{"id":1062,"date":"2023-07-27T19:18:25","date_gmt":"2023-07-27T19:18:25","guid":{"rendered":"https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/"},"modified":"2023-07-27T19:18:25","modified_gmt":"2023-07-27T19:18:25","slug":"asymetria-kurtoza-pyton","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/","title":{"rendered":"Jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w pythonie"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">W statystyce <strong>sko\u015bno\u015b\u0107<\/strong> i <strong>kurtoza<\/strong> to dwa sposoby pomiaru kszta\u0142tu rozk\u0142adu.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Sko\u015bno\u015b\u0107<\/strong> jest miar\u0105 sko\u015bno\u015bci rozk\u0142adu. Warto\u015b\u0107 ta mo\u017ce by\u0107 dodatnia lub ujemna.<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Ujemna sko\u015bno\u015b\u0107 wskazuje, \u017ce ogon znajduje si\u0119 po lewej stronie rozk\u0142adu, kt\u00f3ry rozci\u0105ga si\u0119 w stron\u0119 bardziej ujemnych warto\u015bci.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Dodatnie pochylenie wskazuje, \u017ce ogon znajduje si\u0119 po prawej stronie rozk\u0142adu, kt\u00f3ry rozci\u0105ga si\u0119 w kierunku bardziej dodatnich warto\u015bci.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Warto\u015b\u0107 zero oznacza, \u017ce w rozk\u0142adzie nie ma asymetrii, co oznacza, \u017ce rozk\u0142ad jest doskonale symetryczny.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Kurtoza<\/strong> jest miar\u0105 tego, czy rozk\u0142ad jest ci\u0119\u017cki czy lekki w por\u00f3wnaniu z <a href=\"https:\/\/statorials.org\/pl\/rozk\u0142ad-normalny\/\" target=\"_blank\" rel=\"noopener noreferrer\">rozk\u0142adem normalnym<\/a> .<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Kurtoza rozk\u0142adu normalnego wynosi 3.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Je\u015bli dany rozk\u0142ad ma kurtoz\u0119 mniejsz\u0105 ni\u017c 3, nazywa si\u0119 go <em>playkurtycznym<\/em> , co oznacza, \u017ce ma tendencj\u0119 do tworzenia mniejszej liczby i mniej skrajnych warto\u015bci odstaj\u0105cych ni\u017c rozk\u0142ad normalny.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Je\u015bli dany rozk\u0142ad ma kurtoz\u0119 wi\u0119ksz\u0105 ni\u017c 3, nazywa si\u0119 go <em>leptokurtycznym<\/em> , co oznacza, \u017ce ma tendencj\u0119 do tworzenia wi\u0119kszej liczby warto\u015bci odstaj\u0105cych ni\u017c rozk\u0142ad normalny.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Uwaga:<\/strong> W niekt\u00f3rych wzorach (definicja Fishera) od kurtozy odejmuje si\u0119 3, aby u\u0142atwi\u0107 por\u00f3wnanie z rozk\u0142adem normalnym. Stosuj\u0105c t\u0119 definicj\u0119, rozk\u0142ad mia\u0142by wi\u0119ksz\u0105 kurtoz\u0119 ni\u017c rozk\u0142ad normalny, gdyby mia\u0142 warto\u015b\u0107 kurtozy wi\u0119ksz\u0105 ni\u017c 0.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W tym samouczku wyja\u015bniono, jak obliczy\u0107 zar\u00f3wno sko\u015bno\u015b\u0107, jak i kurtoz\u0119 danego zbioru danych w Pythonie.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad: Sko\u015bno\u015b\u0107 i sp\u0142aszczanie w Pythonie<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce mamy nast\u0119puj\u0105cy zbi\u00f3r danych:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>data = [88, 85, 82, 97, 67, 77, 74, 86, 81, 95, 77, 88, 85, 76, 81]\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Aby obliczy\u0107 przyk\u0142adow\u0105 sko\u015bno\u015b\u0107 i kurtoz\u0119 tego zbioru danych, mo\u017cemy u\u017cy\u0107 funkcji <a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.skew.html\" target=\"_blank\" rel=\"noopener noreferrer\">skew()<\/a> i <a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.kurtosis.html\" target=\"_blank\" rel=\"noopener noreferrer\">kurt()<\/a> z biblioteki Scipy Stata z nast\u0119puj\u0105c\u0105 sk\u0142adni\u0105:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>odchylenie (tablica warto\u015bci, odchylenie = fa\u0142sz)<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>kurt (tablica warto\u015bci, b\u0142\u0105d = fa\u0142sz)<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Argumentu <strong>odchylenie=Fa\u0142sz<\/strong> u\u017cywamy do obliczenia sko\u015bno\u015bci i kurtozy pr\u00f3bki w przeciwie\u0144stwie do sko\u015bno\u015bci i kurtozy populacji.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Oto jak u\u017cywa\u0107 tych funkcji dla naszego konkretnego zbioru danych:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\">data = [88, 85, 82, 97, 67, 77, 74, 86, 81, 95, 77, 88, 85, 76, 81]<\/span>\n\n#calculate sample skewness<\/span>\nskew(data, bias= <span style=\"color: #008000;\">False<\/span> )\n\n0.032697\n\n<span style=\"color: #008080;\">#calculate sample kurtosis<\/span>\nkurtosis(data, bias= <span style=\"color: #008000;\">False<\/span> )\n\n0.118157\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Sko\u015bno\u015b\u0107 wynosi <strong>0,032697<\/strong> , a kurtoza wynosi <strong>0,118157<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Oznacza to, \u017ce rozk\u0142ad jest lekko sko\u015bny dodatnio i ma wi\u0119cej warto\u015bci w ogonach w por\u00f3wnaniu do rozk\u0142adu normalnego.<\/span><\/p>\n<h3> <strong>Dodatkowe \u017ar\u00f3d\u0142o: Kalkulator sko\u015bno\u015bci i kurtozy<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Mo\u017cna tak\u017ce obliczy\u0107 sko\u015bno\u015b\u0107 dla danego zbioru danych, korzystaj\u0105c ze<\/span> <a href=\"https:\/\/statorials.org\/pl\" target=\"_blank\" rel=\"noopener noreferrer\">statystycznego kalkulatora sko\u015bno\u015bci i kurtozy<\/a> <span style=\"color: #000000;\">, kt\u00f3ry automatycznie oblicza sko\u015bno\u015b\u0107 i kurtoz\u0119 dla danego zbioru danych.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>W statystyce sko\u015bno\u015b\u0107 i kurtoza to dwa sposoby pomiaru kszta\u0142tu rozk\u0142adu. Sko\u015bno\u015b\u0107 jest miar\u0105 sko\u015bno\u015bci rozk\u0142adu. Warto\u015b\u0107 ta mo\u017ce by\u0107 dodatnia lub ujemna. Ujemna sko\u015bno\u015b\u0107 wskazuje, \u017ce ogon znajduje si\u0119 po lewej stronie rozk\u0142adu, kt\u00f3ry rozci\u0105ga si\u0119 w stron\u0119 bardziej ujemnych warto\u015bci. Dodatnie pochylenie wskazuje, \u017ce ogon znajduje si\u0119 po prawej stronie rozk\u0142adu, kt\u00f3ry rozci\u0105ga [&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-1062","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 sko\u015bno\u015b\u0107 i kurtoz\u0119 w Pythonie - Statologia<\/title>\n<meta name=\"description\" content=\"Proste wyja\u015bnienie, jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w Pythonie, \u0142\u0105cznie z przyk\u0142adami.\" \/>\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\/asymetria-kurtoza-pyton\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w Pythonie - Statologia\" \/>\n<meta property=\"og:description\" content=\"Proste wyja\u015bnienie, jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w Pythonie, \u0142\u0105cznie z przyk\u0142adami.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T19:18:25+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\/asymetria-kurtoza-pyton\/\",\"url\":\"https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/\",\"name\":\"Jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w Pythonie - Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-27T19:18:25+00:00\",\"dateModified\":\"2023-07-27T19:18:25+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Proste wyja\u015bnienie, jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w Pythonie, \u0142\u0105cznie z przyk\u0142adami.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w pythonie\"}]},{\"@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. Dzi\u0119ki bogatemu do\u015bwiadczeniu i wiedzy specjalistycznej w dziedzinie statystyki ch\u0119tnie dziel\u0119 si\u0119 swoj\u0105 wiedz\u0105, aby wzmocni\u0107 pozycj\u0119 uczni\u00f3w za po\u015brednictwem Statorials. Wiedzie\u0107 wi\u0119cej\",\"sameAs\":[\"https:\/\/statorials.org\/pl\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w Pythonie - Statologia","description":"Proste wyja\u015bnienie, jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w Pythonie, \u0142\u0105cznie z przyk\u0142adami.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/","og_locale":"pl_PL","og_type":"article","og_title":"Jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w Pythonie - Statologia","og_description":"Proste wyja\u015bnienie, jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w Pythonie, \u0142\u0105cznie z przyk\u0142adami.","og_url":"https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/","og_site_name":"Statorials","article_published_time":"2023-07-27T19:18:25+00:00","author":"Benjamin Anderson","twitter_card":"summary_large_image","twitter_misc":{"Napisane przez":"Benjamin Anderson","Szacowany czas czytania":"2 minuty"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/","url":"https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/","name":"Jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w Pythonie - Statologia","isPartOf":{"@id":"https:\/\/statorials.org\/pl\/#website"},"datePublished":"2023-07-27T19:18:25+00:00","dateModified":"2023-07-27T19:18:25+00:00","author":{"@id":"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965"},"description":"Proste wyja\u015bnienie, jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w Pythonie, \u0142\u0105cznie z przyk\u0142adami.","breadcrumb":{"@id":"https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/#breadcrumb"},"inLanguage":"pl-PL","potentialAction":[{"@type":"ReadAction","target":["https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/statorials.org\/pl\/asymetria-kurtoza-pyton\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Dom","item":"https:\/\/statorials.org\/pl\/"},{"@type":"ListItem","position":2,"name":"Jak obliczy\u0107 sko\u015bno\u015b\u0107 i kurtoz\u0119 w pythonie"}]},{"@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. Dzi\u0119ki bogatemu do\u015bwiadczeniu i wiedzy specjalistycznej w dziedzinie statystyki ch\u0119tnie dziel\u0119 si\u0119 swoj\u0105 wiedz\u0105, aby wzmocni\u0107 pozycj\u0119 uczni\u00f3w za po\u015brednictwem Statorials. Wiedzie\u0107 wi\u0119cej","sameAs":["https:\/\/statorials.org\/pl"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/posts\/1062","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/comments?post=1062"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/posts\/1062\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/media?parent=1062"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/categories?post=1062"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/tags?post=1062"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}