{"id":26428,"date":"2023-06-08T16:22:53","date_gmt":"2023-06-08T15:22:53","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26428"},"modified":"2023-06-08T18:56:33","modified_gmt":"2023-06-08T17:56:33","slug":"a-correcao-de-26-testes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26428","title":{"rendered":"A corre\u00e7\u00e3o de 26 testes"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26428' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26428' class='GTTabs_curr'><a  id=\"26428_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26428' ><a  id=\"26428_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_26428'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Um professor corrigiu 26 testes, classificando-os de 1 a 10. Foi agrupando os dados da seguinte maneira.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26429\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26429\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3.png\" data-orig-size=\"471,190\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag221-3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3.png\" class=\"aligncenter wp-image-26429\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3-300x121.png\" alt=\"\" width=\"340\" height=\"137\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3-300x121.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3.png 471w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a><\/p>\n<ol>\n<li>Representa estes dados numa tabela de frequ\u00eancias absolutas.<\/li>\n<li>Qual foi a classifica\u00e7\u00e3o m\u00e9dia desta turma?<\/li>\n<li>Constr\u00f3i um diagrama de extremos e quartis das classifica\u00e7\u00f5es dos testes.<\/li>\n<li>Qual \u00e9 a amplitude interquartil? O que representa esse valor?<\/li>\n<li>Um aluno que faltou ao teste realizou-o na aula seguinte. A sua classifica\u00e7\u00e3o foi de 9 valores. Comenta as altera\u00e7\u00f5es que foram introduzidas na m\u00e9dia e nas medidas de localiza\u00e7\u00e3o usadas na constru\u00e7\u00e3o do diagrama do ponto 3.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26428' onClick='GTTabs_show(1,26428)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26428'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Um professor corrigiu 26 testes, classificando-os de 1 a 10. Foi agrupando os dados da seguinte maneira.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26429\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26429\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3.png\" data-orig-size=\"471,190\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag221-3\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3.png\" class=\"aligncenter wp-image-26429\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3-300x121.png\" alt=\"\" width=\"340\" height=\"137\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3-300x121.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3.png 471w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a><\/p>\n<p>\u00a0<\/p>\n<ol>\n<li>Os dados est\u00e3o representados na tabela de frequ\u00eancias absolutas seguinte.<br \/>\n<table class=\" aligncenter\" style=\"width: 80%; border-collapse: collapse;\">\n<tbody>\n<tr>\n<td><strong>Classifica\u00e7\u00e3o<\/strong><\/td>\n<td>1<\/td>\n<td>2<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<td>8<\/td>\n<td>9<\/td>\n<td>10<\/td>\n<td><strong>Total<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Freq. absoluta<\/strong><\/td>\n<td>2<\/td>\n<td>4<\/td>\n<td>3<\/td>\n<td>1<\/td>\n<td>6<\/td>\n<td>5<\/td>\n<td>2<\/td>\n<td>0<\/td>\n<td>2<\/td>\n<td>1<\/td>\n<td><strong>26<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>A classifica\u00e7\u00e3o m\u00e9dia desta turma foi 4,8, aproximadamente: \\(\\bar x = \\frac{{2 + 8 + 9 + 4 + 30 + 30 + 14 + 0 + 18 + 10}}{{26}} = \\frac{{125}}{{26}} \\approx 4,8\\).<br \/><br \/><\/li>\n<li>Seja \\({x_1},\\;x{}_2,\\; \\ldots {x_{25}},\\;{x_{26}}\\) a lista das classifica\u00e7\u00f5es dos testes, ordenadas por ordem crescente.<br \/>Comecemos por registar os extremos e os quartis da distribui\u00e7\u00e3o das classifica\u00e7\u00f5es:<br \/>(Escreve a lista completa e confirma os valores indicados a seguir.)<br \/>\n<table class=\" aligncenter\" style=\"width: 80%; height: 85px;\">\n<tbody>\n<tr style=\"height: 28px;\">\n<td style=\"height: 28px;\">M\u00ednimo<\/td>\n<td style=\"height: 28px;\">1.\u00ba quartil<\/td>\n<td style=\"height: 28px;\">Mediana<\/td>\n<td style=\"height: 28px;\">3.\u00ba quartil<\/td>\n<td style=\"height: 28px;\">M\u00e1ximo<\/td>\n<\/tr>\n<tr style=\"height: 57px;\">\n<td style=\"height: 57px;\">\\({{x_1} = 1}\\)<\/td>\n<td style=\"height: 57px;\">\\({{x_7} = 3}\\)<\/td>\n<td style=\"height: 57px;\">\\({\\frac{{{x_{13}} + {x_{14}}}}{2} = \\frac{{5 + 5}}{2} = 5}\\)<\/td>\n<td style=\"height: 57px;\">\\({{x_{20}} = 6}\\)<\/td>\n<td style=\"height: 57px;\">\\({{x_{26}} = 10}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nApresenta-se seguidamente um diagrama de extremos e quartis das classifica\u00e7\u00f5es dos testes.<br \/><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3_diagrama.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26444\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26444\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3_diagrama.png\" data-orig-size=\"1180,268\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag221-3_diagrama\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3_diagrama-1024x233.png\" class=\"aligncenter wp-image-26444 size-full\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3_diagrama.png\" alt=\"\" width=\"1180\" height=\"268\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3_diagrama.png 1180w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3_diagrama-300x68.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3_diagrama-1024x233.png 1024w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3_diagrama-768x174.png 768w\" sizes=\"auto, (max-width: 1180px) 100vw, 1180px\" \/><\/a><\/li>\n<li>A amplitude interquartil \u00e9 \\({Q_3} &#8211; {Q_1} = 6 &#8211; 3 = 3\\).<br \/>Este valor representa a amplitude do intervalo em que se encontram, aproximadamente, 50% das classifica\u00e7\u00f5es centrais.<br \/><br \/><\/li>\n<li>O acrescento de uma classifica\u00e7\u00e3o 9, para o aluno que realizou o teste na aula seguinte, vai aumentar o valor da m\u00e9dia: \\({{\\bar x}_{ + 1}} = \\frac{{125 + 9}}{{26 + 1}} = \\frac{{134}}{{27}} \\approx 5,0\\).<br \/>No entanto, n\u00e3o \u00e9 introduzida qualquer altera\u00e7\u00e3o nas medidas de localiza\u00e7\u00e3o usadas na constru\u00e7\u00e3o do diagrama do ponto 3, ainda que, por vezes, esses valores decorram de elementos com posi\u00e7\u00f5es distintas nas duas listas, conforme se pode verificar\u00a0 na tabela seguinte.<br \/>\n<table class=\" aligncenter\" style=\"width: 90%;\">\n<tbody>\n<tr style=\"height: 57px;\">\n<td style=\"height: 57px;\">N.\u00ba de alunos<\/td>\n<td style=\"height: 57px;\">M\u00ednimo<\/td>\n<td style=\"height: 57px;\">1.\u00ba quartil<\/td>\n<td style=\"height: 57px;\">Mediana<\/td>\n<td style=\"height: 57px;\">3.\u00ba quartil<\/td>\n<td style=\"height: 57px;\">M\u00e1ximo<\/td>\n<\/tr>\n<tr style=\"height: 57px;\">\n<td style=\"height: 57px;\">26<\/td>\n<td style=\"height: 57px;\">\\({{x_1} = 1}\\)<\/td>\n<td style=\"height: 57px;\">\\({{x_7} = 3}\\)<\/td>\n<td style=\"height: 57px;\">\\({\\frac{{{x_{13}} + {x_{14}}}}{2} = \\frac{{5 + 5}}{2} = 5}\\)<\/td>\n<td style=\"height: 57px;\">\\({{x_{20}} = 6}\\)<\/td>\n<td style=\"height: 57px;\">\\({{x_{26}} = 10}\\)<\/td>\n<\/tr>\n<tr style=\"height: 57px;\">\n<td style=\"height: 57px;\">27<\/td>\n<td style=\"height: 57px;\">\u00a0\\({{x_1} = 1}\\)<\/td>\n<td style=\"height: 57px;\">\\({{x_7} = 3}\\)<\/td>\n<td style=\"height: 57px;\">\\({x_{14}} = 5\\)<\/td>\n<td style=\"height: 57px;\">\\({x_{21}} = 6\\)<\/td>\n<td style=\"height: 57px;\">\\({{x_{27}} = 10}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26428' onClick='GTTabs_show(0,26428)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um professor corrigiu 26 testes, classificando-os de 1 a 10. Foi agrupando os dados da seguinte maneira. Representa estes dados numa tabela de frequ\u00eancias absolutas. Qual foi a classifica\u00e7\u00e3o m\u00e9dia desta&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":26430,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,717],"tags":[424,718,219,716,719],"series":[],"class_list":["post-26428","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-diagramas-de-extremos-e-quartis","tag-8-o-ano","tag-diagrama-de-extremos-e-quartis","tag-estatistica-2","tag-media","tag-quartis"],"views":93,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag221-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26428","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=26428"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26428\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/26430"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26428"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26428"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26428"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26428"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}