{"id":1244,"date":"2023-07-27T04:01:05","date_gmt":"2023-07-27T04:01:05","guid":{"rendered":"https:\/\/statorials.org\/pt\/variacao-em-r\/"},"modified":"2023-07-27T04:01:05","modified_gmt":"2023-07-27T04:01:05","slug":"variacao-em-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/variacao-em-r\/","title":{"rendered":"Como calcular a varia\u00e7\u00e3o amostral e populacional em r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>A vari\u00e2ncia<\/strong> \u00e9 uma forma de medir qu\u00e3o bem os valores dos dados est\u00e3o distribu\u00eddos em torno da m\u00e9dia.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A f\u00f3rmula para encontrar a vari\u00e2ncia de uma <a href=\"https:\/\/statorials.org\/pt\/populacao-vs.-amostra\/\" target=\"_blank\" rel=\"noopener noreferrer\">popula\u00e7\u00e3o<\/a> \u00e9:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>\u03c3 <sup>2<\/sup><\/strong> = \u03a3 (x <sub>i<\/sub> \u2013 \u03bc) <sup>2<\/sup> \/ N<\/span><\/p>\n<p> <span style=\"color: #000000;\">onde \u03bc \u00e9 a m\u00e9dia da popula\u00e7\u00e3o, x <sub>i<\/sub> \u00e9 o i- <sup>\u00e9simo<\/sup> elemento da popula\u00e7\u00e3o, N \u00e9 o tamanho da popula\u00e7\u00e3o e \u03a3 \u00e9 apenas um s\u00edmbolo sofisticado que significa &#8220;soma&#8221;.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A f\u00f3rmula para encontrar a vari\u00e2ncia de uma <a href=\"https:\/\/statorials.org\/pt\/media-amostral-em-comparacao-com-a-media-populacional\/\" target=\"_blank\" rel=\"noopener noreferrer\">amostra<\/a> \u00e9:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>s <sup>2<\/sup><\/strong> = \u03a3 ( <sub>xi<\/sub> \u2013 <span style=\"text-decoration: overline;\">x<\/span> ) <sup>2<\/sup> \/ (n-1)<\/span><\/p>\n<p> <span style=\"color: #000000;\">onde <span style=\"text-decoration: overline;\">x<\/span> \u00e9 a m\u00e9dia da amostra, x <sub>i<\/sub> \u00e9 o i <sup>-\u00e9simo<\/sup> elemento da amostra e n \u00e9 o tamanho da amostra.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo: Calcular a vari\u00e2ncia amostral e populacional em R<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Suponha que temos o seguinte conjunto de dados em R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define dataset<\/span>\ndata &lt;- c(2, 4, 4, 7, 8, 12, 14, 15, 19, 22)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Podemos calcular a <strong>vari\u00e2ncia da amostra<\/strong> usando a fun\u00e7\u00e3o <strong>var()<\/strong> em R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate sample variance<\/span>\nvar(data)\n\n[1] 46.01111\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">E podemos calcular a <strong>vari\u00e2ncia da popula\u00e7\u00e3o<\/strong> simplesmente multiplicando a vari\u00e2ncia da amostra por (n-1)\/n da seguinte forma:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#determine length of data\n<span style=\"color: #000000;\">n &lt;- <span style=\"color: #3366ff;\">length<\/span> (data)<\/span>\n\n#calculate population variance<\/span>\nvar(data) * (n-1)\/n\n\n[1] 41.41\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Observe que a vari\u00e2ncia da popula\u00e7\u00e3o ser\u00e1 sempre menor que a vari\u00e2ncia da amostra.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Na pr\u00e1tica, geralmente calculamos vari\u00e2ncias amostrais para conjuntos de dados, porque \u00e9 incomum coletar dados para uma popula\u00e7\u00e3o inteira.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo: Calcule a vari\u00e2ncia de uma amostra de v\u00e1rias colunas<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Suponha que temos o seguinte quadro de dados em R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create data frame\n<span style=\"color: #000000;\">data &lt;- data.frame(a=c(1, 3, 4, 4, 6, 7, 8, 12),\n                   b=c(2, 4, 4, 5, 5, 6, 7, 16),\n                   c=c(6, 6, 7, 8, 8, 9, 9, 12))\n\n<span style=\"color: #008080;\">#view data frame<\/span>\ndata\n\n   ABC\n1 1 2 6\n2 3 4 6\n3 4 4 7\n4 4 5 8\n5 6 5 8\n6 7 6 9\n7 8 7 9\n8 12 16 12<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Podemos usar a fun\u00e7\u00e3o <a href=\"https:\/\/statorials.org\/pt\/um-guia-para-aplicar-lapply-sapply-e-tapply-em-r\/\" target=\"_blank\" rel=\"noopener noreferrer\">sapply()<\/a> para calcular a varia\u00e7\u00e3o da amostra de cada coluna no quadro de dados:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find sample variance of each column\n<span style=\"color: #000000;\">sapply(data, var)\n\n        ABC\n11.696429 18.125000 3.839286<\/span>\n<\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">E podemos usar o c\u00f3digo a seguir para calcular o desvio padr\u00e3o amostral de cada coluna, que \u00e9 simplesmente a raiz quadrada da vari\u00e2ncia amostral:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find sample standard deviation of each column\n<span style=\"color: #000000;\">sapply(data, sd)\n\n       ABC\n3.420004 4.257347 1.959410<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><em>Voc\u00ea pode encontrar mais tutoriais de R <a href=\"https:\/\/statorials.org\/pt\/estatologia-explica-conceitos-de-forma-simples-e-direta-facilitamos-o-aprendizado-de-estatistica\/\" target=\"_blank\" rel=\"noopener noreferrer\">aqui<\/a> .<\/em><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A vari\u00e2ncia \u00e9 uma forma de medir qu\u00e3o bem os valores dos dados est\u00e3o distribu\u00eddos em torno da m\u00e9dia. A f\u00f3rmula para encontrar a vari\u00e2ncia de uma popula\u00e7\u00e3o \u00e9: \u03c3 2 = \u03a3 (x i \u2013 \u03bc) 2 \/ N onde \u03bc \u00e9 a m\u00e9dia da popula\u00e7\u00e3o, x i \u00e9 o i- \u00e9simo elemento da [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1244","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Como calcular a vari\u00e2ncia amostral e populacional em R<\/title>\n<meta name=\"description\" content=\"Este tutorial explica como calcular a vari\u00e2ncia amostral e a vari\u00e2ncia populacional em R, com v\u00e1rios exemplos.\" \/>\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\/variacao-em-r\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como calcular a vari\u00e2ncia amostral e populacional em R\" \/>\n<meta property=\"og:description\" content=\"Este tutorial explica como calcular a vari\u00e2ncia amostral e a vari\u00e2ncia populacional em R, com v\u00e1rios exemplos.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/variacao-em-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T04:01:05+00:00\" \/>\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\/variacao-em-r\/\",\"url\":\"https:\/\/statorials.org\/pt\/variacao-em-r\/\",\"name\":\"Como calcular a vari\u00e2ncia amostral e populacional em R\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-27T04:01:05+00:00\",\"dateModified\":\"2023-07-27T04:01:05+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Este tutorial explica como calcular a vari\u00e2ncia amostral e a vari\u00e2ncia populacional em R, com v\u00e1rios exemplos.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/variacao-em-r\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/variacao-em-r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/variacao-em-r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como calcular a varia\u00e7\u00e3o amostral e populacional em r\"}]},{\"@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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