{"id":14,"date":"2023-08-06T22:20:06","date_gmt":"2023-08-06T22:20:06","guid":{"rendered":"https:\/\/statorials.org\/tr\/orta-kare\/"},"modified":"2023-08-06T22:20:06","modified_gmt":"2023-08-06T22:20:06","slug":"orta-kare","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/orta-kare\/","title":{"rendered":"K\u00f6k kare ortalama"},"content":{"rendered":"

Burada k\u00f6k ortalama karenin ne oldu\u011funu ve nas\u0131l hesapland\u0131\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca ortalamay\u0131 kullanman\u0131n avantajlar\u0131n\u0131 ve dezavantajlar\u0131n\u0131 ve ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 \u00f6\u011freneceksiniz. Son olarak yaz\u0131n\u0131n sonunda yer alan hesap makinesi ile herhangi bir veri setinin ortalama karek\u00f6k\u00fcn\u00fc hesaplayabileceksiniz.<\/p>\n

<\/span> Ortalama kare nedir?<\/span><\/h2>\n

K\u00f6k ortalama kare, tan\u0131mlay\u0131c\u0131 istatistiklerin merkezili\u011finin bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. K\u00f6k ortalama kare, verilerin karelerinin aritmetik ortalamas\u0131n\u0131n karek\u00f6k\u00fcne e\u015fittir.<\/strong><\/p>\n

K\u00f6k ortalama<\/strong> kare ayn\u0131 zamanda k\u00f6k<\/strong> ortalama kare<\/em> veya RMS<\/strong> olarak da adland\u0131r\u0131l\u0131r.<\/p>\n

\u0130kinci dereceden ortalaman\u0131n form\u00fcl\u00fc bu nedenle a\u015fa\u011f\u0131daki gibidir: <\/p>\n

\n
\"ortalama<\/figure>\n<\/div>\n

Kare ortalamas\u0131 \u00f6zellikle istatistiksel de\u011fi\u015fken pozitif ve negatif de\u011ferler ald\u0131\u011f\u0131nda kullan\u0131\u015fl\u0131d\u0131r \u00e7\u00fcnk\u00fc her bir veri par\u00e7as\u0131n\u0131n karesi al\u0131nd\u0131\u011f\u0131nda t\u00fcm de\u011ferler pozitif olur. Bu nedenle ortalama kare, i\u015faretinin \u00f6nemli olmad\u0131\u011f\u0131 ancak mutlak de\u011ferinin \u00f6nemli oldu\u011fu de\u011fi\u015fkenleri analiz etmek i\u00e7in kullan\u0131l\u0131r.<\/p>\n

\u00d6rne\u011fin, \u00f6l\u00e7\u00fcm hatalar\u0131n\u0131 incelemek i\u00e7in ortalama kare kullan\u0131l\u0131r, \u00e7\u00fcnk\u00fc bu durumlarda hatan\u0131n pozitif mi yoksa negatif mi oldu\u011funa bakm\u0131yoruz, bunun yerine \u00f6l\u00e7\u00fcm s\u0131ras\u0131nda hatan\u0131n b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc analiz ediyoruz.<\/p>\n

Ayr\u0131ca b\u00fcy\u00fck say\u0131lar\u0131n kareleri k\u00fc\u00e7\u00fck say\u0131lar\u0131n karelerine g\u00f6re \u00e7ok daha y\u00fcksek de\u011ferlere sahip oldu\u011fundan ortadaki karede b\u00fcy\u00fck say\u0131lar k\u00fc\u00e7\u00fck say\u0131lara g\u00f6re daha \u00f6nemlidir.<\/p>\n

Kare ortalama, aritmetik ortalama, a\u011f\u0131rl\u0131kl\u0131 ortalama, geometrik ortalama ve harmonik ortalaman\u0131n yan\u0131 s\u0131ra bir t\u00fcr istatistiksel ortalamad\u0131r. <\/p>\n

<\/span> Ortalama Karek\u00f6k\u00fcn Avantajlar\u0131 ve Dezavantajlar\u0131<\/span><\/h2>\n

\u0130kinci dereceden ortalaman\u0131n di\u011fer ortalama t\u00fcrlerine g\u00f6re avantajlar\u0131 ve dezavantajlar\u0131 vard\u0131r.<\/p>\n

\u0130kinci dereceden ortalaman\u0131n temel avantaj\u0131<\/strong> , ayr\u0131k bir de\u011fi\u015fkenin ortalama de\u011ferine \u00e7ok iyi bir yakla\u015f\u0131m elde etmenize olanak sa\u011flamas\u0131d\u0131r. \u00d6te yandan, kare ortalaman\u0131n en b\u00fcy\u00fck dezavantaj\u0131<\/strong> , birden fazla i\u015flemin ger\u00e7ekle\u015ftirilmesi gerekti\u011finden hesaplamas\u0131n\u0131n olduk\u00e7a karma\u015f\u0131k olmas\u0131d\u0131r.<\/p>\n

Buna kar\u015f\u0131l\u0131k, ortalama karek\u00f6k, hata \u00f6l\u00e7\u00fcmlerini analiz etmek i\u00e7in \u00e7ok kullan\u0131\u015fl\u0131d\u0131r. Her ne kadar bu \u00f6zellik yanl\u0131\u015f bir \u00f6l\u00e7\u00fcm\u00fcn rms sonucunu \u00f6nemli \u00f6l\u00e7\u00fcde de\u011fi\u015ftirece\u011fini ima etse de, y\u00fcksek de\u011ferlere de \u00e7ok daha fazla \u00f6nem verilmektedir. <\/p>\n

<\/span> K\u00f6k ortalama kare nas\u0131l hesaplan\u0131r<\/span><\/h2>\n

K\u00f6k ortalama kareyi hesaplamak i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar ger\u00e7ekle\u015ftirilmelidir:<\/p>\n

    \n
  1. Her istatistiksel verinin karesini hesaplay\u0131n.<\/span><\/li>\n
  2. \u00d6nceki ad\u0131mda hesaplanan t\u00fcm kareleri toplay\u0131n.<\/span><\/li>\n
  3. Sonucu \u00f6rnekteki veri \u00f6\u011fesi say\u0131s\u0131na b\u00f6l\u00fcn.<\/span><\/li>\n
  4. \u00d6nceki de\u011ferin karek\u00f6k\u00fcn\u00fc bulun.<\/span><\/li>\n
  5. Elde edilen sonu\u00e7 istatistiksel numunenin kare ortalamas\u0131d\u0131r.<\/span><\/li>\n<\/ol>\n

    \ud83d\udc49Herhangi bir veri setinin ortalama karek\u00f6k\u00fcn\u00fc hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesini kullanabilirsiniz.<\/u> <\/p>\n

    <\/span> Ortalama kare \u00f6rne\u011fi<\/span><\/h2>\n

    K\u00f6k ortalama kareyi nas\u0131l elde edece\u011fimizi \u00f6\u011frendikten sonra, \u00f6rnek olarak bir veri k\u00fcmesinin ortalama karek\u00f6k\u00fcn\u00fc belirleyece\u011fiz.<\/p>\n

      \n
    • Bir \u00fcniversitenin laboratuvar dersinde profes\u00f6r, \u00f6\u011frencilerinden kimyasallarla bir deney yapmalar\u0131n\u0131 ister. Kimyasal deneyin amac\u0131 toplamda 3 litrelik bir \u00e7\u00f6zelti elde etmektir. \u00d6\u011frenci gruplar\u0131 \u015fu verilere ula\u015ft\u0131: <\/li>\n<\/ul>\n
      \n
      \"egzersiz<\/figure>\n<\/div>\n

      Elde edilen istatistiksel verileri incelemek i\u00e7in, her grubun elde etti\u011fi hatan\u0131n kare ortalamas\u0131n\u0131n de\u011ferini hesaplamaya devam ediyoruz. Bu nedenle ikinci dereceden ortalama form\u00fcl\u00fcn\u00fc uyguluyoruz:<\/p>\n<\/p>\n

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

      Verileri form\u00fclde yerine koyar\u0131z ve ortalaman\u0131n karek\u00f6k\u00fcn\u00fc hesaplar\u0131z:<\/p>\n<\/p>\n

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

      B\u00f6ylece deneyde ortalama karek\u00f6klere g\u00f6re elde edilen ortalama hata 0,88 litredir. <\/p>\n

      <\/span> Ortalama Kare Hesaplay\u0131c\u0131<\/span><\/h2>\n

      Herhangi bir istatistiksel \u00f6rnekten elde edilen verileri, k\u00f6k ortalama karesini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesine girin. Veriler bir bo\u015flukla ayr\u0131lmal\u0131 ve ondal\u0131k ay\u0131r\u0131c\u0131 olarak nokta kullan\u0131larak girilmelidir. <\/p>\n