z<\/strong> = (X \u2013 \u03bc) \/ \u03c3<\/span><\/p>\n burada X analiz etti\u011fimiz de\u011ferdir, \u03bc ortalamad\u0131r ve \u03c3 standart sapmad\u0131r.<\/span><\/p>\n Z puan\u0131 pozitif, negatif veya s\u0131f\u0131r olabilir.<\/strong><\/span><\/p>\n Pozitif z puan\u0131 belirli bir de\u011ferin ortalaman\u0131n \u00fczerinde oldu\u011funu, negatif z puan\u0131 belirli bir de\u011ferin ortalaman\u0131n alt\u0131nda oldu\u011funu ve az s\u0131f\u0131r puan\u0131 belirli bir de\u011ferin ortalamaya e\u015fit oldu\u011funu g\u00f6sterir.<\/span><\/p>\n Birka\u00e7 \u00f6rnek bunu a\u00e7\u0131k\u00e7a ortaya koymal\u0131d\u0131r.<\/span><\/p>\n Diyelim ki belirli bir bitki grubunun y\u00fcksekli\u011fini (in\u00e7 cinsinden) g\u00f6steren a\u015fa\u011f\u0131daki veri setine sahibiz:<\/span><\/p>\n 5, 7, 7, 8, 9, 10, 13, 17, 17, 18, 19, 19, 20<\/span><\/p>\n Bu veri setinin \u00f6rnek ortalamas\u0131 13<\/strong> ve \u00f6rnek standart sapmas\u0131 5,51’dir<\/strong> .<\/span><\/p>\n 1. Bu veri k\u00fcmesindeki \u201c8\u201d de\u011ferinin z-puan\u0131n\u0131 bulun.<\/strong><\/span><\/p>\n Z-puan\u0131n\u0131 \u015fu \u015fekilde hesaplayabilirsiniz:<\/span><\/p>\n z<\/strong> = (X \u2013 \u03bc) \/ \u03c3 = (8 \u2013 13) \/ 5,51 = -0,91<\/strong><\/span><\/p>\n Bu, \u201c8\u201d de\u011ferinin ortalaman\u0131n 0,91 standart sapma alt\u0131nda<\/em> oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n 2. Bu veri k\u00fcmesindeki \u201c13\u201d de\u011ferinin z-puan\u0131n\u0131 bulun.<\/strong><\/span><\/p>\n Z-puan\u0131n\u0131 \u015fu \u015fekilde hesaplayabilirsiniz:<\/span><\/p>\n z<\/strong> = (X \u2013 \u03bc) \/ \u03c3 = (13 \u2013 13) \/ 5,46 = 0<\/strong><\/span><\/p>\n Bu, \u201c13\u201d de\u011ferinin tam olarak ortalamaya e\u015fit oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n 3. Bu veri k\u00fcmesindeki \u201c20\u201d de\u011ferinin z-puan\u0131n\u0131 bulun.<\/strong><\/span><\/p>\n Z-puan\u0131n\u0131 \u015fu \u015fekilde hesaplayabilirsiniz:<\/span><\/p>\n z<\/strong> = (X \u2013 \u03bc) \/ \u03c3 = (20 \u2013 13) \/ 5,46 = 1,28<\/strong><\/span><\/p>\n Bu da \u201c20\u201d de\u011ferinin ortalaman\u0131n 1,28 standart sapma \u00fczerinde<\/em> oldu\u011fu anlam\u0131na geliyor.<\/span><\/p>\n AZ grafi\u011fi bize de\u011ferlerin y\u00fczde ka\u00e7\u0131n\u0131n belirli Z puanlar\u0131n\u0131n alt\u0131na d\u00fc\u015ft\u00fc\u011f\u00fcn\u00fc s\u00f6yler. Birka\u00e7 \u00f6rnek bunu a\u00e7\u0131k\u00e7a ortaya koymal\u0131d\u0131r.<\/span><\/p>\n \u00d6rnek 1: Negatif Z puanlar\u0131<\/strong><\/span><\/p>\n Daha \u00f6nce veri setimizdeki “8” ham de\u011ferinin -0,91<\/strong> z puan\u0131na sahip oldu\u011funu bulmu\u015ftuk. Z tablosuna g\u00f6re de\u011ferlerin %18,14’\u00fc bu de\u011ferden d\u00fc\u015f\u00fckt\u00fcr.<\/span> <\/p>\n \u00d6rnek 2: S\u0131f\u0131ra e\u015fit Z-Skorlar\u0131<\/strong><\/span><\/p>\n Daha \u00f6nce veri setimizdeki ham de\u011fer “13”\u00fcn z puan\u0131n\u0131n 0<\/strong> oldu\u011funu bulmu\u015ftuk. Z tablosuna g\u00f6re de\u011ferlerin %50,00’i bu de\u011ferden k\u00fc\u00e7\u00fckt\u00fcr.<\/span> <\/p>\n \u00d6rnek 3: Pozitif Z puanlar\u0131<\/strong><\/span><\/p>\n Daha \u00f6nce veri setimizdeki “20” ham de\u011ferinin 1,28<\/strong> z puan\u0131na sahip oldu\u011funu bulmu\u015ftuk. Z tablosuna g\u00f6re de\u011ferlerin %89,97\u2019si bu de\u011ferden d\u00fc\u015f\u00fckt\u00fcr.<\/span> <\/p>\n Z puanlar\u0131, negatif sonsuzluk ile pozitif sonsuzluk aras\u0131nda herhangi bir de\u011feri alabilir, ancak \u00e7o\u011fu z puan\u0131, ortalaman\u0131n 2 standart sapmas\u0131 dahilindedir. Asl\u0131nda istatistiktetemel kural<\/a> olarak bilinen ve normal da\u011f\u0131l\u0131ma sahip belirli bir veri seti i\u00e7in \u015funu belirten bir kural vard\u0131r:<\/span><\/p>\n Z-puan\u0131n\u0131n mutlak de\u011feri ne kadar y\u00fcksek olursa, ham de\u011fer veri k\u00fcmesinin ortalamas\u0131ndan o kadar uzak olur. Z-puan\u0131n\u0131n mutlak de\u011feri ne kadar d\u00fc\u015f\u00fckse, ham de\u011fer veri k\u00fcmesinin ortalamas\u0131na o kadar yak\u0131nd\u0131r.<\/span><\/p>\n \u0130lgili konular:<\/strong><\/span><\/p>\n Ba\u015fparmak Hesaplay\u0131c\u0131 Kurallar\u0131<\/a> \u0130statistiklerde z-puan\u0131 bize bir de\u011ferin ortalamadan ka\u00e7 standart sapma oldu\u011funu s\u00f6yler. Z-puan\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z: z = (X \u2013 \u03bc) \/ \u03c3 burada X analiz etti\u011fimiz de\u011ferdir, \u03bc ortalamad\u0131r ve \u03c3 standart sapmad\u0131r. Z puan\u0131 pozitif, negatif veya s\u0131f\u0131r olabilir. Pozitif z puan\u0131 belirli bir de\u011ferin ortalaman\u0131n \u00fczerinde oldu\u011funu, negatif z puan\u0131 belirli […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-557","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\n \u00d6rnekler: Z puan\u0131n\u0131n hesaplanmas\u0131<\/strong><\/span><\/h2>\n
Z puanlar\u0131 nas\u0131l yorumlan\u0131r?<\/strong><\/span><\/h2>\n
![\"Negatif](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/zscorenegatif1.jpg\")
<\/p>\n![\"Z](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/zscorenegatif2.jpg\")
<\/p>\n![\"Pozitif](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/zscorenegatif3.jpg\")
<\/p>\n \u00c7\u00f6z\u00fcm<\/strong><\/span><\/h2>\n
\n
Excel’de temel kural nas\u0131l uygulan\u0131r?<\/a>
<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"