{"id":138,"date":"2023-08-05T01:51:31","date_gmt":"2023-08-05T01:51:31","guid":{"rendered":"https:\/\/statorials.org\/tr\/simetrik-dagilim-1\/"},"modified":"2023-08-05T01:51:31","modified_gmt":"2023-08-05T01:51:31","slug":"simetrik-dagilim-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/simetrik-dagilim-1\/","title":{"rendered":"Simetrik da\u011f\u0131l\u0131m"},"content":{"rendered":"

Bu makalede simetrik da\u011f\u0131l\u0131mlar\u0131n ne oldu\u011funu, simetrik da\u011f\u0131l\u0131m \u00f6rneklerini ve bir da\u011f\u0131l\u0131m\u0131n simetrik mi yoksa asimetrik mi oldu\u011funu nas\u0131l belirleyece\u011finizi \u00f6\u011freneceksiniz. <\/p>\n

<\/span> Simetrik da\u011f\u0131l\u0131m nedir?<\/span><\/h2>\n

\u0130statistikte simetrik da\u011f\u0131l\u0131m<\/strong> , ortalaman\u0131n solunda ve sa\u011f\u0131nda ayn\u0131 say\u0131da de\u011fere sahip olan da\u011f\u0131l\u0131md\u0131r. Ba\u015fka bir deyi\u015fle simetrik bir da\u011f\u0131l\u0131mda ortalama bir simetri eksenidir.<\/p>\n

\u00d6rne\u011fin normal da\u011f\u0131l\u0131m simetrik bir da\u011f\u0131l\u0131md\u0131r.<\/p>\n

T\u00fcm simetrik da\u011f\u0131l\u0131mlarda ortalama medyana e\u015fittir. Ancak da\u011f\u0131l\u0131m ayn\u0131 zamanda tek modlu ise (istatistiksel mod tek bir de\u011ferdir), ortalama, medyan ve mod e\u015fde\u011ferdir.<\/p>\n

Mant\u0131ksal olarak simetrik da\u011f\u0131l\u0131m\u0131n ne oldu\u011funu tam olarak anlamak i\u00e7in ortalama, medyan ve modun ne oldu\u011fu konusunda net olman\u0131z gerekir. Bu istatistiksel kavramlar\u0131n anlam\u0131n\u0131 burada inceleyebilirsiniz: <\/p>\n

\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Ortalama, medyan ve mod nedir?<\/a> <\/div>\n

<\/span> Simetrik da\u011f\u0131l\u0131m \u00f6rnekleri<\/span><\/h2>\n

Simetrik da\u011f\u0131l\u0131m\u0131n tan\u0131m\u0131 dikkate al\u0131nd\u0131\u011f\u0131nda bu t\u00fcr da\u011f\u0131l\u0131ma bir \u00f6rnek a\u015fa\u011f\u0131da g\u00f6sterilmi\u015ftir: <\/p>\n

\"simetrik<\/figure>\n

Grafi\u011fin g\u00f6sterdi\u011fi gibi da\u011f\u0131l\u0131m simetriktir \u00e7\u00fcnk\u00fc ortalama t\u00fcm verilerin tam ortas\u0131nda yer al\u0131r, yani e\u011frinin solundaki kuyruk sa\u011fdaki kuyrukla ayn\u0131d\u0131r. Bu durumda mod tek modlu oldu\u011fundan ortalama, medyan ve mod ayn\u0131d\u0131r.<\/p>\n

\u0130ki farkl\u0131 t\u00fcrdeki simetrik olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n iki a\u00e7\u0131k \u00f6rne\u011fi normal da\u011f\u0131l\u0131m ve tekd\u00fcze da\u011f\u0131l\u0131md\u0131r \u00e7\u00fcnk\u00fc ortalaman\u0131n solunda ve sa\u011f\u0131nda ayn\u0131 say\u0131da de\u011fere sahiptirler.<\/p>\n

\u00d6te yandan bir da\u011f\u0131l\u0131m simetrik ve iki modlu da olabilir, yani iki modlu olabilir. A\u015fa\u011f\u0131daki \u00f6rne\u011fe bak\u0131n: <\/p>\n

\"\u00e7ift<\/figure>\n

Bu di\u011fer \u00f6rnekte g\u00f6rebilece\u011finiz gibi, iki modlu bir da\u011f\u0131l\u0131m simetrik de olabilir, \u00e7\u00fcnk\u00fc di\u011fer de\u011ferlerden ba\u011f\u0131ms\u0131z olarak ortalama ve medyan merkezde olabilir. Ancak bu durumda modun mutlaka ortalamaya ve moda e\u015fit olmas\u0131 gerekmez. <\/p>\n

<\/span> Simetrilerine g\u00f6re di\u011fer da\u011f\u0131l\u0131m t\u00fcrleri<\/span><\/h2>\n

Simetrik da\u011f\u0131l\u0131mlar\u0131n yan\u0131 s\u0131ra iki t\u00fcr asimetrik da\u011f\u0131l\u0131m daha vard\u0131r.<\/p>\n

    \n
  • Simetrik da\u011f\u0131l\u0131m<\/strong> : Da\u011f\u0131l\u0131m, ortalaman\u0131n solunda ve sa\u011f\u0131nda ayn\u0131 say\u0131da de\u011fere sahiptir.<\/li>\n
  • Pozitif \u00e7arp\u0131k da\u011f\u0131l\u0131m<\/strong> : Da\u011f\u0131l\u0131m\u0131n ortalaman\u0131n sa\u011f\u0131nda soluna g\u00f6re daha farkl\u0131 de\u011ferleri vard\u0131r.<\/li>\n
  • Negatif \u00e7arp\u0131k da\u011f\u0131l\u0131m<\/strong> : Da\u011f\u0131l\u0131m\u0131n ortalaman\u0131n solunda sa\u011f\u0131na g\u00f6re daha farkl\u0131 de\u011ferleri vard\u0131r. <\/li>\n<\/ul>\n
    \"asimetri<\/figure>\n

    <\/span> Bir da\u011f\u0131l\u0131m\u0131n simetrik olup olmad\u0131\u011f\u0131 nas\u0131l anla\u015f\u0131l\u0131r?<\/span><\/h2>\n

    Bir da\u011f\u0131l\u0131m\u0131n simetrik olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Pearson asimetri katsay\u0131s\u0131n\u0131 hesaplamam\u0131z gerekir; bunun form\u00fcl\u00fc \u015fu \u015fekildedir:<\/p>\n<\/p>\n

    \"A_p=\\cfrac{\\mu-Mo}{\\sigma}\"<\/p>\n<\/p>\n

    Alt\u0131n<\/p>\n<\/p>\n

    \"A_p\"<\/p>\n

    Pearson katsay\u0131s\u0131d\u0131r,<\/p>\n

    \"\\mu\"<\/p>\n

    aritmetik ortalama,<\/p>\n

    \"Mo\"<\/p>\n

    mod (istatistikler) ve<\/p>\n

    \"\\sigma\"<\/p>\n

    Standart sapma.<\/p>\n

    Dolay\u0131s\u0131yla Pearson asimetri katsay\u0131s\u0131n\u0131n i\u015faretine ba\u011fl\u0131 olarak da\u011f\u0131l\u0131m simetrik veya asimetrik olacakt\u0131r:<\/p>\n

      \n
    • Pearson \u00e7arp\u0131kl\u0131k katsay\u0131s\u0131n\u0131n pozitif olmas\u0131 da\u011f\u0131l\u0131m\u0131n pozitif \u00e7arp\u0131k oldu\u011fu anlam\u0131na gelir.<\/li>\n
    • Pearson \u00e7arp\u0131kl\u0131k katsay\u0131s\u0131n\u0131n negatif olmas\u0131 da\u011f\u0131l\u0131m\u0131n negatif \u00e7arp\u0131k oldu\u011fu anlam\u0131na gelir.<\/li>\n
    • Pearson \u00e7arp\u0131kl\u0131k katsay\u0131s\u0131n\u0131n s\u0131f\u0131r olmas\u0131 da\u011f\u0131l\u0131m\u0131n simetrik oldu\u011fu anlam\u0131na gelir.<\/li>\n<\/ul>\n

      Ancak Pearson katsay\u0131s\u0131 ancak da\u011f\u0131l\u0131m\u0131n tek modlu olmas\u0131 durumunda hesaplanabilir, aksi takdirde form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibi olan Fisher asimetri katsay\u0131s\u0131n\u0131n kullan\u0131lmas\u0131 gerekir:<\/p>\n<\/p>\n

      \"\\displaystyle\\gamma_1=\\frac{\\displaystyle<\/p>\n<\/p>\n

      Alt\u0131n<\/p>\n<\/p>\n

      \"\\mu\"<\/p>\n

      aritmetik ortalama,<\/p>\n

      \"\\sigma\"<\/p>\n

      standart sapma ve<\/p>\n

      \"N\"<\/p>\n

      toplam veri say\u0131s\u0131.<\/p>\n

      Fisher asimetri katsay\u0131s\u0131n\u0131n yorumu Pearson katsay\u0131s\u0131yla ayn\u0131d\u0131r: Pozitifse da\u011f\u0131l\u0131m\u0131n pozitif asimetrik oldu\u011fu, negatifse da\u011f\u0131l\u0131m\u0131n negatif asimetrik oldu\u011fu ve s\u0131f\u0131rsa da\u011f\u0131l\u0131m\u0131n simetrik oldu\u011fu anlam\u0131na gelir.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Bu makalede simetrik da\u011f\u0131l\u0131mlar\u0131n ne oldu\u011funu, simetrik da\u011f\u0131l\u0131m \u00f6rneklerini ve bir da\u011f\u0131l\u0131m\u0131n simetrik mi yoksa asimetrik mi oldu\u011funu nas\u0131l belirleyece\u011finizi \u00f6\u011freneceksiniz. Simetrik da\u011f\u0131l\u0131m nedir? \u0130statistikte simetrik da\u011f\u0131l\u0131m , ortalaman\u0131n solunda ve sa\u011f\u0131nda ayn\u0131 say\u0131da de\u011fere sahip olan da\u011f\u0131l\u0131md\u0131r. Ba\u015fka bir deyi\u015fle simetrik bir da\u011f\u0131l\u0131mda ortalama bir simetri eksenidir. \u00d6rne\u011fin normal da\u011f\u0131l\u0131m simetrik bir da\u011f\u0131l\u0131md\u0131r. T\u00fcm […]<\/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-138","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"\n\u25b7 Simetrik da\u011f\u0131l\u0131m nedir? 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