{"id":26299,"date":"2023-06-06T21:33:03","date_gmt":"2023-06-06T20:33:03","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26299"},"modified":"2023-06-07T22:47:30","modified_gmt":"2023-06-07T21:47:30","slug":"classificacao-no-teste-de-matematica","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26299","title":{"rendered":"Classifica\u00e7\u00e3o no teste de Matem\u00e1tica"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26299' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26299' class='GTTabs_curr'><a  id=\"26299_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26299' ><a  id=\"26299_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_26299'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A professora do Manuel est\u00e1 a observar as classifica\u00e7\u00f5es nos testes de Matem\u00e1tica de quatro alunos do 10.\u00ba ano.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26301\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26301\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a.png\" data-orig-size=\"788,145\" 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_Pag215-T1-a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a.png\" class=\"aligncenter wp-image-26301\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a-300x55.png\" alt=\"\" width=\"520\" height=\"96\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a-300x55.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a-768x141.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a.png 788w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/a><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26303\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26303\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-b.png\" data-orig-size=\"435,575\" 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_Pag215-T1-b\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-b.png\" class=\"alignright wp-image-26303\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-b-227x300.png\" alt=\"\" width=\"270\" height=\"357\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-b-227x300.png 227w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-b.png 435w\" sizes=\"auto, (max-width: 270px) 100vw, 270px\" \/><\/a>Registou a sua aprecia\u00e7\u00e3o sobre os quatro alunos na folha ao lado para entregar \u00e0 Diretora de Turma.<\/p>\n<ol>\n<li>Associa a cada aluno a aprecia\u00e7\u00e3o da professora.<\/li>\n<li>Calcula a m\u00e9dia das classifica\u00e7\u00f5es de cada aluno.<\/li>\n<li>\u00c9 poss\u00edvel distinguir os alunos apenas pela mediana das suas classifica\u00e7\u00f5es? Porqu\u00ea?<\/li>\n<li>Para cada aluno, determina a amplitude das suas classifica\u00e7\u00f5es. Somente pela leitura dessas amplitudes, podemos distinguir os alunos? Porqu\u00ea?&nbsp;<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26299' onClick='GTTabs_show(1,26299)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26299'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>A professora do Manuel est\u00e1 a observar as classifica\u00e7\u00f5es nos testes de Matem\u00e1tica de quatro alunos do 10.\u00ba ano.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26301\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26301\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a.png\" data-orig-size=\"788,145\" 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_Pag215-T1-a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a.png\" class=\"aligncenter wp-image-26301\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a-300x55.png\" alt=\"\" width=\"520\" height=\"96\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a-300x55.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a-768x141.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a.png 788w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/a><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26303\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26303\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-b.png\" data-orig-size=\"435,575\" 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_Pag215-T1-b\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-b.png\" class=\"alignright wp-image-26303\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-b-227x300.png\" alt=\"\" width=\"270\" height=\"357\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-b-227x300.png 227w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-b.png 435w\" sizes=\"auto, (max-width: 270px) 100vw, 270px\" \/><\/a>Registou a sua aprecia\u00e7\u00e3o sobre os quatro alunos na folha ao lado para entregar \u00e0 Diretora de Turma.<\/p>\n<\/blockquote>\n<ol>\n<li>Associando a cada aluno a aprecia\u00e7\u00e3o da professora, temos:<br>A &#8211; Let\u00edcia, B &#8211; Jo\u00e3o, C &#8211; C\u00e1tia e D &#8211; Manuel.<br><br><\/li>\n<li>Segue a m\u00e9dia das classifica\u00e7\u00f5es de cada aluno:<br>\\({{\\bar x}_M} = \\frac{{2 + 20 + \\cdots + 6 + 12}}{{11}} = \\frac{{110}}{{11}} = 10\\)<br>\\({{\\bar x}_C} = \\frac{{19 + 17 + \\cdots + 3 + 2}}{{11}} = \\frac{{110}}{{11}} = 10\\)<br>\\({{\\bar x}_J} = \\frac{{9 + 8 + \\cdots + 12 + 8}}{{11}} = \\frac{{110}}{{11}} = 10\\)<br>\\({{\\bar x}_L} = \\frac{{1 + 4 + \\cdots + 17 + 18}}{{11}} = \\frac{{110}}{{11}} = 10\\)<br><br><\/li>\n<li>Comecemos por ordenar as classifica\u00e7\u00f5es por ordem crescente:<br>\n<table class=\" aligncenter\" style=\"width: 80%; border-collapse: collapse;\">\n<tbody>\n<tr style=\"height: 28px;\">\n<td style=\"height: 28px;\">Manuel<\/td>\n<td style=\"height: 28px;\">3<\/td>\n<td style=\"height: 28px;\">4<\/td>\n<td style=\"height: 28px;\">5<\/td>\n<td style=\"height: 28px;\">6<\/td>\n<td style=\"height: 28px;\">7<\/td>\n<td style=\"background-color: #77e324; height: 28px;\">11<\/td>\n<td style=\"height: 28px;\">12<\/td>\n<td style=\"height: 28px;\">12<\/td>\n<td style=\"height: 28px;\">14<\/td>\n<td style=\"height: 28px;\">16<\/td>\n<td style=\"height: 28px;\">20<\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"height: 28px;\">C\u00e1tia<\/td>\n<td style=\"height: 28px;\">2<\/td>\n<td style=\"height: 28px;\">3<\/td>\n<td style=\"height: 28px;\">4<\/td>\n<td style=\"height: 28px;\">6<\/td>\n<td style=\"height: 28px;\">7<\/td>\n<td style=\"background-color: #77e324; height: 28px;\">11<\/td>\n<td style=\"height: 28px;\">12<\/td>\n<td style=\"height: 28px;\">14<\/td>\n<td style=\"height: 28px;\">15<\/td>\n<td style=\"height: 28px;\">17<\/td>\n<td style=\"height: 28px;\">19<\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"height: 28px;\">Jo\u00e3o<\/td>\n<td style=\"height: 28px;\">8<\/td>\n<td style=\"height: 28px;\">8<\/td>\n<td style=\"height: 28px;\">9<\/td>\n<td style=\"height: 28px;\">9<\/td>\n<td style=\"height: 28px;\">9<\/td>\n<td style=\"background-color: #77e324; height: 28px;\">11<\/td>\n<td style=\"height: 28px;\">11<\/td>\n<td style=\"height: 28px;\">11<\/td>\n<td style=\"height: 28px;\">11<\/td>\n<td style=\"height: 28px;\">11<\/td>\n<td style=\"height: 28px;\">12<\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"height: 28px;\">Let\u00edcia<\/td>\n<td style=\"height: 28px;\">1<\/td>\n<td style=\"height: 28px;\">4<\/td>\n<td style=\"height: 28px;\">5<\/td>\n<td style=\"height: 28px;\">6<\/td>\n<td style=\"height: 28px;\">9<\/td>\n<td style=\"background-color: #77e324; height: 28px;\">11<\/td>\n<td style=\"height: 28px;\">11<\/td>\n<td style=\"height: 28px;\">13<\/td>\n<td style=\"height: 28px;\">15<\/td>\n<td style=\"height: 28px;\">17<\/td>\n<td style=\"height: 28px;\">18<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nN\u00e3o \u00e9 poss\u00edvel distinguir os alunos apenas pela mediana das suas classifica\u00e7\u00f5es, pois \u00e9 igual em todos: \\(\\tilde x = 11\\).<br><br><\/li>\n<li>A amplitude das suas classifica\u00e7\u00f5es s\u00e3o as seguintes:<br>Manuel: \\(20 &#8211; 3 = 17\\)<br>C\u00e1tia: \\(19 &#8211; 2 = 17\\)<br>Jo\u00e3o: \\(12 &#8211; 8 = 4\\)<br>Let\u00edcia: \\(18 &#8211; 1 = 17\\)<br>Apenas pela leitura dessas amplitudes, n\u00e3o podemos distinguir os alunos, pois tr\u00eas deles apresentam a mesma amplitude de classifica\u00e7\u00f5es.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26299' onClick='GTTabs_show(0,26299)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A professora do Manuel est\u00e1 a observar as classifica\u00e7\u00f5es nos testes de Matem\u00e1tica de quatro alunos do 10.\u00ba ano. Registou a sua aprecia\u00e7\u00e3o sobre os quatro alunos na folha ao lado&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":26302,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,717],"tags":[424,219,716,115],"series":[],"class_list":["post-26299","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-estatistica-2","tag-media","tag-mediana"],"views":82,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag215-T1-a_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26299","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=26299"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26299\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/26302"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26299"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26299"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26299"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26299"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}