131 b\u00f6l\u00fcmlerinin hesaplanmas\u0131yla ilgili bir \u00f6rnek sunuyoruz. <\/p>\n<\/p>\n

\"[30,40)\"<\/p>\n<\/p>\n

\"\\begin{array}{l}\\text{L\\'imite<\/p>\n<\/p>\n

\"\\text{Amplitud}=40-30=10\"<\/p>\n<\/p>\n

\"[30,40)\\quad\\longrightarrow\\<\/p>\n<\/p>\n

<\/span> S\u0131n\u0131f aral\u0131klar\u0131 ve frekans tablolar\u0131<\/span><\/h2>\n

Tipik olarak veriler s\u0131n\u0131f aral\u0131klar\u0131na g\u00f6re grupland\u0131r\u0131ld\u0131\u011f\u0131nda her s\u0131n\u0131f\u0131n frekanslar\u0131 bulunur ve sonu\u00e7lar bir frekans tablosuna yerle\u015ftirilir.<\/p>\n

Yani frekans tablosu, de\u011ferlerin s\u0131raland\u0131\u011f\u0131 ve de\u011ferlerin her biri i\u00e7in t\u00fcm frekans t\u00fcrlerinin listelendi\u011fi bir tablodur. Yani her sat\u0131r bir de\u011fere (veya s\u0131n\u0131f aral\u0131\u011f\u0131na) kar\u015f\u0131l\u0131k gelir ve her s\u00fctun farkl\u0131 bir frekans tipidir.<\/p>\n

Verilerin s\u0131n\u0131f aral\u0131klar\u0131na g\u00f6re grupland\u0131r\u0131ld\u0131\u011f\u0131 \u00f6rnek bir s\u0131kl\u0131k tablosunu burada g\u00f6rebilirsiniz: <\/p>\n

\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Grupland\u0131r\u0131lm\u0131\u015f veriler i\u00e7in frekans tablosu \u00f6rne\u011fi<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"

Bu yaz\u0131m\u0131zda istatistikte s\u0131n\u0131f aral\u0131klar\u0131n\u0131n ne oldu\u011funu, \u00f6zelliklerinin neler oldu\u011funu ve s\u0131n\u0131f aral\u0131klar\u0131n\u0131n \u00f6rneklerini \u00f6\u011freneceksiniz. Ders aral\u0131\u011f\u0131 nedir? \u0130statistikte, bir s\u0131n\u0131f aral\u0131\u011f\u0131 (veya basit\u00e7e s\u0131n\u0131f ), g\u00f6zlemlenen de\u011ferlerin bir gruplamas\u0131d\u0131r. Yani s\u0131n\u0131f aral\u0131klar\u0131 bir \u00f6rneklemdeki verilerin b\u00f6l\u00fcnd\u00fc\u011f\u00fc gruplard\u0131r. \u00d6rne\u011fin, s\u0131n\u0131f aral\u0131\u011f\u0131 [50,55), 50 (dahil) ile 55 (dahil de\u011fil) aras\u0131ndaki t\u00fcm de\u011ferleri i\u00e7erir. S\u0131n\u0131f aral\u0131klar\u0131 \u00e7ok […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-200","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"\n\u25b7 Ders aral\u0131\u011f\u0131 nedir? 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