{"id":91,"date":"2023-08-05T14:09:49","date_gmt":"2023-08-05T14:09:49","guid":{"rendered":"https:\/\/statorials.org\/tr\/istatistiksel-mod\/"},"modified":"2023-08-05T14:09:49","modified_gmt":"2023-08-05T14:09:49","slug":"istatistiksel-mod","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/istatistiksel-mod\/","title":{"rendered":"Moda (istatistikler)"},"content":{"rendered":"

Bu makalede istatistiklerde hangi modun oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. Grupland\u0131r\u0131lm\u0131\u015f veriler ve gruplanmam\u0131\u015f veriler i\u00e7in istatistiksel modu nas\u0131l bulaca\u011f\u0131n\u0131z\u0131, farkl\u0131 mod t\u00fcrlerini ve bu istatistiksel \u00f6l\u00e7\u00fcm\u00fcn birka\u00e7 \u00f6rne\u011fini \u00f6\u011freneceksiniz. <\/p>\n

<\/span> \u0130statistiklerde mod nedir?<\/span><\/h2>\n

\u0130statistikte mod, veri k\u00fcmesindeki mutlak frekans\u0131 en y\u00fcksek olan de\u011ferdir, yani mod, bir veri k\u00fcmesinde en \u00e7ok tekrarlanan de\u011ferdir.<\/strong><\/p>\n

Bu nedenle, istatistiksel bir veri k\u00fcmesinin modunu hesaplamak i\u00e7in, her veri \u00f6\u011fesinin \u00f6rnekte ka\u00e7 kez g\u00f6r\u00fcnd\u00fc\u011f\u00fcn\u00fc sayman\u0131z yeterlidir; en \u00e7ok tekrarlanan veri, mod olacakt\u0131r.<\/p>\n

Mod, istatistiksel bir da\u011f\u0131l\u0131m\u0131 tan\u0131mlamak i\u00e7in kullan\u0131l\u0131r, \u00e7\u00fcnk\u00fc en \u00e7ok tekrarlanan de\u011fer genellikle da\u011f\u0131l\u0131m\u0131n merkezindedir.<\/p>\n

Modun istatistiksel mod<\/strong> veya modal de\u011fer<\/strong> oldu\u011fu da s\u00f6ylenebilir. Benzer \u015fekilde, veriler aral\u0131klar halinde grupland\u0131r\u0131ld\u0131\u011f\u0131nda en \u00e7ok tekrarlanan aral\u0131k, modal aral\u0131k<\/strong> veya modal s\u0131n\u0131ft\u0131r<\/strong> .<\/p>\n

Genel olarak Mo<\/em> terimi istatistiksel modun sembol\u00fc olarak kullan\u0131l\u0131r; \u00f6rne\u011fin X da\u011f\u0131t\u0131m modu Mo(X)’t\u00fcr.<\/p>\n

Modun, medyan ve ortalaman\u0131n yan\u0131 s\u0131ra merkez konumun da istatistiksel bir \u00f6l\u00e7\u00fcs\u00fc oldu\u011funu unutmay\u0131n. A\u015fa\u011f\u0131da bu istatistiksel \u00f6nlemlerin her birinin ne anlama geldi\u011fini g\u00f6rece\u011fiz. <\/p>\n

<\/span> \u0130statistiklerdeki mod t\u00fcrleri<\/span><\/h2>\n

\u0130statistiklerde, en \u00e7ok tekrarlanan de\u011ferlerin say\u0131s\u0131na g\u00f6re s\u0131n\u0131fland\u0131r\u0131lan \u00e7e\u015fitli mod t\u00fcrleri vard\u0131r:<\/p>\n

    \n
  • Tek modlu mod<\/strong> : Maksimum tekrar say\u0131s\u0131na sahip yaln\u0131zca bir de\u011fer vard\u0131r. \u00d6rne\u011fin, [1, 4, 2, 4, 5, 3].<\/span><\/li>\n
  • Bimodal mod<\/strong> : Maksimum tekrar say\u0131s\u0131 iki farkl\u0131 de\u011ferde ger\u00e7ekle\u015fir ve her iki de\u011fer de ayn\u0131 say\u0131da tekrarlan\u0131r. \u00d6rne\u011fin, [2, 6, 7, 2, 3, 6, 9].<\/span><\/li>\n
  • Multimodal mod<\/strong> : \u00dc\u00e7 veya daha fazla de\u011fer ayn\u0131 maksimum tekrar say\u0131s\u0131na sahiptir. \u00d6rne\u011fin, [3, 3, 4, 1, 3, 4, 2, 1, 4, 5, 2, 1].<\/span> <\/li>\n<\/ul>\n

    <\/span> \u0130statistiksel mod nas\u0131l bulunur?<\/span><\/h2>\n

    Bir veri k\u00fcmesinin istatistiksel modunu bulmak i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 izlemelisiniz:<\/p>\n

      \n
    1. Verileri s\u0131raya koyun. Bu ad\u0131m zorunlu de\u011fildir ancak say\u0131lar\u0131 saymay\u0131 kolayla\u015ft\u0131racakt\u0131r.<\/span><\/li>\n
    2. Her say\u0131n\u0131n ka\u00e7 kez g\u00f6r\u00fcnd\u00fc\u011f\u00fcn\u00fc say\u0131n.<\/span><\/li>\n
    3. En s\u0131k g\u00f6r\u00fcnen say\u0131 istatistiksel moddur.<\/span> <\/li>\n<\/ol>\n

      <\/span> \u0130statistiksel mod \u00f6rnekleri<\/span><\/h2>\n

      Modan\u0131n istatistiklerdeki tan\u0131m\u0131 g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, kavram\u0131 daha iyi anlayabilmeniz i\u00e7in a\u015fa\u011f\u0131da her moda t\u00fcr\u00fcn\u00fcn bir \u00f6rne\u011fini g\u00f6rebilirsiniz.<\/p>\n

      <\/span> Tek modlu mod \u00f6rne\u011fi<\/span><\/h3>\n
        \n
      • A\u015fa\u011f\u0131daki veri k\u00fcmesinin modu nedir?<\/li>\n<\/ul>\n

        \"5<\/p>\n<\/p>\n

        Rakamlar s\u0131ralanmam\u0131\u015ft\u0131r, bu nedenle modu bulmay\u0131 kolayla\u015ft\u0131rmak i\u00e7in \u00f6nce onlar\u0131 s\u0131ralayaca\u011f\u0131z.<\/p>\n<\/p>\n

        \"2<\/p>\n<\/p>\n

        2 ve 9 say\u0131lar\u0131 iki kez g\u00f6r\u00fcn\u00fcyor, ancak 5 say\u0131s\u0131 \u00fc\u00e7 kez tekrarlan\u0131yor. Bu nedenle veri serisinin modu 5 numarad\u0131r. <\/p>\n<\/p>\n

        \"Mo=5\"<\/p>\n<\/p>\n

        <\/span> \u0130ki modlu mod \u00f6rne\u011fi<\/span><\/h3>\n
          \n
        • A\u015fa\u011f\u0131daki veri setinin modunu hesaplay\u0131n:<\/li>\n<\/ul>\n

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

          \"0<\/p>\n<\/p>\n

          \u0130lk \u00f6nce say\u0131lar\u0131 s\u0131raya koyuyoruz:<\/p>\n<\/p>\n

          \"0<\/p>\n<\/p>\n

          \"7<\/p>\n<\/p>\n

          G\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi 6 say\u0131s\u0131 ve 8 say\u0131s\u0131 toplamda d\u00f6rt kez kar\u015f\u0131m\u0131za \u00e7\u0131k\u0131yor, bu da maksimum tekrar say\u0131s\u0131d\u0131r. Bu nedenle, bu durumda bu iki modlu bir moddur ve iki say\u0131, veri k\u00fcmesinin modudur: <\/p>\n<\/p>\n

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

          <\/span> \u00c7ok modlu mod \u00f6rne\u011fi<\/span><\/h3>\n
            \n
          • A\u015fa\u011f\u0131daki veri k\u00fcmesi modunu bulun:<\/li>\n<\/ul>\n

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

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

            \"31<\/p>\n<\/p>\n

            \u00c7ok fazla veri oldu\u011fundan, saymay\u0131 kolayla\u015ft\u0131rmak i\u00e7in \u00f6nce bunlar\u0131 artan d\u00fczende s\u0131ral\u0131yoruz: <\/p>\n<\/p>\n

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

            \"20<\/p>\n<\/p>\n

            \"27<\/p>\n<\/p>\n

            En \u00e7ok tekrarlanan say\u0131lar 20, 27 ve 31’dir, her \u00fc\u00e7 say\u0131 da be\u015fer kez tekrarlan\u0131r. Bu \u00f6rne\u011fin modu bu nedenle \u00e7ok modludur. <\/p>\n<\/p>\n

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

            <\/span> moda hesap makinesi<\/span><\/h2>\n

            Modunu hesaplamak i\u00e7in herhangi bir istatistiksel \u00f6rnekten verileri a\u015fa\u011f\u0131daki \u00e7evrimi\u00e7i hesap makinesine girin. Veriler bir bo\u015flukla ayr\u0131lmal\u0131 ve ondal\u0131k ay\u0131r\u0131c\u0131 olarak nokta kullan\u0131larak girilmelidir. <\/p>\n