{"id":119,"date":"2023-08-05T05:58:55","date_gmt":"2023-08-05T05:58:55","guid":{"rendered":"https:\/\/statorials.org\/pl\/sturges-zasada-1\/"},"modified":"2023-08-05T05:58:55","modified_gmt":"2023-08-05T05:58:55","slug":"sturges-zasada-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/sturges-zasada-1\/","title":{"rendered":"Regu\u0142a sturgesa"},"content":{"rendered":"<p>W tym artykule wyja\u015bniono, czym jest regu\u0142a Sturgesa i jaki jest jej wz\u00f3r. Znajdziesz tu tak\u017ce konkretny przyk\u0142ad regu\u0142y Sturgesa krok po kroku, a dodatkowo kalkulator regu\u0142 Sturgesa dost\u0119pny online. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-regla-de-sturges\"><\/span> Na czym polega regu\u0142a Sturgesa?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Regu\u0142a Sturgesa<\/strong> to regu\u0142a u\u017cywana do obliczania idealnej liczby klas lub przedzia\u0142\u00f3w, na kt\u00f3re nale\u017cy podzieli\u0107 zbi\u00f3r danych.<\/p>\n<p> <strong>Wz\u00f3r na regu\u0142\u0119 Sturgesa<\/strong> stwierdza, \u017ce liczba klas jest r\u00f3wna jeden plus dwa logarytmy podstawy ca\u0142kowitej liczby danych.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-698dc950acb10ce0e5c969138924f8e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c=1+\\log_2(N)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Z\u0142oto<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> to liczba klas lub interwa\u0142\u00f3w i<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7354bae77b50b7d1faed3e8ea7a3511a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"N\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> to ca\u0142kowita liczba obserwacji w pr\u00f3bie. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2px dashed #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> Wi\u0119kszo\u015b\u0107 kalkulator\u00f3w umo\u017cliwia obliczenia wy\u0142\u0105cznie przy u\u017cyciu logarytm\u00f3w o podstawie 10. W takim przypadku mo\u017cesz u\u017cy\u0107 r\u00f3wnowa\u017cnej formu\u0142y:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e603cacb4a44525f80831af2616a1bbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c=1+\\cfrac{\\log(N)}{\\log(2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"120\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<\/div>\n<p> Regu\u0142a Sturgesa zosta\u0142a stworzona w 1926 roku przez niemieckiego statystyka Herberta Sturgesa. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-regla-de-sturges\"><\/span> Przyk\u0142ad regu\u0142y Sturgesa<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Teraz, gdy wiemy, czym jest regu\u0142a Sturgesa, rozwi\u0105zuj\u0105c krok po kroku \u0107wiczenie, zobaczymy, w jaki spos\u00f3b obliczane s\u0105 przedzia\u0142y zbioru danych przy u\u017cyciu regu\u0142y Sturgesa w statystyce.<\/p>\n<ul>\n<li> Zmierzono wielko\u015b\u0107 pr\u00f3by 50 r\u00f3\u017cnych os\u00f3b i wszystkie warto\u015bci zapisano w poni\u017cszej tabeli danych. Zastosuj regu\u0142\u0119 Sturgesa, aby podzieli\u0107 zbi\u00f3r danych na przedzia\u0142y, a nast\u0119pnie wykre\u015bl dane na histogramie. <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/table-de-donnees-exemple-hauteurs-50.png\" alt=\"\" class=\"wp-image-2658\" width=\"278\" height=\"308\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Najpierw musimy podzieli\u0107 dane na przedzia\u0142y. W sumie jest 50 element\u00f3w danych, dlatego u\u017cywamy regu\u0142y Sturgesa z t\u0105 warto\u015bci\u0105:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9929b0c8f1f7cdf5a6160c07e0205c46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}c=1+\\log_2(N)\\\\[2ex]c=1+\\log_2(50)\\\\[2ex]c=1+5,64\\\\[2ex]c=6,64\\\\[2ex]c\\approx 7\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"163\" width=\"123\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Konieczne jest zatem rozdzielenie danych i pogrupowanie ich w siedem przedzia\u0142\u00f3w. Musimy teraz zna\u0107 szeroko\u015b\u0107 ka\u017cdego przedzia\u0142u. Aby to zrobi\u0107, po prostu podziel warto\u015b\u0107 maksymaln\u0105 minus warto\u015b\u0107 minimalna przez ca\u0142kowit\u0105 liczb\u0119 przedzia\u0142\u00f3w:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d2262a449f1f5c4b97b56a42634f5c96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a=\\cfrac{\\text{valor m\\'aximo}-\\text{valor m\\'inimo}}{c}=\\cfrac{205-145}{7}=8,57\\approx 9\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"455\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> W skr\u00f3cie musi by\u0107 7 przedzia\u0142\u00f3w o amplitudzie 9, zatem odst\u0119py obliczone metod\u0105 Sturgesa wynosz\u0105: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-99799593eebc0e84d41d373a87702a19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"[145,154)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0462d79f704bce614d9809cae68048d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"[154,163)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f641927f9e99b65d4110400e0b179ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"[163,172)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c72d71a970f7f0015b23148d661df394_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"[172,181)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9220265d8613852762ac5390aa753bce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"[181,190)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3a009436f79f59d54aff2e6eec655a8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"[190,199)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7c6484fb09d31cd972ce7e82c58d7832_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"[199,208)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Po obliczeniu przedzia\u0142\u00f3w musimy policzy\u0107, ile razy dana cz\u0119\u015b\u0107 danych pojawia si\u0119 w ka\u017cdym przedziale i skonstruowa\u0107 tabel\u0119 cz\u0119sto\u015bci: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/regle-de-sturges-tableau-de-frequences.png\" alt=\"\" class=\"wp-image-2664\" width=\"196\" height=\"271\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Na koniec, z tabeli cz\u0119sto\u015bci, mo\u017cemy utworzy\u0107 histogram, aby przedstawi\u0107 wykres danych: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/histogramme-regle-sturges.png\" alt=\"Histogram regu\u0142y Sturgesa, statystyki\" class=\"wp-image-2665\" width=\"512\" height=\"330\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Zobacz:<\/strong> <a href=\"https:\/\/statorials.org\/pl\/histogram\/\">jak zrobi\u0107 histogram<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-regla-de-sturges\"><\/span> Kalkulator regu\u0142 Sturgesa<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Wprowad\u017a ca\u0142kowit\u0105 liczb\u0119 pr\u00f3bek danych i kliknij \u201eOblicz\u201d, w\u00f3wczas kalkulator zwr\u00f3ci liczb\u0119 przedzia\u0142\u00f3w obliczon\u0105 wed\u0142ug regu\u0142y Sturgesa.<\/p>\n<form action=\"\" method=\"post\">\n<ul style=\"color:#1C2C92;\">\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Ca\u0142kowita liczba danych = <input name=\"datos\" style=\"border:1.5px solid #1C2C92; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" placeholder=\"50\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el n\u00famero total de datos aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/span> <\/li>\n<\/ul>\n<div style=\"text-align:center\"><input align=\"center\" style=\"font-size:105%; border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"Oblicz\"><\/div>\n<\/form>\n","protected":false},"excerpt":{"rendered":"<p>W tym artykule wyja\u015bniono, czym jest regu\u0142a Sturgesa i jaki jest jej wz\u00f3r. Znajdziesz tu tak\u017ce konkretny przyk\u0142ad regu\u0142y Sturgesa krok po kroku, a dodatkowo kalkulator regu\u0142 Sturgesa dost\u0119pny online. Na czym polega regu\u0142a Sturgesa? Regu\u0142a Sturgesa to regu\u0142a u\u017cywana do obliczania idealnej liczby klas lub przedzia\u0142\u00f3w, na kt\u00f3re nale\u017cy podzieli\u0107 zbi\u00f3r danych. Wz\u00f3r na [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-119","post","type-post","status-publish","format-standard","hentry","category-statystyka"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Regu\u0142a Sturgesa: wz\u00f3r, przyk\u0142ad i kalkulator<\/title>\n<meta name=\"description\" content=\"Tutaj znajdziesz czym jest regu\u0142a Sturgesa, jaki jest jej wz\u00f3r, konkretny przyk\u0142ad, a tak\u017ce kalkulator regu\u0142y Sturgesa.\" \/>\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\/sturges-zasada-1\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Regu\u0142a Sturgesa: wz\u00f3r, przyk\u0142ad i kalkulator\" \/>\n<meta property=\"og:description\" content=\"Tutaj znajdziesz czym jest regu\u0142a Sturgesa, jaki jest jej wz\u00f3r, konkretny przyk\u0142ad, a tak\u017ce kalkulator regu\u0142y Sturgesa.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/sturges-zasada-1\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-05T05:58:55+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-698dc950acb10ce0e5c969138924f8e8_l3.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\/sturges-zasada-1\/\",\"url\":\"https:\/\/statorials.org\/pl\/sturges-zasada-1\/\",\"name\":\"\u25b7 Regu\u0142a Sturgesa: wz\u00f3r, przyk\u0142ad i kalkulator\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-08-05T05:58:55+00:00\",\"dateModified\":\"2023-08-05T05:58:55+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Tutaj znajdziesz czym jest regu\u0142a Sturgesa, jaki jest jej wz\u00f3r, konkretny przyk\u0142ad, a tak\u017ce kalkulator regu\u0142y Sturgesa.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/sturges-zasada-1\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/sturges-zasada-1\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/sturges-zasada-1\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Regu\u0142a sturgesa\"}]},{\"@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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