{"id":1627,"date":"2023-07-25T14:37:56","date_gmt":"2023-07-25T14:37:56","guid":{"rendered":"https:\/\/statorials.org\/pl\/wazone-odchylenie-standardowe-w-r\/"},"modified":"2023-07-25T14:37:56","modified_gmt":"2023-07-25T14:37:56","slug":"wazone-odchylenie-standardowe-w-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/wazone-odchylenie-standardowe-w-r\/","title":{"rendered":"Jak obliczy\u0107 wa\u017cone odchylenie standardowe w r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Wa\u017cone odchylenie standardowe<\/strong> jest u\u017cyteczn\u0105 metod\u0105 pomiaru rozproszenia warto\u015bci w zbiorze danych, gdy niekt\u00f3re warto\u015bci w zbiorze danych maj\u0105 wy\u017csze wagi ni\u017c inne.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Wz\u00f3r na obliczenie wa\u017conego odchylenia standardowego jest nast\u0119puj\u0105cy:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14345 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pondere_sd1.png\" alt=\"\" width=\"218\" height=\"92\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>N:<\/strong> Ca\u0142kowita liczba <a href=\"https:\/\/statorials.org\/pl\/obserwacja-w-statystyce\/\" target=\"_blank\" rel=\"noopener\">obserwacji<\/a><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>M:<\/strong> Liczba niezerowych wag<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>w <sub>i<\/sub> :<\/strong> wektor wagi<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>i<\/sub> :<\/strong> wektor warto\u015bci danych<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x<\/span> :<\/strong> \u015arednia wa\u017cona<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Naj\u0142atwiejszym sposobem obliczenia wa\u017conego odchylenia standardowego w R jest u\u017cycie funkcji <strong>wt.var()<\/strong> z pakietu <strong>Hmisc<\/strong> , kt\u00f3ra wykorzystuje nast\u0119puj\u0105c\u0105 sk\u0142adni\u0119:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define data values<\/span>\nx &lt;- c(4, 7, 12, 13, ...)\n\n<span style=\"color: #008080;\">#define weights\n<\/span>wt &lt;- c(.5, 1, 2, 2, ...)\n\n<span style=\"color: #008080;\">#calculate weighted variance\n<\/span>weighted_var &lt;- wtd. <span style=\"color: #3366ff;\">var<\/span> (x, wt)\n\n<span style=\"color: #008080;\">#calculate weighted standard deviation\n<\/span>weighted_sd &lt;- sqrt(weighted_var)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Poni\u017csze przyk\u0142ady pokazuj\u0105, jak w praktyce wykorzysta\u0107 t\u0119 funkcj\u0119.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 1: Wa\u017cone odchylenie standardowe dla wektora<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak obliczy\u0107 wa\u017cone odchylenie standardowe dla pojedynczego wektora w R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #993300;\">library<\/span> (Hmisc)\n\n<span style=\"color: #008080;\">#define data values<\/span> \nx &lt;- c(14, 19, 22, 25, 29, 31, 31, 38, 40, 41)\n\n<span style=\"color: #008080;\">#define weights<\/span>\nwt &lt;- c(1, 1, 1.5, 2, 2, 1.5, 1, 2, 3, 2)\n\n<span style=\"color: #008080;\">#calculate weighted variance<\/span> \nweighted_var &lt;- wtd. <span style=\"color: #3366ff;\">var<\/span> (x, wt)\n\n<span style=\"color: #008080;\">#calculate weighted standard deviation\n<\/span>sqrt(weighted_var)\n\n[1] 8.570051\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Wa\u017cone odchylenie standardowe wynosi <strong>8,57<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 2: Wa\u017cone odchylenie standardowe dla kolumny w ramce danych<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak obliczy\u0107 wa\u017cone odchylenie standardowe dla kolumny ramki danych w R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #993300;\">library<\/span> (Hmisc)\n<span style=\"color: #008080;\">\n#define data frame\n<span style=\"color: #000000;\">df &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (team=c('A', 'A', 'A', 'A', 'A', 'B', 'B', 'C'),\n                 wins=c(2, 9, 11, 12, 15, 17, 18, 19),\n                 dots=c(1, 2, 2, 2, 3, 3, 3, 3))\n\n<span style=\"color: #008080;\">#define weights\n<\/span>wt &lt;- c(1, 1, 1.5, 2, 2, 1.5, 1, 2)\n\n<span style=\"color: #008080;\">#calculate weighted standard deviation of points\n<\/span>sqrt(wtd. <span style=\"color: #3366ff;\">var<\/span> (df$points, wt))\n\n[1] 0.6727938\n<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Wa\u017cone odchylenie standardowe dla kolumny punkt\u00f3w wynosi <strong>0,673<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 3: Wa\u017cone odchylenie standardowe dla wielu kolumn w ramce danych<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak u\u017cywa\u0107 funkcji <a href=\"https:\/\/statorials.org\/pl\/przewodnik-dotyczacy-stosowania-lapply-sapply-i-tapply-w-r\/\" target=\"_blank\" rel=\"noopener\">sapply()<\/a> w j\u0119zyku R do obliczania wa\u017conego odchylenia standardowego dla wielu kolumn w ramce danych:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #993300;\">library<\/span> (Hmisc)\n<span style=\"color: #008080;\">\n#define data frame\n<span style=\"color: #000000;\">df &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (team=c('A', 'A', 'A', 'A', 'A', 'B', 'B', 'C'),\n                 wins=c(2, 9, 11, 12, 15, 17, 18, 19),\n                 dots=c(1, 2, 2, 2, 3, 3, 3, 3))\n\n<span style=\"color: #008080;\">#define weights\n<\/span>wt &lt;- c(1, 1, 1.5, 2, 2, 1.5, 1, 2)\n\n<span style=\"color: #008080;\">#calculate weighted standard deviation of points and wins\n<\/span>sapply(df[c(' <span style=\"color: #008000;\">wins<\/span> ', ' <span style=\"color: #008000;\">points<\/span> ')], function(x) sqrt(wtd. <span style=\"color: #3366ff;\">var<\/span> (x, wt)))\n\n     win points \n4.9535723 0.6727938 \n<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Wa\u017cone odchylenie standardowe dla kolumny zwyci\u0119stw wynosi <strong>4,954<\/strong> , a wa\u017cone odchylenie standardowe dla kolumny punkt\u00f3w wynosi <strong>0,673<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pl\/wazone-odchylenie-standardowe-w-excelu\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 wa\u017cone odchylenie standardowe w programie Excel<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/odchylenie-standardowe-w-r\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 odchylenie standardowe w R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/wspo\u0142czynnik-zmiennosci-r\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 wsp\u00f3\u0142czynnik zmienno\u015bci R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/plaza-w-r\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 zasi\u0119g w R<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Wa\u017cone odchylenie standardowe jest u\u017cyteczn\u0105 metod\u0105 pomiaru rozproszenia warto\u015bci w zbiorze danych, gdy niekt\u00f3re warto\u015bci w zbiorze danych maj\u0105 wy\u017csze wagi ni\u017c inne. Wz\u00f3r na obliczenie wa\u017conego odchylenia standardowego jest nast\u0119puj\u0105cy: Z\u0142oto: N: Ca\u0142kowita liczba obserwacji M: Liczba niezerowych wag w i : wektor wagi x i : wektor warto\u015bci danych x : \u015arednia wa\u017cona [&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-1627","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 obliczy\u0107 wa\u017cone odchylenie standardowe w R<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, wraz z przyk\u0142adami, jak obliczy\u0107 wa\u017cone odchylenie standardowe w R.\" \/>\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\/wazone-odchylenie-standardowe-w-r\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak obliczy\u0107 wa\u017cone odchylenie standardowe w R\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, wraz z przyk\u0142adami, jak obliczy\u0107 wa\u017cone odchylenie standardowe w R.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/wazone-odchylenie-standardowe-w-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-25T14:37:56+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pondere_sd1.png\" \/>\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\/wazone-odchylenie-standardowe-w-r\/\",\"url\":\"https:\/\/statorials.org\/pl\/wazone-odchylenie-standardowe-w-r\/\",\"name\":\"Jak obliczy\u0107 wa\u017cone odchylenie standardowe w R\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-25T14:37:56+00:00\",\"dateModified\":\"2023-07-25T14:37:56+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, wraz z przyk\u0142adami, jak obliczy\u0107 wa\u017cone odchylenie standardowe w R.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/wazone-odchylenie-standardowe-w-r\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/wazone-odchylenie-standardowe-w-r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/wazone-odchylenie-standardowe-w-r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak obliczy\u0107 wa\u017cone odchylenie standardowe w r\"}]},{\"@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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