{"id":1354,"date":"2023-07-26T18:07:04","date_gmt":"2023-07-26T18:07:04","guid":{"rendered":"https:\/\/statorials.org\/pt\/interpretar-pontuacoes-z\/"},"modified":"2023-07-26T18:07:04","modified_gmt":"2023-07-26T18:07:04","slug":"interpretar-pontuacoes-z","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/interpretar-pontuacoes-z\/","title":{"rendered":"Como interpretar pontua\u00e7\u00f5es z: com exemplos"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Nas estat\u00edsticas, uma <strong>pontua\u00e7\u00e3o z<\/strong> nos diz<\/span> <span style=\"color: #000000;\">quantos desvios padr\u00e3o um determinado valor est\u00e1 em rela\u00e7\u00e3o <a href=\"https:\/\/statorials.org\/pt\/mede-a-tendencia-central\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00e0 m\u00e9dia<\/a> . Usamos a seguinte f\u00f3rmula para calcular uma pontua\u00e7\u00e3o z:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>z<\/strong> = (X \u2013 \u03bc) \/ \u03c3<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">X \u00e9 um \u00fanico valor de dados brutos<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u03bc \u00e9 a m\u00e9dia<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u03c3 \u00e9 o desvio padr\u00e3o<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Uma pontua\u00e7\u00e3o z para um valor individual pode ser interpretada da seguinte forma:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Escore z positivo:<\/strong> o valor individual est\u00e1 acima da m\u00e9dia.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Escore z negativo:<\/strong> o valor individual \u00e9 inferior \u00e0 m\u00e9dia.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Uma pontua\u00e7\u00e3o z de 0:<\/strong> o valor individual \u00e9 igual \u00e0 m\u00e9dia.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Quanto maior o valor absoluto do escore z, mais distante um valor individual est\u00e1 da m\u00e9dia.<\/span><\/p>\n<p> <span style=\"color: #000000;\">O exemplo a seguir mostra como calcular e interpretar pontua\u00e7\u00f5es z.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo: c\u00e1lculo e interpreta\u00e7\u00e3o de pontua\u00e7\u00f5es Z<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Suponha que as notas de um determinado exame tenham distribui\u00e7\u00e3o normal com m\u00e9dia 80 e desvio padr\u00e3o 4.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pergunta 1:<\/strong> Encontre a pontua\u00e7\u00e3o z para uma pontua\u00e7\u00e3o no exame de 87.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Podemos usar as seguintes etapas para calcular a pontua\u00e7\u00e3o z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">A m\u00e9dia \u00e9 \u03bc = 80<\/span><\/li>\n<li> <span style=\"color: #000000;\">O desvio padr\u00e3o \u00e9 \u03c3 = 4<\/span><\/li>\n<li> <span style=\"color: #000000;\">O valor individual que nos interessa \u00e9<\/span><\/li>\n<li> <span style=\"color: #000000;\">Assim, z = (X \u2013 \u03bc) \/ \u03c3 = (87 \u2013 80) \/4 = <strong>1,75<\/strong> .<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Isso nos diz que uma pontua\u00e7\u00e3o de 87 no exame est\u00e1 <strong>1,75 desvios padr\u00e3o <em>acima<\/em> da m\u00e9dia<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pergunta 2:<\/strong> Encontre a pontua\u00e7\u00e3o z para uma pontua\u00e7\u00e3o de 75 no exame.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Podemos usar as seguintes etapas para calcular a pontua\u00e7\u00e3o z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">A m\u00e9dia \u00e9 \u03bc = 80<\/span><\/li>\n<li> <span style=\"color: #000000;\">O desvio padr\u00e3o \u00e9 \u03c3 = 4<\/span><\/li>\n<li> <span style=\"color: #000000;\">O valor individual que nos interessa \u00e9 X = 75<\/span><\/li>\n<li> <span style=\"color: #000000;\">Assim, z = (X \u2013 \u03bc) \/ \u03c3 = (75 \u2013 80) \/4 = \u2013 <strong>1,25<\/strong> .<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Isso nos diz que uma pontua\u00e7\u00e3o de 75 no teste est\u00e1 <strong>1,25 desvios padr\u00e3o <em>abaixo<\/em> da m\u00e9dia<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pergunta 3:<\/strong> Encontre a pontua\u00e7\u00e3o z para uma pontua\u00e7\u00e3o de 80 no exame.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Podemos usar as seguintes etapas para calcular a pontua\u00e7\u00e3o z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">A m\u00e9dia \u00e9 \u03bc = 80<\/span><\/li>\n<li> <span style=\"color: #000000;\">O desvio padr\u00e3o \u00e9 \u03c3 = 4<\/span><\/li>\n<li> <span style=\"color: #000000;\">O valor individual que nos interessa \u00e9 X = 80<\/span><\/li>\n<li> <span style=\"color: #000000;\">Assim, z = (X \u2013 \u03bc) \/ \u03c3 = (80 \u2013 80) \/4 = <strong>0<\/strong> .<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Isso nos diz que uma pontua\u00e7\u00e3o de avalia\u00e7\u00e3o de 80 \u00e9 <strong>exatamente igual \u00e0 m\u00e9dia<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Por que as pontua\u00e7\u00f5es Z s\u00e3o \u00fateis?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">As pontua\u00e7\u00f5es Z s\u00e3o \u00fateis porque nos d\u00e3o uma ideia de como um valor individual se compara ao resto de uma distribui\u00e7\u00e3o.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Por exemplo, uma pontua\u00e7\u00e3o de 87 em um exame \u00e9 boa? Bem, depende da m\u00e9dia e do desvio padr\u00e3o de todos os resultados dos exames.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Se as pontua\u00e7\u00f5es dos exames para toda a popula\u00e7\u00e3o fossem normalmente distribu\u00eddas com m\u00e9dia de 90 e desvio padr\u00e3o de 4, calcular\u00edamos a pontua\u00e7\u00e3o z para 87 da seguinte forma:<\/span><\/p>\n<p> <span style=\"color: #000000;\">z = (X \u2013 \u03bc) \/ \u03c3 = (87 \u2013 90) \/4 = <strong>-0,75<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Como esse valor \u00e9 negativo, isso nos diz que uma pontua\u00e7\u00e3o de 87 no exame \u00e9, na verdade, <em>inferior<\/em> \u00e0 pontua\u00e7\u00e3o m\u00e9dia do exame para a popula\u00e7\u00e3o. Especificamente, uma pontua\u00e7\u00e3o de 87 no exame est\u00e1 <strong>0,75 desvios padr\u00e3o abaixo da m\u00e9dia<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Resumindo, as pontua\u00e7\u00f5es z nos d\u00e3o uma ideia de como os valores individuais se comparam \u00e0 m\u00e9dia.<\/span><\/p>\n<h3> <strong>Como calcular pontua\u00e7\u00f5es Z na pr\u00e1tica<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Os tutoriais a seguir mostram exemplos passo a passo de como calcular pontua\u00e7\u00f5es z em diferentes softwares estat\u00edsticos:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pt\/pontuacao-z-excel\/\" target=\"_blank\" rel=\"noopener\">Como calcular pontua\u00e7\u00f5es Z no Excel<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/pontuacao-zr\/\" target=\"_blank\" rel=\"noopener\">Como calcular pontua\u00e7\u00f5es Z em R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/pontuacao-z-python\/\" target=\"_blank\" rel=\"noopener\">Como calcular pontua\u00e7\u00f5es Z em Python<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/pontuacao-z-spss\/\" target=\"_blank\" rel=\"noopener\">Como calcular pontua\u00e7\u00f5es Z no SPSS<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Nas estat\u00edsticas, uma pontua\u00e7\u00e3o z nos diz quantos desvios padr\u00e3o um determinado valor est\u00e1 em rela\u00e7\u00e3o \u00e0 m\u00e9dia . Usamos a seguinte f\u00f3rmula para calcular uma pontua\u00e7\u00e3o z: z = (X \u2013 \u03bc) \/ \u03c3 Ouro: X \u00e9 um \u00fanico valor de dados brutos \u03bc \u00e9 a m\u00e9dia \u03c3 \u00e9 o desvio padr\u00e3o Uma pontua\u00e7\u00e3o [&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-1354","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 interpretar pontua\u00e7\u00f5es Z: com exemplos<\/title>\n<meta name=\"description\" content=\"Este tutorial fornece uma explica\u00e7\u00e3o simples de como interpretar pontua\u00e7\u00f5es z em estat\u00edsticas, incluindo 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\/interpretar-pontuacoes-z\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como interpretar pontua\u00e7\u00f5es Z: com exemplos\" \/>\n<meta property=\"og:description\" content=\"Este tutorial fornece uma explica\u00e7\u00e3o simples de como interpretar pontua\u00e7\u00f5es z em estat\u00edsticas, incluindo v\u00e1rios exemplos.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/interpretar-pontuacoes-z\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-26T18:07:04+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=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/interpretar-pontuacoes-z\/\",\"url\":\"https:\/\/statorials.org\/pt\/interpretar-pontuacoes-z\/\",\"name\":\"Como interpretar pontua\u00e7\u00f5es Z: com exemplos\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-26T18:07:04+00:00\",\"dateModified\":\"2023-07-26T18:07:04+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Este tutorial fornece uma explica\u00e7\u00e3o simples de como interpretar pontua\u00e7\u00f5es z em estat\u00edsticas, incluindo v\u00e1rios exemplos.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/interpretar-pontuacoes-z\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/interpretar-pontuacoes-z\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/interpretar-pontuacoes-z\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como interpretar pontua\u00e7\u00f5es z: com exemplos\"}]},{\"@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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