{"id":138,"date":"2023-08-05T01:17:41","date_gmt":"2023-08-05T01:17:41","guid":{"rendered":"https:\/\/statorials.org\/pt\/coeficiente-de-achatamento\/"},"modified":"2023-08-05T01:17:41","modified_gmt":"2023-08-05T01:17:41","slug":"coeficiente-de-achatamento","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/coeficiente-de-achatamento\/","title":{"rendered":"Coeficiente de achatamento"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 o coeficiente de curtose e como calcular o coeficiente de curtose. Voc\u00ea encontrar\u00e1 a f\u00f3rmula do coeficiente de curtose, como seu resultado \u00e9 interpretado e, al\u00e9m disso, poder\u00e1 calcular o coeficiente de curtose de qualquer amostra de dados com uma calculadora online. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-coeficiente-de-curtosis\"><\/span> Qual \u00e9 o coeficiente de curtose?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O <strong>coeficiente de curtose<\/strong> \u00e9 um coeficiente que permite determinar a curtose de uma distribui\u00e7\u00e3o. Em outras palavras, o coeficiente de curtose \u00e9 utilizado para saber se uma distribui\u00e7\u00e3o \u00e9 leptoc\u00fartica, platic\u00fartica ou mesoc\u00fartica.<\/p>\n<p> A curtose \u00e9 uma caracter\u00edstica de uma distribui\u00e7\u00e3o que indica seu grau de concentra\u00e7\u00e3o em torno da m\u00e9dia, portanto, o c\u00e1lculo do coeficiente de curtose ajuda a quantificar a curtose de uma distribui\u00e7\u00e3o. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-coeficiente-de-curtosis\"><\/span> F\u00f3rmula do coeficiente de curtose<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para calcular o coeficiente de curtose, voc\u00ea deve primeiro somar todas as diferen\u00e7as entre os dados e a m\u00e9dia elevada \u00e0 pot\u00eancia de quatro, depois dividir pelo n\u00famero total de dados e o desvio padr\u00e3o elevado \u00e0 pot\u00eancia de quatro e, finalmente, subtrair tr\u00eas .<\/p>\n<p> Em outras palavras, a <strong>f\u00f3rmula do coeficiente de curtose<\/strong> \u00e9 a seguinte:<\/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-90817c2e65eaadd93ca788fd87067144_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle g_2=\\frac{1}{N}\\cdot\\frac{\\displaystyle \\sum_{i=1}^N(x_i-\\mu)^4}{\\sigma^4}-3\" title=\"Rendered by QuickLaTeX.com\" height=\"73\" width=\"202\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> A f\u00f3rmula do coeficiente de curtose para <strong>dados agrupados em tabelas de frequ\u00eancia<\/strong> :<\/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-d7d2fd2426582c6ec35fab553a2922be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle g_2=\\frac{1}{N}\\cdot\\frac{\\displaystyle \\sum_{i=1}^N f_i\\cdot(x_i-\\mu)^4}{\\sigma^4}-3\" title=\"Rendered by QuickLaTeX.com\" height=\"73\" width=\"232\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Por fim, a f\u00f3rmula do coeficiente de curtose para <strong>dados agrupados<\/strong> :<\/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-46118fdded8bfd0f49b423b704893f96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle g_2=\\frac{1}{N}\\cdot\\frac{\\displaystyle \\sum_{i=1}^N f_i\\cdot(c_i-\\mu)^4}{\\sigma^4}-3\" title=\"Rendered by QuickLaTeX.com\" height=\"73\" width=\"230\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-056a86612914d05ca2e8e22994a8ac69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 o coeficiente de curtose.<\/li>\n<li style=\"margin-bottom:5px\">\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 dados.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o i-\u00e9simo ponto de dados da s\u00e9rie.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a <a href=\"https:\/\/statorials.org\/pt\/media-aritmetica\/\">m\u00e9dia aritm\u00e9tica<\/a> da distribui\u00e7\u00e3o.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-eaaf379fee5e67946f3fedf5631047b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o <a href=\"https:\/\/statorials.org\/pt\/desvio-padrao-ou-desvio-padrao\/\">desvio padr\u00e3o (ou desvio t\u00edpico)<\/a> da distribui\u00e7\u00e3o.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fcb89ec1b112c79bfb56f1c210f6bb67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f_i\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a frequ\u00eancia absoluta do conjunto de dados it.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1f20a6892ce371ba90592748cd2c20ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"c_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 a nota da classe do i-\u00e9simo grupo.<\/li>\n<\/ul>\n<p> Observe que em todas as f\u00f3rmulas do coeficiente de curtose, 3 \u00e9 subtra\u00eddo porque \u00e9 o valor da curtose da distribui\u00e7\u00e3o normal. Portanto, o coeficiente de curtose \u00e9 calculado tendo como refer\u00eancia a curtose da distribui\u00e7\u00e3o normal. \u00c9 por isso que \u00e0s vezes nas estat\u00edsticas se diz que se calcula <strong>uma curtose excessiva<\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"interpretacion-del-coeficiente-de-curtosis\"><\/span> Interpreta\u00e7\u00e3o do coeficiente de curtose<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>interpreta\u00e7\u00e3o do coeficiente de curtose<\/strong> \u00e9 a seguinte:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Se o coeficiente de curtose for positivo, a distribui\u00e7\u00e3o \u00e9 leptoc\u00fartica.<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">Se o coeficiente de curtose for zero, a distribui\u00e7\u00e3o \u00e9 mesoc\u00fartica.<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\">Se o coeficiente de curtose for negativo, a distribui\u00e7\u00e3o \u00e9 platic\u00fartica.<\/span> <\/li>\n<\/ul>\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\/types-daplatissement.png\" alt=\"tipos de lisonjeiro\" class=\"wp-image-3045\" width=\"742\" height=\"188\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Resumindo, quanto maior o coeficiente de curtose significa que a distribui\u00e7\u00e3o tem mais curtose e, inversamente, quanto menor o coeficiente de curtose significa que a distribui\u00e7\u00e3o tem menos curtose. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-del-coeficiente-de-curtosis\"><\/span> Calculadora de coeficiente de achatamento<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Insira um conjunto de dados na calculadora abaixo para calcular seu coeficiente de curtose. Os dados devem ser separados por espa\u00e7o e inseridos usando o ponto final como separador decimal. <\/p>\n<form action=\"\" method=\"post\"><textarea name=\"datos\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"1 2 3 9.7 10 65.91 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los datos aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"Calcular\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-del-coeficiente-de-curtosis\"><\/span> Propriedades do coeficiente de curtose<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O coeficiente de curtose tem as seguintes propriedades:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">O coeficiente de curtose \u00e9 uma medida adimensional.<\/span><\/li>\n<li style=\"margin-bottom:12px\"> <span style=\"color:#101010;font-weight: normal;\">O coeficiente de curtose \u00e9 calculado utilizando a curtose da distribui\u00e7\u00e3o normal (g <sub>2<\/sub> =3) como refer\u00eancia.<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\">O coeficiente de curtose \u00e9 invariante em rela\u00e7\u00e3o \u00e0s mudan\u00e7as de escala, ou seja, mesmo que seja aplicada uma transforma\u00e7\u00e3o linear \u00e0 vari\u00e1vel estat\u00edstica, o valor do coeficiente de curtose \u00e9 o mesmo.<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 o coeficiente de curtose e como calcular o coeficiente de curtose. Voc\u00ea encontrar\u00e1 a f\u00f3rmula do coeficiente de curtose, como seu resultado \u00e9 interpretado e, al\u00e9m disso, poder\u00e1 calcular o coeficiente de curtose de qualquer amostra de dados com uma calculadora online. Qual \u00e9 o coeficiente de curtose? 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-138","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>Coeficiente de achatamento: f\u00f3rmula, interpreta\u00e7\u00e3o e calculadora<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 o coeficiente de curtose, como ele \u00e9 calculado (f\u00f3rmula) e uma calculadora para calcular o coeficiente de curtose.\" \/>\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\/coeficiente-de-achatamento\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Coeficiente de achatamento: f\u00f3rmula, interpreta\u00e7\u00e3o e calculadora\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 o coeficiente de curtose, como ele \u00e9 calculado (f\u00f3rmula) e uma calculadora para calcular o coeficiente de curtose.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/coeficiente-de-achatamento\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-05T01:17:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-90817c2e65eaadd93ca788fd87067144_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=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/coeficiente-de-achatamento\/\",\"url\":\"https:\/\/statorials.org\/pt\/coeficiente-de-achatamento\/\",\"name\":\"Coeficiente de achatamento: f\u00f3rmula, interpreta\u00e7\u00e3o e calculadora\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-05T01:17:41+00:00\",\"dateModified\":\"2023-08-05T01:17:41+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 o coeficiente de curtose, como ele \u00e9 calculado (f\u00f3rmula) e uma calculadora para calcular o coeficiente de curtose.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/coeficiente-de-achatamento\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/coeficiente-de-achatamento\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/coeficiente-de-achatamento\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Coeficiente de achatamento\"}]},{\"@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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