{"id":2508,"date":"2023-07-21T23:16:20","date_gmt":"2023-07-21T23:16:20","guid":{"rendered":"https:\/\/statorials.org\/pl\/wysrodkuj-dane-w-pythonie\/"},"modified":"2023-07-21T23:16:20","modified_gmt":"2023-07-21T23:16:20","slug":"wysrodkuj-dane-w-pythonie","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/wysrodkuj-dane-w-pythonie\/","title":{"rendered":"Jak wy\u015brodkowa\u0107 dane w pythonie: z przyk\u0142adami"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Centrowanie<\/strong> zbioru danych oznacza odj\u0119cie <a href=\"https:\/\/statorials.org\/pl\/mierzy-tendencje-centralna\/\" target=\"_blank\" rel=\"noopener\">\u015bredniej warto\u015bci<\/a> ka\u017cdej pojedynczej <a href=\"https:\/\/statorials.org\/pl\/obserwacja-w-statystyce\/\" target=\"_blank\" rel=\"noopener\">obserwacji<\/a> w zbiorze danych.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Po wy\u015brodkowaniu zestawu danych \u015brednia warto\u015b\u0107 zestawu danych wynosi zero.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017csze przyk\u0142ady pokazuj\u0105, jak wy\u015brodkowa\u0107 dane w Pythonie.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 1: Wy\u015brodkuj warto\u015bci tablicy NumPy<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce mamy nast\u0119puj\u0105c\u0105 tablic\u0119 NumPy:<\/span><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n\n<span style=\"color: #008080;\">#create NumPy array<\/span>\ndata = np. <span style=\"color: #3366ff;\">array<\/span> ([4, 6, 9, 13, 14, 17, 18, 19, 19, 21])\n\n<span style=\"color: #008080;\">#display mean of array<\/span>\n<span style=\"color: #008000;\">print<\/span> ( <span style=\"color: #3366ff;\">data.mean<\/span> ())\n\n14.0<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Mo\u017cemy zdefiniowa\u0107 <a href=\"https:\/\/statorials.org\/pl\/karta-cyfrowa\/\" target=\"_blank\" rel=\"noopener\">funkcj\u0119<\/a> odejmowania \u015bredniej warto\u015bci tablicy od ka\u017cdej indywidualnej obserwacji:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create function to data center\n<span style=\"color: #000000;\">center_function = <span style=\"color: #008000;\">lambda<\/span> x: x - x. <span style=\"color: #3366ff;\">mean<\/span> ()<\/span>\n\n#apply function to original NumPy array\n<span style=\"color: #000000;\">data_centered = center_function(data)\n<\/span>\n#view updated Array\n<span style=\"color: #000000;\"><span style=\"color: #008000;\">print<\/span> (data_centered)\n\narray([-10., -8., -5., -1., 0., 3., 4., 5., 5., 7.])\n<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Wynikowe warto\u015bci s\u0105 wy\u015brodkowanymi warto\u015bciami zbioru danych.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poniewa\u017c \u015brednia w oryginalnej tabeli wynosi\u0142a 14, funkcja ta po prostu odj\u0119\u0142a 14 od ka\u017cdej indywidualnej warto\u015bci w oryginalnej tabeli.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Na przyk\u0142ad:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Pierwsza warto\u015b\u0107 wy\u015brodkowanej tablicy = 4 \u2013 14 = <strong>-10<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">2. warto\u015b\u0107 tablicy wy\u015brodkowanej = 6 \u2013 14 = <strong>-8<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Trzecia warto\u015b\u0107 w wy\u015brodkowanej tablicy = 9 \u2013 14 = <strong>-5<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">I tak dalej.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Mo\u017cemy r\u00f3wnie\u017c sprawdzi\u0107, czy \u015brednia tabeli wy\u015brodkowanej wynosi zero:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#display mean of centered array<\/span>\n<span style=\"color: #008000;\">print<\/span> ( <span style=\"color: #3366ff;\">data_centered.mean<\/span> ())\n\n0.0<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 2: Wy\u015brodkuj kolumny ramki danych Pandas<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce mamy nast\u0119puj\u0105c\u0105 ramk\u0119 DataFrame pand:<\/span><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n\n<span style=\"color: #008080;\">#createDataFrame\n<\/span>df = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">x<\/span> ': [1, 4, 5, 6, 6, 8, 9],\n                   ' <span style=\"color: #ff0000;\">y<\/span> ': [7, 7, 8, 8, 8, 9, 12],\n                   ' <span style=\"color: #ff0000;\">z<\/span> ': [3, 3, 4, 4, 6, 7, 7]})\n\n<span style=\"color: #008080;\">#view DataFrame\n<\/span><span style=\"color: #008000;\">print<\/span> (df)\n\n   X Y Z\n0 1 7 3\n1 4 7 3\n2 5 8 4\n3 6 8 4\n4 6 8 6\n5 8 9 7\n6 9 12 7<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Mo\u017cemy u\u017cy\u0107 funkcji pandas <strong>Apply()<\/strong> do wy\u015brodkowania warto\u015bci ka\u017cdej kolumny w DataFrame:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#center the values in each column of the DataFrame<\/span>\ndf_centered = df. <span style=\"color: #3366ff;\">apply<\/span> ( <span style=\"color: #008000;\">lambda<\/span> x: <span style=\"color: #3366ff;\">xx.mean<\/span> ())\n\n<span style=\"color: #008080;\">#view centered DataFrame<\/span>\n<span style=\"color: #008000;\">print<\/span> (df_centered)\n\n\t        X Y Z\n0 -4.571429 -1.428571 -1.857143\n1 -1.571429 -1.428571 -1.857143\n2 -0.571429 -0.428571 -0.857143\n3 0.428571 -0.428571 -0.857143\n4 0.428571 -0.428571 1.142857\n5 2.428571 0.571429 2.142857\n6 3.428571 3.571429 2.142857 \n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Mo\u017cemy nast\u0119pnie sprawdzi\u0107, czy \u015brednia warto\u015b\u0107 ka\u017cdej kolumny wynosi zero:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#display mean of each column in the DataFrame<\/span>\ndf_centered. <span style=\"color: #3366ff;\">mean<\/span> ()\n\nx 2.537653e-16\ny-2.537653e-16\nz 3.806479e-16\ndtype:float64\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u015arednie kolumn s\u0105 wy\u015bwietlane w notacji naukowej, ale ka\u017cda warto\u015b\u0107 wynosi zasadniczo zero.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017csze samouczki wyja\u015bniaj\u0105, jak wykonywa\u0107 inne typowe operacje w Pythonie:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pl\/sredni-rozmiar-w-pythonie\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 \u015bredni\u0105 obci\u0119t\u0105 w Pythonie<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/oznacza-b\u0142ad-kwadratowy-pythona\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 \u015bredni b\u0142\u0105d kwadratowy (MSE) w Pythonie<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/pandy-srednie-wybrane-kolumny\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 \u015bredni\u0105 z wybranych kolumn w Pandach<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Centrowanie zbioru danych oznacza odj\u0119cie \u015bredniej warto\u015bci ka\u017cdej pojedynczej obserwacji w zbiorze danych. Po wy\u015brodkowaniu zestawu danych \u015brednia warto\u015b\u0107 zestawu danych wynosi zero. Poni\u017csze przyk\u0142ady pokazuj\u0105, jak wy\u015brodkowa\u0107 dane w Pythonie. Przyk\u0142ad 1: Wy\u015brodkuj warto\u015bci tablicy NumPy Za\u0142\u00f3\u017cmy, \u017ce mamy nast\u0119puj\u0105c\u0105 tablic\u0119 NumPy: import numpy as np #create NumPy array data = np. array ([4, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-2508","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jak wycentrowa\u0107 dane w Pythonie (z przyk\u0142adami) - Statologia<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, jak wy\u015brodkowa\u0107 dane w Pythonie, podaj\u0105c kilka przyk\u0142ad\u00f3w.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pl\/wysrodkuj-dane-w-pythonie\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak wycentrowa\u0107 dane w Pythonie (z przyk\u0142adami) - Statologia\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, jak wy\u015brodkowa\u0107 dane w Pythonie, podaj\u0105c kilka przyk\u0142ad\u00f3w.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/wysrodkuj-dane-w-pythonie\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-21T23:16:20+00:00\" \/>\n<meta name=\"author\" content=\"Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/wysrodkuj-dane-w-pythonie\/\",\"url\":\"https:\/\/statorials.org\/pl\/wysrodkuj-dane-w-pythonie\/\",\"name\":\"Jak wycentrowa\u0107 dane w Pythonie (z przyk\u0142adami) - Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-21T23:16:20+00:00\",\"dateModified\":\"2023-07-21T23:16:20+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, jak wy\u015brodkowa\u0107 dane w Pythonie, podaj\u0105c kilka przyk\u0142ad\u00f3w.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/wysrodkuj-dane-w-pythonie\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/wysrodkuj-dane-w-pythonie\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/wysrodkuj-dane-w-pythonie\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak wy\u015brodkowa\u0107 dane w pythonie: z przyk\u0142adami\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pl\/#website\",\"url\":\"https:\/\/statorials.org\/pl\/\",\"name\":\"Statorials\",\"description\":\"Tw\u00f3j przewodnik po kompetencjach statystycznych!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pl-PL\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\",\"name\":\"Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pl-PL\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin Anderson\"},\"description\":\"Cze\u015b\u0107, jestem Benjamin i jestem emerytowanym profesorem statystyki, kt\u00f3ry zosta\u0142 oddanym nauczycielem Statorials. 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