{"id":575,"date":"2023-07-29T10:57:35","date_gmt":"2023-07-29T10:57:35","guid":{"rendered":"https:\/\/statorials.org\/pl\/asymetria-w-excelu\/"},"modified":"2023-07-29T10:57:35","modified_gmt":"2023-07-29T10:57:35","slug":"asymetria-w-excelu","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/asymetria-w-excelu\/","title":{"rendered":"Jak obliczy\u0107 sko\u015bno\u015b\u0107 w programie excel"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Sko\u015bno\u015b\u0107<\/strong> jest miar\u0105 sko\u015bno\u015bci zbioru lub rozk\u0142adu danych. Warto\u015b\u0107 ta mo\u017ce by\u0107 dodatnia lub ujemna. Warto to wiedzie\u0107, poniewa\u017c pomaga nam zrozumie\u0107 kszta\u0142t rozk\u0142adu.<\/span><\/p>\n<p> <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><\/p>\n<p> <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><\/p>\n<p> <span style=\"color: #000000;\">Warto\u015b\u0107 zero oznacza, \u017ce w rozk\u0142adzie nie ma asymetrii, co oznacza, \u017ce rozk\u0142ad jest doskonale symetryczny. Jest to niezwyk\u0142e i rzadko spotykane w praktyce.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Jak obliczy\u0107 sko\u015bno\u015b\u0107 w programie Excel<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Excel udost\u0119pnia nast\u0119puj\u0105c\u0105 wbudowan\u0105 funkcj\u0119 obliczania sko\u015bno\u015bci rozk\u0142adu:<\/span><\/p>\n<p style=\"text-align: left;\"> <span style=\"color: #000000;\"><strong>=SKEW (tablica warto\u015bci)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ta funkcja wykorzystuje nast\u0119puj\u0105cy wz\u00f3r do obliczenia sko\u015bno\u015bci:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Asymetria = [n\/(n-1)(n-2)] * \u03a3[(x <sub>i<\/sub> \u2013 <span style=\"text-decoration: overline;\">x<\/span> )\/s] <sup>3<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<p> <span style=\"color: #000000;\">n = wielko\u015b\u0107 pr\u00f3bki<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03a3 = fantazyjny symbol oznaczaj\u0105cy \u201esum\u0119\u201d<\/span><\/p>\n<p> <span style=\"color: #000000;\">x <sub>i<\/sub> = warto\u015b\u0107 <sup>i-tej<\/sup> warto\u015bci w zbiorze danych<\/span><\/p>\n<p> <span style=\"color: #000000;\"><span style=\"text-decoration: overline;\">x<\/span> = \u015brednia<\/span><\/p>\n<p> <span style=\"color: #000000;\">s = odchylenie standardowe<\/span><\/p>\n<p> <span style=\"color: #000000;\">Formu\u0142a jest nieco skomplikowana, ale na szcz\u0119\u015bcie Excel wykonuje te obliczenia za Ciebie, wi\u0119c nie musisz tego robi\u0107 r\u0119cznie.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Przyk\u0142ad: obliczanie asymetrii w programie Excel<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce mamy nast\u0119puj\u0105cy zbi\u00f3r danych zawieraj\u0105cy wyniki egzamin\u00f3w 20 uczni\u00f3w:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5233 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/inclinaisonexcel0.png\" alt=\"Przyk\u0142ad tabeli warto\u015bci w programie Excel\" width=\"545\" height=\"569\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Mo\u017cemy obliczy\u0107 sko\u015bno\u015b\u0107 rozk\u0142adu za pomoc\u0105 <strong>=SKEW(A2:A21)<\/strong><\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5234 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/inclinaisonexcel1.png\" alt=\"Jak obliczy\u0107 sko\u015bno\u015b\u0107 w programie Excel\" width=\"560\" height=\"609\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">To m\u00f3wi nam, \u017ce sko\u015bno\u015b\u0107 tego zbioru danych wynosi <strong>-0,1849<\/strong> . Poniewa\u017c ta warto\u015b\u0107 jest ujemna, wiemy, \u017ce ogon rozk\u0142adu rozci\u0105ga si\u0119 w lewo.<\/span><\/p>\n<blockquote>\n<p> <span style=\"color: #000000;\"><strong>Uwaga techniczna:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Funkcja SKEW() zwr\u00f3ci b\u0142\u0105d #DIV\/0! w dw\u00f3ch nast\u0119puj\u0105cych scenariuszach:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Je\u015bli jest mniej ni\u017c trzy punkty danych<\/span><\/li>\n<li> <span style=\"color: #000000;\">Je\u015bli odchylenie standardowe pr\u00f3bki wynosi zero<\/span><\/li>\n<\/ul>\n<\/blockquote>\n<h2> <span style=\"color: #000000;\"><strong>Dodatkowe \u017ar\u00f3d\u0142o: Kalkulator sko\u015bno\u015bci i kurtozy<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Mo\u017cna tak\u017ce obliczy\u0107 sko\u015bno\u015b\u0107 dla danego zbioru danych, korzystaj\u0105c ze <a href=\"https:\/\/statorials.org\/pl\" target=\"_blank\" rel=\"noopener\">statystycznego kalkulatora sko\u015bno\u015bci i kurtozy<\/a> , kt\u00f3ry automatycznie oblicza sko\u015bno\u015b\u0107 i kurtoz\u0119 dla danego zbioru danych. Wystarczy wpisa\u0107 nieprzetworzone warto\u015bci danych dla swojego zbioru danych w polu wej\u015bciowym, a nast\u0119pnie klikn\u0105\u0107 \u201eOblicz\u201d.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Oto jak na przyk\u0142ad obliczy\u0107 sko\u015bno\u015b\u0107 zbioru danych na podstawie powy\u017cszego przyk\u0142adu:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5236 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/inclinaisonexcel2.png\" alt=\"Przyk\u0142ad kalkulatora asymetrii\" width=\"500\" height=\"707\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Nale\u017cy pami\u0119ta\u0107, \u017ce warto\u015b\u0107 sko\u015bno\u015bci z kalkulatora jest zgodna z warto\u015bci\u0105 sko\u015bno\u015bci znalezion\u0105 w Excelu.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sko\u015bno\u015b\u0107 jest miar\u0105 sko\u015bno\u015bci zbioru lub rozk\u0142adu danych. Warto\u015b\u0107 ta mo\u017ce by\u0107 dodatnia lub ujemna. Warto to wiedzie\u0107, poniewa\u017c pomaga nam zrozumie\u0107 kszta\u0142t rozk\u0142adu. 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 [&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-575","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 asymetri\u0119 w programie Excel - Statologia<\/title>\n<meta name=\"description\" content=\"Proste wyja\u015bnienie sposobu obliczania sko\u015bno\u015bci dla danego zbioru danych w programie Excel wraz z przyk\u0142adem.\" \/>\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-w-excelu\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak obliczy\u0107 asymetri\u0119 w programie Excel - Statologia\" \/>\n<meta property=\"og:description\" content=\"Proste wyja\u015bnienie sposobu obliczania sko\u015bno\u015bci dla danego zbioru danych w programie Excel wraz z przyk\u0142adem.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/asymetria-w-excelu\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T10:57:35+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/inclinaisonexcel0.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\/asymetria-w-excelu\/\",\"url\":\"https:\/\/statorials.org\/pl\/asymetria-w-excelu\/\",\"name\":\"Jak obliczy\u0107 asymetri\u0119 w programie Excel - Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-29T10:57:35+00:00\",\"dateModified\":\"2023-07-29T10:57:35+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Proste wyja\u015bnienie sposobu obliczania sko\u015bno\u015bci dla danego zbioru danych w programie Excel wraz z przyk\u0142adem.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/asymetria-w-excelu\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/asymetria-w-excelu\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/asymetria-w-excelu\/#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 w programie excel\"}]},{\"@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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