{"id":120,"date":"2023-08-05T05:58:55","date_gmt":"2023-08-05T05:58:55","guid":{"rendered":"https:\/\/statorials.org\/pt\/regra-de-sturge-1\/"},"modified":"2023-08-05T05:58:55","modified_gmt":"2023-08-05T05:58:55","slug":"regra-de-sturge-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/regra-de-sturge-1\/","title":{"rendered":"Regra de sturges"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 a regra de Sturges e qual \u00e9 sua f\u00f3rmula. Voc\u00ea tamb\u00e9m encontrar\u00e1 um exemplo concreto passo a passo da regra de Sturges e, al\u00e9m disso, uma calculadora online da regra de Sturges. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-regla-de-sturges\"><\/span> Qual \u00e9 a regra de Sturges?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>A regra de Sturges<\/strong> \u00e9 uma regra usada para calcular o n\u00famero ideal de classes ou intervalos nos quais um conjunto de dados deve ser dividido.<\/p>\n<p> A <strong>f\u00f3rmula da regra de Sturges<\/strong> afirma que o n\u00famero de classes \u00e9 igual a um mais o logaritmo de base dois do n\u00famero total de dados.<\/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> Ouro<\/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> \u00e9 o n\u00famero de classes ou intervalos e<\/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> \u00e9 o n\u00famero total de observa\u00e7\u00f5es na amostra. <\/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\"> A maioria das calculadoras s\u00f3 permite c\u00e1lculos com logaritmos de base 10. Neste caso, voc\u00ea pode usar esta f\u00f3rmula equivalente:<\/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> A regra de Sturges foi criada em 1926 pelo estat\u00edstico alem\u00e3o Herbert Sturges. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-regla-de-sturges\"><\/span> Exemplo de regra de Sturges<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agora que sabemos o que \u00e9 a regra de Sturges, veremos, resolvendo um exerc\u00edcio passo a passo, como os intervalos de um conjunto de dados s\u00e3o calculados usando a regra de Sturges em estat\u00edstica.<\/p>\n<ul>\n<li> O tamanho da amostra de 50 pessoas diferentes foi medido e todos os valores foram registrados na tabela de dados a seguir. Aplique a regra de Sturges para dividir o conjunto de dados em intervalos e, em seguida, represente os dados em um histograma. <\/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> Primeiro, precisamos separar os dados em intervalos. No total existem 50 elementos de dados, ent\u00e3o usamos a regra de Sturges com este valor:<\/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> \u00c9 necess\u00e1rio, portanto, separar os dados e agrup\u00e1-los em sete intervalos. Precisamos agora saber a largura de cada intervalo, para isso basta dividir o valor m\u00e1ximo menos o valor m\u00ednimo pelo n\u00famero total de intervalos:<\/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> Resumindo, deve haver 7 intervalos com amplitude de 9, ent\u00e3o os intervalos calculados pelo m\u00e9todo de Sturges s\u00e3o: <\/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> Depois de calcularmos os intervalos, precisamos contar o n\u00famero de vezes que um dado aparece em cada intervalo e construir a tabela de frequ\u00eancia: <\/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> Finalmente, a partir da tabela de frequ\u00eancia, podemos criar o histograma para representar graficamente os dados: <\/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=\"Histograma da regra de Sturges, estat\u00edsticas\" 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>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/histograma\/\">como fazer um histograma<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-regla-de-sturges\"><\/span> Calculadora de regras de Sturges<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Insira o n\u00famero total de amostras de dados e clique em \u201cCalcular\u201d, ent\u00e3o a calculadora retornar\u00e1 o n\u00famero de intervalos calculados de acordo com a regra de Sturges.<\/p>\n<form action=\"\" method=\"post\">\n<ul style=\"color:#1C2C92;\">\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">N\u00famero total de dados = <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=\"Calcular\"><\/div>\n<\/form>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 a regra de Sturges e qual \u00e9 sua f\u00f3rmula. Voc\u00ea tamb\u00e9m encontrar\u00e1 um exemplo concreto passo a passo da regra de Sturges e, al\u00e9m disso, uma calculadora online da regra de Sturges. Qual \u00e9 a regra de Sturges? A regra de Sturges \u00e9 uma regra usada para calcular o [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-120","post","type-post","status-publish","format-standard","hentry","category-estatisticas"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Regra de Sturges: f\u00f3rmula, exemplo e calculadora<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a regra de Sturges, qual a sua f\u00f3rmula, um exemplo concreto e, tamb\u00e9m, uma calculadora da regra de Sturges.\" \/>\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\/pt\/regra-de-sturge-1\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Regra de Sturges: f\u00f3rmula, exemplo e calculadora\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a regra de Sturges, qual a sua f\u00f3rmula, um exemplo concreto e, tamb\u00e9m, uma calculadora da regra de Sturges.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/regra-de-sturge-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=\"Dr. benjamim anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. benjamim anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo estimado de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/regra-de-sturge-1\/\",\"url\":\"https:\/\/statorials.org\/pt\/regra-de-sturge-1\/\",\"name\":\"\u25b7 Regra de Sturges: f\u00f3rmula, exemplo e calculadora\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-05T05:58:55+00:00\",\"dateModified\":\"2023-08-05T05:58:55+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a regra de Sturges, qual a sua f\u00f3rmula, um exemplo concreto e, tamb\u00e9m, uma calculadora da regra de Sturges.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/regra-de-sturge-1\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/regra-de-sturge-1\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/regra-de-sturge-1\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Regra de sturges\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pt\/#website\",\"url\":\"https:\/\/statorials.org\/pt\/\",\"name\":\"Statorials\",\"description\":\"O seu guia para a literacia estat\u00edstica!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-PT\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\",\"name\":\"Dr. benjamim anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-PT\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr. benjamim anderson\"},\"description\":\"Ol\u00e1, sou Benjamin, um professor aposentado de estat\u00edstica que se tornou professor dedicado na Statorials. 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