<\/span> Yar\u0131m<\/span><\/h3>\n Ortalamay\u0131<\/strong> hesaplamak i\u00e7in t\u00fcm de\u011ferleri toplay\u0131n ve ard\u0131ndan toplam veri say\u0131s\u0131na b\u00f6l\u00fcn. Ortalaman\u0131n form\u00fcl\u00fc bu nedenle a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n![\"\\displaystyle\\overline{x}=\\frac{\\displaystyle\\sum_{i=1}^n](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9c89528c734e47bf196befc03d1b7896_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
\u0130statistiklerde ortalama, aritmetik ortalama<\/strong> veya ortalama<\/strong> olarak da bilinir. <\/p>\n \u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Aritmetik Ortalama Hesaplay\u0131c\u0131<\/a><\/div>\n<\/span> Medyan<\/span><\/h3>\n Medyan<\/strong> , en k\u00fc\u00e7\u00fckten en b\u00fcy\u00fc\u011fe do\u011fru s\u0131ralanan t\u00fcm verilerin ortadaki de\u011feridir. Ba\u015fka bir deyi\u015fle medyan s\u0131ral\u0131 veri setini iki e\u015fit par\u00e7aya b\u00f6ler.<\/p>\n Medyan\u0131n hesaplanmas\u0131, toplam veri say\u0131s\u0131n\u0131n \u00e7ift veya tek olmas\u0131na ba\u011fl\u0131d\u0131r:<\/p>\n
\n- Toplam veri say\u0131s\u0131 tek<\/strong> ise medyan verinin tam ortas\u0131nda kalan de\u011fer olacakt\u0131r. Yani s\u0131ralanan verinin (n+1)\/2 konumundaki de\u011feri.<\/span><\/li>\n
![\"Me=x_{\\frac{n+1}{2}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-77dc6f0bf6f823a8a8eea705245e20a3_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
- Toplam veri noktas\u0131 say\u0131s\u0131 \u00e7ift ise<\/strong> medyan, merkezde bulunan iki veri noktas\u0131n\u0131n ortalamas\u0131 olacakt\u0131r. Yani s\u0131ral\u0131 verinin n\/2 ve n\/2+1 konumlar\u0131nda bulunan de\u011ferlerin aritmetik ortalamas\u0131d\u0131r.<\/span><\/li>\n
![\"Me=\\cfrac{x_{\\frac{n}{2}}+x_{\\frac{n}{2}+1}}{2}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bbb83dd436c25bf409381af4b9ac6daf_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/ul>\n
Alt\u0131n<\/p>\n<\/p>\n
![\"n\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" "\\"Rendered")
<\/p>\n
\u00f6rnekteki toplam veri say\u0131s\u0131d\u0131r ve Me<\/em> simgesi medyan\u0131 g\u00f6sterir. <\/p>\n \u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Medyan hesaplay\u0131c\u0131<\/a><\/div>\n<\/span> Moda<\/span><\/h3>\n \u0130statistikte mod<\/strong> , veri k\u00fcmesindeki mutlak frekans\u0131 en y\u00fcksek olan de\u011ferdir, yani mod, bir veri k\u00fcmesinde en \u00e7ok tekrarlanan de\u011ferdir.<\/p>\n Bu nedenle, mod i\u00e7in \u00f6zel bir form\u00fcl yoktur, ancak 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 veriler mod olacakt\u0131r.<\/p>\n
Modun istatistiksel mod<\/strong> veya modal de\u011fer<\/strong> oldu\u011fu da s\u00f6ylenebilir. <\/p>\n \u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Moda hesaplay\u0131c\u0131s\u0131<\/a> <\/div>\n<\/span> \u0130statistiksel da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcmleri i\u00e7in form\u00fcller <\/span><\/h2>\n<\/span> Standart sapma<\/span><\/h3>\n Standart sapma olarak da adland\u0131r\u0131lan standart sapma, veri serisindeki sapmalar\u0131n karelerinin toplam\u0131n\u0131n karek\u00f6k\u00fcn\u00fcn toplam g\u00f6zlem say\u0131s\u0131na b\u00f6l\u00fcnmesine e\u015fittir.<\/p>\n
Bu nedenle standart sapman\u0131n form\u00fcl\u00fc<\/strong> \u015fu \u015fekildedir: <\/p>\n<\/p>\n![\"\\displaystyle\\sigma=\\sqrt{\\frac{\\displaystyle\\sum_{i=1}^n(x_i-\\overline{x})^2}{n}}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8fae96eb8656eacbcd8a634c33fab81d_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Standart sapma hesaplay\u0131c\u0131s\u0131<\/a><\/div>\n<\/span> Varyans<\/span><\/h3>\n Varyans<\/strong> , toplam g\u00f6zlem say\u0131s\u0131na g\u00f6re art\u0131klar\u0131n karelerinin toplam\u0131na e\u015fittir. Dolay\u0131s\u0131yla bu istatistiksel \u00f6l\u00e7\u00fcm\u00fcn form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n![\"Var(X)=\\cfrac{\\displaystyle\\sum_{i=1}^n\\left(x_i-\\overline{x}\\right)^2}{n}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bb29913eaa58ffb28bbc5b81d6785683_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
Alt\u0131n:<\/p>\n
\n- \n
![\"X\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-996ff7036e644e89f8ac379fa58d0cf7_l3.png\" "\\"Rendered")
<\/p>\n
varyans\u0131n\u0131 hesaplamak istedi\u011finiz rastgele de\u011fi\u015fkendir.<\/li>\n
- \n
![\"x_i\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dad27a9703483183e1afd245f5232b83_l3.png\" "\\"Rendered")
<\/p>\n
veri de\u011feri<\/p>\n
![\"i\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-31318c5dcb226c69e0818e5f7d2422b5_l3.png\" "\\"Rendered")
<\/p>\n
.<\/li>\n
- \n
<\/p>\n
toplam g\u00f6zlem say\u0131s\u0131d\u0131r.<\/li>\n
- \n
![\"\\overline{X}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5b485d4231dfeb4b50ddf271c3abb0b3_l3.png\" "\\"Rendered")
<\/p>\n
rastgele de\u011fi\u015fkenin ortalamas\u0131d\u0131r<\/p>\n
<\/p>\n
. <\/li>\n<\/ul>\n
\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Bo\u015fluk hesaplay\u0131c\u0131<\/a> <\/div>\n<\/span> De\u011fi\u015fim katsay\u0131s\u0131<\/span><\/h3>\n \u0130statistikte varyasyon katsay\u0131s\u0131<\/strong> , bir veri k\u00fcmesinin ortalamas\u0131na g\u00f6re da\u011f\u0131l\u0131m\u0131n\u0131 belirlemek i\u00e7in kullan\u0131lan bir da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. De\u011fi\u015fim katsay\u0131s\u0131, verinin standart sapmas\u0131n\u0131n ortalamas\u0131na b\u00f6l\u00fcnmesi ve ard\u0131ndan de\u011ferin y\u00fczde olarak ifade edilmesi i\u00e7in 100 ile \u00e7arp\u0131lmas\u0131yla hesaplan\u0131r. <\/p>\n<\/p>\n![\"CV=\\cfrac{\\sigma}{\\overline{x}}\\cdot](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0ebd63772f3bb0853b10b1996c34a5de_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> De\u011fi\u015fim katsay\u0131s\u0131 hesaplay\u0131c\u0131s\u0131<\/a><\/div>\n<\/span> D\u00fczenli<\/span><\/h3>\n \u0130statistiksel aral\u0131k,<\/strong> bir \u00f6rnekteki verilerin maksimum de\u011feri ile minimum de\u011feri aras\u0131ndaki fark\u0131 g\u00f6steren bir da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. Bu nedenle, bir pop\u00fclasyonun veya istatistiksel \u00f6rneklemin kapsam\u0131n\u0131 hesaplamak i\u00e7in maksimum de\u011ferin minimum de\u011ferden \u00e7\u0131kar\u0131lmas\u0131 gerekir. <\/p>\n<\/p>\n![\"R=\\text{M\\'ax}-\\text{M\\'in}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d09e48dfa9b5b1e1fbc30ac856d46166_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> \u0130statistiksel aral\u0131k \u00f6rne\u011fi<\/a><\/div>\n<\/span> \u00c7eyrekler aras\u0131 aral\u0131k<\/span><\/h3>\n \u00c7eyrekler aras\u0131 aral\u0131k<\/strong> olarak da adland\u0131r\u0131lan \u00e7eyrekler aras\u0131<\/strong> aral\u0131k, \u00fc\u00e7\u00fcnc\u00fc ve birinci \u00e7eyrekler aras\u0131ndaki fark\u0131 g\u00f6steren istatistiksel da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcs\u00fcd\u00fcr.<\/p>\n Bu nedenle, bir istatistiksel veri setinin \u00e7eyrekler aras\u0131 aral\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in \u00f6nce \u00fc\u00e7\u00fcnc\u00fc ve birinci \u00e7eyrekleri bulman\u0131z ve ard\u0131ndan bunlar\u0131 \u00e7\u0131karman\u0131z gerekir. <\/p>\n<\/p>\n
![\"IQR=Q_3-Q_1\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e77f65ff74b67f18e258e2a273be1d1c_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> \u00c7eyrekler Aras\u0131 Aral\u0131k Hesaplay\u0131c\u0131<\/a><\/div>\n<\/span> orta fark<\/span><\/h3>\n Ortalama<\/strong> mutlak sapma olarak da adland\u0131r\u0131lan ortalama<\/strong> sapma, mutlak sapmalar\u0131n ortalamas\u0131d\u0131r. Bu nedenle ortalama sapma, her veri \u00f6\u011fesinin aritmetik ortalamadan sapmalar\u0131n\u0131n toplam\u0131n\u0131n veri \u00f6\u011felerinin toplam say\u0131s\u0131na b\u00f6l\u00fcnmesine e\u015fittir. <\/p>\n<\/p>\n![\"D_{\\overline{x}}=\\cfrac{\\sum_{i=1}^n|x_i-\\overline{x}|}{n}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-61abff21d429fe1de05fc4344be7029a_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Ortalama sapma hesaplay\u0131c\u0131s\u0131<\/a> <\/div>\n<\/span> \u0130statistiksel konum \u00f6l\u00e7\u00fcmleri i\u00e7in form\u00fcller <\/span><\/h2>\n<\/span> \u00e7eyrekler<\/span><\/h3>\n \u0130statistikte \u00e7eyrekler<\/strong> , s\u0131ral\u0131 bir veri k\u00fcmesini d\u00f6rt e\u015fit par\u00e7aya b\u00f6len \u00fc\u00e7 de\u011ferdir. B\u00f6ylece birinci, ikinci ve \u00fc\u00e7\u00fcnc\u00fc \u00e7eyrekler t\u00fcm istatistiksel verilerin s\u0131ras\u0131yla %25, %50 ve %75’ini temsil etmektedir.<\/p>\n \u00c7eyrekler b\u00fcy\u00fck Q ve \u00e7eyrek endeksi ile temsil edilir, dolay\u0131s\u0131yla ilk \u00e7eyrek Q 1<\/sub> , ikinci \u00e7eyrek Q 2<\/sub> ve \u00fc\u00e7\u00fcnc\u00fc \u00e7eyrek Q 3’t\u00fcr<\/sub> .<\/p>\n \u00c7eyrek form\u00fcl\u00fc<\/strong> \u015f\u00f6yledir:<\/p>\n<\/p>\n![\"\\cfrac{k\\cdot](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d2193deb142e070e4b6127666afe349d_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
L\u00fctfen unutmay\u0131n:<\/strong> Bu form\u00fcl bize \u00e7eyre\u011fin de\u011ferini de\u011fil \u00e7eyre\u011fin konumunu s\u00f6yler. \u00c7eyrek, form\u00fcl taraf\u0131ndan elde edilen konumda bulunan veriler olacakt\u0131r.<\/p>\n Ancak bazen bu form\u00fcl\u00fcn sonucu bize ondal\u0131k bir say\u0131 verecektir. Bu nedenle sonucun ondal\u0131k say\u0131 olup olmamas\u0131na ba\u011fl\u0131 olarak iki durumu birbirinden ay\u0131rmam\u0131z gerekir:<\/p>\n
\n- Form\u00fcl\u00fcn sonucu ondal\u0131k k\u0131sm\u0131 olmayan bir say\u0131<\/strong> ise \u00e7eyrek, yukar\u0131daki form\u00fcl\u00fcn sa\u011flad\u0131\u011f\u0131 konumdaki verilerdir.<\/li>\n
- Form\u00fcl sonucu ondal\u0131k k\u0131sm\u0131 olan bir say\u0131ysa<\/strong> \u00e7eyrek de\u011feri a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak hesaplan\u0131r:<\/li>\n<\/ul>\n
![\"Q=x_i+d\\cdot](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4af89ae2d7be917607f734400fab5a66_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
Burada x i<\/sub><\/em> ve x i+1,<\/sub><\/em> birinci form\u00fclle elde edilen say\u0131n\u0131n aralar\u0131nda bulundu\u011fu konumlar\u0131n say\u0131lar\u0131d\u0131r ve d<\/em> , birinci form\u00fclle elde edilen say\u0131n\u0131n ondal\u0131k k\u0131sm\u0131d\u0131r. <\/p>\n \u27a4<\/span> Bak\u0131n\u0131z:<\/strong> \u00c7eyrek Hesaplay\u0131c\u0131<\/a><\/div>\n<\/span> ondal\u0131k dilimler<\/span><\/h3>\n \u0130statistikte ondal\u0131k say\u0131lar<\/strong> , s\u0131ral\u0131 bir veri k\u00fcmesini on e\u015fit par\u00e7aya b\u00f6len dokuz de\u011ferdir. B\u00f6ylece birinci, ikinci, \u00fc\u00e7\u00fcnc\u00fc,\u2026 ondal\u0131k dilim numunenin veya pop\u00fclasyonun %10, %20, %30,\u2026’unu temsil eder.<\/p>\n Ondal\u0131k dilimler b\u00fcy\u00fck D harfi ve ondal\u0131k indeks ile temsil edilir, yani ilk ondal\u0131k dilim D 1<\/sub> , ikinci ondal\u0131k dilim D 2<\/sub> , \u00fc\u00e7\u00fcnc\u00fc ondal\u0131k dilim D 3<\/sub> vb.<\/p>\n Ondal\u0131k form\u00fcl<\/strong> a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n![\"\\cfrac{k\\cdot](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d84ca1bdd1a62a50e87decde4d360daa_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
L\u00fctfen unutmay\u0131n:<\/strong> Bu form\u00fcl bize ondal\u0131k dilimin de\u011ferini de\u011fil, ondal\u0131k dilimin konumunu s\u00f6yler. Ondal\u0131k k\u0131s\u0131m, form\u00fcl taraf\u0131ndan elde edilen konumda bulunan veriler olacakt\u0131r.<\/p>\n Ancak bazen bu form\u00fcl\u00fcn sonucu bize ondal\u0131k say\u0131 verir, bu nedenle sonucun ondal\u0131k say\u0131 olup olmad\u0131\u011f\u0131na ba\u011fl\u0131 olarak iki durumu ay\u0131rmam\u0131z gerekir:<\/p>\n
\n- Form\u00fcl\u00fcn sonucu ondal\u0131k k\u0131sm\u0131 olmayan bir say\u0131<\/strong> ise, ondal\u0131k k\u0131s\u0131m yukar\u0131daki form\u00fcl\u00fcn sa\u011flad\u0131\u011f\u0131 konumda bulunan verilerdir.<\/li>\n
- Form\u00fcl\u00fcn sonucu ondal\u0131k k\u0131sm\u0131 olan bir say\u0131<\/strong> ise, ondal\u0131k de\u011fer a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak hesaplan\u0131r:<\/li>\n<\/ul>\n
![\"D=x_i+d\\cdot](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dea1a6ff3ec04aca29983e36653e2f4b_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
Burada x i<\/sub><\/em> ve x i+1,<\/sub><\/em> birinci form\u00fclle elde edilen say\u0131n\u0131n aralar\u0131nda bulundu\u011fu konumlar\u0131n say\u0131lar\u0131d\u0131r ve d<\/em> , birinci form\u00fclle elde edilen say\u0131n\u0131n ondal\u0131k k\u0131sm\u0131d\u0131r. <\/p>\n \u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Ondal\u0131k hesaplay\u0131c\u0131<\/a><\/div>\n<\/span> y\u00fczdelikler<\/span><\/h3>\n \u0130statistikte y\u00fczdelikler<\/strong> , s\u0131ral\u0131 bir veri k\u00fcmesini y\u00fcz e\u015fit par\u00e7aya b\u00f6len de\u011ferlerdir. Yani y\u00fczdelik dilim, veri k\u00fcmesinin belirli bir y\u00fczdesinin alt\u0131na d\u00fc\u015ft\u00fc\u011f\u00fc de\u011feri belirtir.<\/p>\n Y\u00fczdelikler b\u00fcy\u00fck harf P ve y\u00fczdelik endeksi ile temsil edilir, yani ilk y\u00fczdelik dilim P 1<\/sub> , 40. y\u00fczdelik dilim P 40<\/sub> , 79. y\u00fczdelik dilim P 79<\/sub> vb.<\/p>\n Y\u00fczdelik form\u00fcl<\/strong> \u015f\u00f6yledir:<\/p>\n<\/p>\n![\"\\cfrac{k\\cdot](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5fc5a249710b5577ae4d328a066f9943_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
L\u00fctfen unutmay\u0131n:<\/strong> Bu form\u00fcl bize y\u00fczdelik dilimin konumunu belirtir, ancak de\u011ferini vermez. Y\u00fczdelik dilim, form\u00fcl\u00fcn elde etti\u011fi konumda bulunan veriler olacakt\u0131r.<\/p>\n Ancak bazen bu form\u00fcl\u00fcn sonucu bize ondal\u0131k say\u0131 verir, bu nedenle sonucun ondal\u0131k say\u0131 olup olmad\u0131\u011f\u0131na ba\u011fl\u0131 olarak iki durumu ay\u0131rmam\u0131z gerekir:<\/p>\n
\n- Form\u00fcl\u00fcn sonucu ondal\u0131k k\u0131sm\u0131 olmayan bir say\u0131<\/strong> ise y\u00fczdelik dilim yukar\u0131daki form\u00fcl\u00fcn sa\u011flad\u0131\u011f\u0131 konumdaki verilere kar\u015f\u0131l\u0131k gelir.<\/li>\n
- Form\u00fcl sonucu ondal\u0131k k\u0131sm\u0131 olan bir say\u0131ysa<\/strong> , tam y\u00fczdelik de\u011fer a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak hesaplan\u0131r:<\/li>\n<\/ul>\n
![\"P=x_i+d\\cdot](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-671e09af64fc816839e3bbc582efd36e_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
Burada x i<\/sub><\/em> ve x i+1,<\/sub><\/em> birinci form\u00fclle elde edilen say\u0131n\u0131n aralar\u0131nda bulundu\u011fu konumlar\u0131n say\u0131lar\u0131d\u0131r ve d<\/em> , birinci form\u00fclle elde edilen say\u0131n\u0131n ondal\u0131k k\u0131sm\u0131d\u0131r. <\/p>\n \u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Y\u00fczdelik Hesaplay\u0131c\u0131<\/a> <\/div>\n<\/span> \u0130statistiksel \u015fekil \u00f6l\u00e7\u00fcm form\u00fclleri <\/span><\/h2>\n<\/span>asimetri katsay\u0131s\u0131<\/span><\/h3>\n \u00c7arp\u0131kl\u0131k katsay\u0131s\u0131 veya \u00e7arp\u0131kl\u0131k endeksi, bir da\u011f\u0131l\u0131m\u0131n \u00e7arp\u0131kl\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131lan istatistiksel bir katsay\u0131d\u0131r. Yani asimetri katsay\u0131s\u0131n\u0131 hesaplayarak, da\u011f\u0131l\u0131m\u0131n asimetri t\u00fcr\u00fcn\u00fc, bunun grafiksel bir g\u00f6sterimini yapmaya gerek kalmadan \u00f6\u011frenebilirsiniz.<\/p>\n
Asimetri katsay\u0131s\u0131n\u0131n form\u00fcl\u00fc<\/strong> a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n![\"\\displaystyle\\gamma_1=\\frac{\\overline{x}_3}{\\sigma^3}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a61d9a6a488046490b5dcf71e3906bcb_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
E\u015fde\u011fer olarak, Fisher asimetri katsay\u0131s\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki iki form\u00fclden herhangi biri kullan\u0131labilir:<\/p>\n<\/p>\n
![\"\\displaystyle\\gamma_1=\\frac{\\displaystyle](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-94cbf4c3956145cb861488cb726c8469_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
![\"\\displaystyle\\gamma_1=\\frac{\\operatorname{E}[X^3]](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b58aae86c4d7f8fec18ef689ec08c5db_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
Alt\u0131n<\/p>\n<\/p>\n
![\"E\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-638a7387bd72763290cc777a9b509c38_l3.png\" "\\"Rendered")
<\/p>\n
matematiksel beklenti,<\/p>\n
![\"\\overline{x}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a39858a792fb4fe9a3173e004701f2a7_l3.png\" "\\"Rendered")
<\/p>\n
aritmetik ortalama,<\/p>\n
![\"\\sigma\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-eaaf379fee5e67946f3fedf5631047b1_l3.png\" "\\"Rendered")
<\/p>\n
standart sapma ve<\/p>\n
<\/p>\n
toplam veri say\u0131s\u0131. <\/p>\n
\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Asimetri katsay\u0131s\u0131<\/a><\/div>\n<\/span>bas\u0131kl\u0131k katsay\u0131s\u0131<\/span><\/h3>\n Keskinlik olarak da adland\u0131r\u0131lan bas\u0131kl\u0131k, bir da\u011f\u0131l\u0131m\u0131n ortalama etraf\u0131nda ne kadar yo\u011funla\u015ft\u0131\u011f\u0131n\u0131 g\u00f6sterir. Ba\u015fka bir deyi\u015fle bas\u0131kl\u0131k, bir da\u011f\u0131l\u0131m\u0131n dik mi yoksa d\u00fcz m\u00fc oldu\u011funu g\u00f6sterir. Spesifik olarak, bir da\u011f\u0131l\u0131m\u0131n bas\u0131kl\u0131\u011f\u0131 ne kadar b\u00fcy\u00fck olursa, o kadar dik (veya daha keskin) olur.<\/p>\n
Bas\u0131kl\u0131k katsay\u0131s\u0131n\u0131n form\u00fcl\u00fc<\/strong> a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n![\"\\displaystyle](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8fb9dd9a6a3d52fa0f197321a711ffb1_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n
Alt\u0131n<\/p>\n<\/p>\n
<\/p>\n
g\u00f6zleme kar\u015f\u0131l\u0131k gelen de\u011ferdir<\/p>\n
<\/p>\n
,<\/p>\n
<\/p>\n
aritmetik ortalama,<\/p>\n
<\/p>\n
standart sapma ve<\/p>\n
<\/p>\n
toplam veri say\u0131s\u0131. <\/p>\n
\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> D\u00fczle\u015ftirme Katsay\u0131s\u0131 Hesaplay\u0131c\u0131s\u0131<\/a> <\/div>\n<\/span> T\u00fcm istatistiksel form\u00fcllerin \u00f6zet tablosu<\/span><\/h2>\n Son olarak size temel istatistiksel form\u00fclleri \u00f6zetleyen bir tablo b\u0131rak\u0131yoruz. <\/p>\n![\"istatistiksel](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/formules-statistiques-.png\")
<\/figure>\n
<\/p>\n<\/p>\n
\u0130statistiklerde ortalama, aritmetik ortalama<\/strong> veya ortalama<\/strong> olarak da bilinir. <\/p>\n Medyan<\/strong> , en k\u00fc\u00e7\u00fckten en b\u00fcy\u00fc\u011fe do\u011fru s\u0131ralanan t\u00fcm verilerin ortadaki de\u011feridir. Ba\u015fka bir deyi\u015fle medyan s\u0131ral\u0131 veri setini iki e\u015fit par\u00e7aya b\u00f6ler.<\/p>\n Medyan\u0131n hesaplanmas\u0131, toplam veri say\u0131s\u0131n\u0131n \u00e7ift veya tek olmas\u0131na ba\u011fl\u0131d\u0131r:<\/p>\n Alt\u0131n<\/p>\n<\/p>\n \u00f6rnekteki toplam veri say\u0131s\u0131d\u0131r ve Me<\/em> simgesi medyan\u0131 g\u00f6sterir. <\/p>\n \u0130statistikte mod<\/strong> , veri k\u00fcmesindeki mutlak frekans\u0131 en y\u00fcksek olan de\u011ferdir, yani mod, bir veri k\u00fcmesinde en \u00e7ok tekrarlanan de\u011ferdir.<\/p>\n Bu nedenle, mod i\u00e7in \u00f6zel bir form\u00fcl yoktur, ancak 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 veriler mod olacakt\u0131r.<\/p>\n Modun istatistiksel mod<\/strong> veya modal de\u011fer<\/strong> oldu\u011fu da s\u00f6ylenebilir. <\/p>\n Standart sapma olarak da adland\u0131r\u0131lan standart sapma, veri serisindeki sapmalar\u0131n karelerinin toplam\u0131n\u0131n karek\u00f6k\u00fcn\u00fcn toplam g\u00f6zlem say\u0131s\u0131na b\u00f6l\u00fcnmesine e\u015fittir.<\/p>\n Bu nedenle standart sapman\u0131n form\u00fcl\u00fc<\/strong> \u015fu \u015fekildedir: <\/p>\n<\/p>\n Varyans<\/strong> , toplam g\u00f6zlem say\u0131s\u0131na g\u00f6re art\u0131klar\u0131n karelerinin toplam\u0131na e\u015fittir. Dolay\u0131s\u0131yla bu istatistiksel \u00f6l\u00e7\u00fcm\u00fcn form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n Alt\u0131n:<\/p>\n varyans\u0131n\u0131 hesaplamak istedi\u011finiz rastgele de\u011fi\u015fkendir.<\/li>\n veri de\u011feri<\/p>\n .<\/li>\n toplam g\u00f6zlem say\u0131s\u0131d\u0131r.<\/li>\n rastgele de\u011fi\u015fkenin ortalamas\u0131d\u0131r<\/p>\n . <\/li>\n<\/ul>\n \u0130statistikte varyasyon katsay\u0131s\u0131<\/strong> , bir veri k\u00fcmesinin ortalamas\u0131na g\u00f6re da\u011f\u0131l\u0131m\u0131n\u0131 belirlemek i\u00e7in kullan\u0131lan bir da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. De\u011fi\u015fim katsay\u0131s\u0131, verinin standart sapmas\u0131n\u0131n ortalamas\u0131na b\u00f6l\u00fcnmesi ve ard\u0131ndan de\u011ferin y\u00fczde olarak ifade edilmesi i\u00e7in 100 ile \u00e7arp\u0131lmas\u0131yla hesaplan\u0131r. <\/p>\n<\/p>\n \u0130statistiksel aral\u0131k,<\/strong> bir \u00f6rnekteki verilerin maksimum de\u011feri ile minimum de\u011feri aras\u0131ndaki fark\u0131 g\u00f6steren bir da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. Bu nedenle, bir pop\u00fclasyonun veya istatistiksel \u00f6rneklemin kapsam\u0131n\u0131 hesaplamak i\u00e7in maksimum de\u011ferin minimum de\u011ferden \u00e7\u0131kar\u0131lmas\u0131 gerekir. <\/p>\n<\/p>\n \u00c7eyrekler aras\u0131 aral\u0131k<\/strong> olarak da adland\u0131r\u0131lan \u00e7eyrekler aras\u0131<\/strong> aral\u0131k, \u00fc\u00e7\u00fcnc\u00fc ve birinci \u00e7eyrekler aras\u0131ndaki fark\u0131 g\u00f6steren istatistiksel da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcs\u00fcd\u00fcr.<\/p>\n Bu nedenle, bir istatistiksel veri setinin \u00e7eyrekler aras\u0131 aral\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in \u00f6nce \u00fc\u00e7\u00fcnc\u00fc ve birinci \u00e7eyrekleri bulman\u0131z ve ard\u0131ndan bunlar\u0131 \u00e7\u0131karman\u0131z gerekir. <\/p>\n<\/p>\n Ortalama<\/strong> mutlak sapma olarak da adland\u0131r\u0131lan ortalama<\/strong> sapma, mutlak sapmalar\u0131n ortalamas\u0131d\u0131r. Bu nedenle ortalama sapma, her veri \u00f6\u011fesinin aritmetik ortalamadan sapmalar\u0131n\u0131n toplam\u0131n\u0131n veri \u00f6\u011felerinin toplam say\u0131s\u0131na b\u00f6l\u00fcnmesine e\u015fittir. <\/p>\n<\/p>\n \u0130statistikte \u00e7eyrekler<\/strong> , s\u0131ral\u0131 bir veri k\u00fcmesini d\u00f6rt e\u015fit par\u00e7aya b\u00f6len \u00fc\u00e7 de\u011ferdir. B\u00f6ylece birinci, ikinci ve \u00fc\u00e7\u00fcnc\u00fc \u00e7eyrekler t\u00fcm istatistiksel verilerin s\u0131ras\u0131yla %25, %50 ve %75’ini temsil etmektedir.<\/p>\n \u00c7eyrekler b\u00fcy\u00fck Q ve \u00e7eyrek endeksi ile temsil edilir, dolay\u0131s\u0131yla ilk \u00e7eyrek Q 1<\/sub> , ikinci \u00e7eyrek Q 2<\/sub> ve \u00fc\u00e7\u00fcnc\u00fc \u00e7eyrek Q 3’t\u00fcr<\/sub> .<\/p>\n \u00c7eyrek form\u00fcl\u00fc<\/strong> \u015f\u00f6yledir:<\/p>\n<\/p>\n L\u00fctfen unutmay\u0131n:<\/strong> Bu form\u00fcl bize \u00e7eyre\u011fin de\u011ferini de\u011fil \u00e7eyre\u011fin konumunu s\u00f6yler. \u00c7eyrek, form\u00fcl taraf\u0131ndan elde edilen konumda bulunan veriler olacakt\u0131r.<\/p>\n Ancak bazen bu form\u00fcl\u00fcn sonucu bize ondal\u0131k bir say\u0131 verecektir. Bu nedenle sonucun ondal\u0131k say\u0131 olup olmamas\u0131na ba\u011fl\u0131 olarak iki durumu birbirinden ay\u0131rmam\u0131z gerekir:<\/p>\n Burada x i<\/sub><\/em> ve x i+1,<\/sub><\/em> birinci form\u00fclle elde edilen say\u0131n\u0131n aralar\u0131nda bulundu\u011fu konumlar\u0131n say\u0131lar\u0131d\u0131r ve d<\/em> , birinci form\u00fclle elde edilen say\u0131n\u0131n ondal\u0131k k\u0131sm\u0131d\u0131r. <\/p>\n \u0130statistikte ondal\u0131k say\u0131lar<\/strong> , s\u0131ral\u0131 bir veri k\u00fcmesini on e\u015fit par\u00e7aya b\u00f6len dokuz de\u011ferdir. B\u00f6ylece birinci, ikinci, \u00fc\u00e7\u00fcnc\u00fc,\u2026 ondal\u0131k dilim numunenin veya pop\u00fclasyonun %10, %20, %30,\u2026’unu temsil eder.<\/p>\n Ondal\u0131k dilimler b\u00fcy\u00fck D harfi ve ondal\u0131k indeks ile temsil edilir, yani ilk ondal\u0131k dilim D 1<\/sub> , ikinci ondal\u0131k dilim D 2<\/sub> , \u00fc\u00e7\u00fcnc\u00fc ondal\u0131k dilim D 3<\/sub> vb.<\/p>\n Ondal\u0131k form\u00fcl<\/strong> a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n L\u00fctfen unutmay\u0131n:<\/strong> Bu form\u00fcl bize ondal\u0131k dilimin de\u011ferini de\u011fil, ondal\u0131k dilimin konumunu s\u00f6yler. Ondal\u0131k k\u0131s\u0131m, form\u00fcl taraf\u0131ndan elde edilen konumda bulunan veriler olacakt\u0131r.<\/p>\n Ancak bazen bu form\u00fcl\u00fcn sonucu bize ondal\u0131k say\u0131 verir, bu nedenle sonucun ondal\u0131k say\u0131 olup olmad\u0131\u011f\u0131na ba\u011fl\u0131 olarak iki durumu ay\u0131rmam\u0131z gerekir:<\/p>\n Burada x i<\/sub><\/em> ve x i+1,<\/sub><\/em> birinci form\u00fclle elde edilen say\u0131n\u0131n aralar\u0131nda bulundu\u011fu konumlar\u0131n say\u0131lar\u0131d\u0131r ve d<\/em> , birinci form\u00fclle elde edilen say\u0131n\u0131n ondal\u0131k k\u0131sm\u0131d\u0131r. <\/p>\n \u0130statistikte y\u00fczdelikler<\/strong> , s\u0131ral\u0131 bir veri k\u00fcmesini y\u00fcz e\u015fit par\u00e7aya b\u00f6len de\u011ferlerdir. Yani y\u00fczdelik dilim, veri k\u00fcmesinin belirli bir y\u00fczdesinin alt\u0131na d\u00fc\u015ft\u00fc\u011f\u00fc de\u011feri belirtir.<\/p>\n Y\u00fczdelikler b\u00fcy\u00fck harf P ve y\u00fczdelik endeksi ile temsil edilir, yani ilk y\u00fczdelik dilim P 1<\/sub> , 40. y\u00fczdelik dilim P 40<\/sub> , 79. y\u00fczdelik dilim P 79<\/sub> vb.<\/p>\n Y\u00fczdelik form\u00fcl<\/strong> \u015f\u00f6yledir:<\/p>\n<\/p>\n L\u00fctfen unutmay\u0131n:<\/strong> Bu form\u00fcl bize y\u00fczdelik dilimin konumunu belirtir, ancak de\u011ferini vermez. Y\u00fczdelik dilim, form\u00fcl\u00fcn elde etti\u011fi konumda bulunan veriler olacakt\u0131r.<\/p>\n Ancak bazen bu form\u00fcl\u00fcn sonucu bize ondal\u0131k say\u0131 verir, bu nedenle sonucun ondal\u0131k say\u0131 olup olmad\u0131\u011f\u0131na ba\u011fl\u0131 olarak iki durumu ay\u0131rmam\u0131z gerekir:<\/p>\n Burada x i<\/sub><\/em> ve x i+1,<\/sub><\/em> birinci form\u00fclle elde edilen say\u0131n\u0131n aralar\u0131nda bulundu\u011fu konumlar\u0131n say\u0131lar\u0131d\u0131r ve d<\/em> , birinci form\u00fclle elde edilen say\u0131n\u0131n ondal\u0131k k\u0131sm\u0131d\u0131r. <\/p>\n \u00c7arp\u0131kl\u0131k katsay\u0131s\u0131 veya \u00e7arp\u0131kl\u0131k endeksi, bir da\u011f\u0131l\u0131m\u0131n \u00e7arp\u0131kl\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullan\u0131lan istatistiksel bir katsay\u0131d\u0131r. Yani asimetri katsay\u0131s\u0131n\u0131 hesaplayarak, da\u011f\u0131l\u0131m\u0131n asimetri t\u00fcr\u00fcn\u00fc, bunun grafiksel bir g\u00f6sterimini yapmaya gerek kalmadan \u00f6\u011frenebilirsiniz.<\/p>\n Asimetri katsay\u0131s\u0131n\u0131n form\u00fcl\u00fc<\/strong> a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n E\u015fde\u011fer olarak, Fisher asimetri katsay\u0131s\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki iki form\u00fclden herhangi biri kullan\u0131labilir:<\/p>\n<\/p>\n Alt\u0131n<\/p>\n<\/p>\n matematiksel beklenti,<\/p>\n aritmetik ortalama,<\/p>\n standart sapma ve<\/p>\n toplam veri say\u0131s\u0131. <\/p>\n Keskinlik olarak da adland\u0131r\u0131lan bas\u0131kl\u0131k, bir da\u011f\u0131l\u0131m\u0131n ortalama etraf\u0131nda ne kadar yo\u011funla\u015ft\u0131\u011f\u0131n\u0131 g\u00f6sterir. Ba\u015fka bir deyi\u015fle bas\u0131kl\u0131k, bir da\u011f\u0131l\u0131m\u0131n dik mi yoksa d\u00fcz m\u00fc oldu\u011funu g\u00f6sterir. Spesifik olarak, bir da\u011f\u0131l\u0131m\u0131n bas\u0131kl\u0131\u011f\u0131 ne kadar b\u00fcy\u00fck olursa, o kadar dik (veya daha keskin) olur.<\/p>\n Bas\u0131kl\u0131k katsay\u0131s\u0131n\u0131n form\u00fcl\u00fc<\/strong> a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n Alt\u0131n<\/p>\n<\/p>\n g\u00f6zleme kar\u015f\u0131l\u0131k gelen de\u011ferdir<\/p>\n ,<\/p>\n aritmetik ortalama,<\/p>\n standart sapma ve<\/p>\n toplam veri say\u0131s\u0131. <\/p>\n Son olarak size temel istatistiksel form\u00fclleri \u00f6zetleyen bir tablo b\u0131rak\u0131yoruz. <\/p>\n<\/span> Medyan<\/span><\/h3>\n
\n
<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/ul>\n<\/p>\n<\/span> Moda<\/span><\/h3>\n
<\/span> \u0130statistiksel da\u011f\u0131l\u0131m \u00f6l\u00e7\u00fcmleri i\u00e7in form\u00fcller <\/span><\/h2>\n
<\/span> Standart sapma<\/span><\/h3>\n
<\/p>\n<\/p>\n<\/span> Varyans<\/span><\/h3>\n
<\/p>\n<\/p>\n\n
<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/span> De\u011fi\u015fim katsay\u0131s\u0131<\/span><\/h3>\n
<\/p>\n<\/p>\n<\/span> D\u00fczenli<\/span><\/h3>\n
<\/p>\n<\/p>\n<\/span> \u00c7eyrekler aras\u0131 aral\u0131k<\/span><\/h3>\n
<\/p>\n<\/p>\n<\/span> orta fark<\/span><\/h3>\n
<\/p>\n<\/p>\n<\/span> \u0130statistiksel konum \u00f6l\u00e7\u00fcmleri i\u00e7in form\u00fcller <\/span><\/h2>\n
<\/span> \u00e7eyrekler<\/span><\/h3>\n
<\/p>\n<\/p>\n\n
<\/p>\n<\/p>\n<\/span> ondal\u0131k dilimler<\/span><\/h3>\n
<\/p>\n<\/p>\n\n
<\/p>\n<\/p>\n<\/span> y\u00fczdelikler<\/span><\/h3>\n
<\/p>\n<\/p>\n\n
<\/p>\n<\/p>\n<\/span> \u0130statistiksel \u015fekil \u00f6l\u00e7\u00fcm form\u00fclleri <\/span><\/h2>\n
<\/span>asimetri katsay\u0131s\u0131<\/span><\/h3>\n
<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/span>bas\u0131kl\u0131k katsay\u0131s\u0131<\/span><\/h3>\n
<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/p>\n<\/span> T\u00fcm istatistiksel form\u00fcllerin \u00f6zet tablosu<\/span><\/h2>\n
<\/figure>\n