{"id":22,"date":"2011-10-10T12:40:04","date_gmt":"2011-10-10T10:40:04","guid":{"rendered":"http:\/\/blog.metu.edu.tr\/erdinc\/?p=22"},"modified":"2016-05-28T17:53:33","modified_gmt":"2016-05-28T17:53:33","slug":"histogram","status":"publish","type":"post","link":"https:\/\/blog.metu.edu.tr\/erdinc\/2011\/10\/10\/histogram\/","title":{"rendered":"Histogram"},"content":{"rendered":"

Matematik \u00f6\u011fretim program\u0131nda 8. s\u0131n\u0131fta yer alan histogram konusunda baz\u0131 kafa kar\u0131\u015f\u0131kl\u0131klar\u0131 bulunmaktad\u0131r. \u00d6zellikle histogram\u0131n nas\u0131l olu\u015fturulaca\u011f\u0131 hakk\u0131nda farkl\u0131 kaynaklarda \u00e7eli\u015fkili bilgiler bulunmaktad\u0131r. Histogramla ilgili en s\u0131k kar\u015f\u0131la\u015ft\u0131\u011f\u0131m\u0131z soru ise grup geni\u015fli\u011finin belirlenmesi ile ilgilidir. Bu yaz\u0131da bu konuya a\u00e7\u0131kl\u0131k getirmek istiyorum.<\/p>\n

Histogramlar \u00f6zetlenmi\u015f veri s\u0131kl\u0131\u011f\u0131 (frekans\u0131) bilgisinin s\u00fctunlarla temsil edildi\u011fi grafiklerdir. Histogramlar bir veri k\u00fcmesinin da\u011f\u0131l\u0131m\u0131n\u0131 \u00f6zetlemek amac\u0131yla kullan\u0131l\u0131r. A\u015fa\u011f\u0131da belirli bir veri k\u00fcmesi i\u00e7in olu\u015fturulmu\u015f s\u0131kl\u0131k tablosu ve histogram g\u00f6r\u00fcnmektedir.<\/p>\n

\u00d6rnek: <\/strong><\/em><\/p>\n

Bir ba\u011fdaki 29 adet ceviz a\u011fac\u0131n\u0131n y\u00fckseklikleri \u015f\u00f6yledir;<\/p>\n

28, 13, 19, 15, 14, 21, 17, 21, 16, 18, 20, 20, 19, 19, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 24, 26, 25, 27, 28<\/em><\/p>\n


\n<\/em><\/p>\n

\n\n\n\n\n\n\n\n\n\n
Y\u00fckseklik aral\u0131\u011f\u0131<\/strong><\/td>\n\n

A\u011fa\u00e7 say\u0131s\u0131 (s\u0131kl\u0131k)<\/strong><\/p>\n<\/td>\n<\/tr>\n

13-15<\/td>\n3<\/td>\n<\/tr>\n
\n

16-18<\/p>\n<\/td>\n

3<\/td>\n<\/tr>\n
\n

19-21<\/p>\n<\/td>\n

\n

8<\/p>\n<\/td>\n<\/tr>\n

\n

22-24<\/p>\n<\/td>\n

\n

10<\/p>\n<\/td>\n<\/tr>\n

\n

25-27<\/p>\n<\/td>\n

\n

3<\/p>\n<\/td>\n<\/tr>\n

\n

28-30<\/p>\n<\/td>\n

\n

2<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

\"image001\"<\/p>\n

Histogramla ilgili Kafalar Neden Kar\u0131\u015f\u0131k? <\/strong><\/p>\n

Matematik \u00f6\u011fretim program\u0131nda 8. S\u0131n\u0131f d\u00fczeyinde i\u015flenen bu konu hakk\u0131nda farkl\u0131 kaynaklarda birbiri ile \u00e7eli\u015fen bilgiler g\u00f6ze \u00e7arpmaktad\u0131r.<\/p>\n

\u00d6zellikle grup geni\u015fli\u011finin belirlenmesi konusu bazen tam bir kar\u0131\u015f\u0131kl\u0131\u011fa d\u00f6n\u00fc\u015fmektedir.<\/p>\n

Bu kar\u0131\u015f\u0131kl\u0131\u011f\u0131n kayna\u011f\u0131nda \u00f6\u011fretim programlar\u0131n\u0131n ilk s\u00fcr\u00fcm\u00fcnde grup geni\u015fli\u011finin \u201ctek say\u0131\u201d olarak belirlenmesinin \u201ctavsiye\u201d edilmesi bulunmaktad\u0131r. Bu tavsiyeyi pek \u00e7ok ikincil kaynak bir kural olarak alg\u0131lam\u0131\u015f ve buna g\u00f6re sorular haz\u0131rlam\u0131\u015ft\u0131r.<\/p>\n

Oysa grup geni\u015fli\u011finin tek say\u0131 al\u0131nmas\u0131 sadece belirli durumlarda i\u015fe yarayabilen bir uygulamad\u0131r, \u00e7ift say\u0131 da al\u0131nabilir.<\/p>\n

Bakanl\u0131k bu durumu program kitab\u0131nda d\u00fczeltti. Fakat hem bu d\u00fczeltmenin yeterince bilinmemesinden, hem de gere\u011finden fazla kar\u0131\u015f\u0131k yaz\u0131lmas\u0131ndan dolay\u0131 kafalar hala kar\u0131\u015f\u0131k.<\/p>\n

A\u015fa\u011f\u0131da bu konuda k\u0131sa bir a\u00e7\u0131klama bulunmaktad\u0131r.<\/p>\n

Histogramda Grup Geni\u015fli\u011finin Belirlenmesi<\/strong><\/p>\n

Histogram olu\u015fturulurken a\u00e7\u0131kl\u0131\u011f\u0131n hesap yap\u0131larak “bulunmas\u0131<\/em>“, grup say\u0131s\u0131 ve grup geni\u015fli\u011finin takdir edilerek “belirlenmesi<\/em>” gerekmektedir.<\/p>\n

A\u00e7\u0131kl\u0131k (a)<\/em>:<\/strong> Veri k\u00fcmesindeki en b\u00fcy\u00fck de\u011fer ile en k\u00fc\u00e7\u00fck de\u011fer aras\u0131ndaki fark.<\/p>\n

Grup say\u0131s\u0131 (s<\/em>):<\/strong> Grafikteki s\u00fctun say\u0131s\u0131d\u0131r. Her s\u00fctun bir gruba ait s\u0131kl\u0131\u011f\u0131 temsil eder. Grup say\u0131s\u0131, karar verilerek elde edilen bir de\u011ferdir. Da\u011f\u0131l\u0131m\u0131 yeterince iyi yans\u0131tabilecek bir se\u00e7im yap\u0131l\u0131r.<\/p>\n

Grup geni\u015fli\u011fi (g<\/em>):<\/strong> Her bir veri grubunun geni\u015fli\u011fidir. Belirtilen aral\u0131kta ka\u00e7 tane de\u011fer oldu\u011fu s\u00fctunda \u00f6zetlenmektedir. Grup geni\u015fli\u011fi a\u00e7\u0131kl\u0131k ve grup say\u0131s\u0131 dikkate al\u0131narak belirlenen bir de\u011ferdir. Grup geni\u015fli\u011fi belirlenirken a\u015fa\u011f\u0131daki e\u015fitsizlik dikkate al\u0131narak g<\/em> i\u00e7in en k\u00fc\u00e7\u00fck do\u011fal say\u0131 de\u011feri se\u00e7ilir. B\u00f6l\u00fcm bir do\u011fal say\u0131 oldu\u011funda da, yine e\u015fitsizlik gere\u011fi (hi\u00e7 bir verinin grafi\u011fin kapsama alan\u0131 d\u0131\u015f\u0131nda kalmamas\u0131 i\u00e7in) bir \u00fcst do\u011fal say\u0131 grup geni\u015fli\u011fi olarak al\u0131n\u0131r.<\/p>\n

\"\"<\/a><\/p>\n

(Not: Baz\u0131 \u00f6zel histogram \u00e7izimlerinde her grubun ortas\u0131nda bir do\u011fal say\u0131 de\u011feri belirleyebilmek i\u00e7in g\u2019nin tek say\u0131 olmas\u0131 tercih edilir.)<\/em><\/p>\n

\u00d6rnek:<\/p>\n

A\u00e7\u0131kl\u0131k 52 olarak bulunup grup say\u0131s\u0131 10 olarak belirlendi\u011finde:<\/p>\n

\"image003\"<\/p>\n

Bu sonucu dikkate alarak grup geni\u015fli\u011fi 6 olarak belirlenebilir.<\/p>\n

\u00d6rnek bir uygulama i\u00e7in: <\/strong><\/p>\n

http:\/\/www.stat.sc.edu\/~west\/javahtml\/Histogram.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Matematik \u00f6\u011fretim program\u0131nda 8. s\u0131n\u0131fta yer alan histogram konusunda baz\u0131 kafa kar\u0131\u015f\u0131kl\u0131klar\u0131 bulunmaktad\u0131r. \u00d6zellikle histogram\u0131n nas\u0131l olu\u015fturulaca\u011f\u0131 hakk\u0131nda farkl\u0131 kaynaklarda \u00e7eli\u015fkili bilgiler bulunmaktad\u0131r. Histogramla ilgili en s\u0131k kar\u015f\u0131la\u015ft\u0131\u011f\u0131m\u0131z soru ise grup geni\u015fli\u011finin belirlenmesi ile ilgilidir. Bu yaz\u0131da bu konuya a\u00e7\u0131kl\u0131k getirmek istiyorum.<\/p>\n","protected":false},"author":559,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[8],"tags":[13,15,16,17],"class_list":["post-22","post","type-post","status-publish","format-standard","hentry","category-kavram-aciklamasi","tag-aciklik","tag-grup-genisligi","tag-grup-sayisi","tag-histogram"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/erdinc\/wp-json\/wp\/v2\/posts\/22","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/erdinc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/erdinc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/erdinc\/wp-json\/wp\/v2\/users\/559"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/erdinc\/wp-json\/wp\/v2\/comments?post=22"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/erdinc\/wp-json\/wp\/v2\/posts\/22\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/erdinc\/wp-json\/wp\/v2\/media?parent=22"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/erdinc\/wp-json\/wp\/v2\/categories?post=22"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/erdinc\/wp-json\/wp\/v2\/tags?post=22"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}