{"id":26501,"date":"2023-06-09T09:58:28","date_gmt":"2023-06-09T08:58:28","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26501"},"modified":"2023-06-09T16:34:13","modified_gmt":"2023-06-09T15:34:13","slug":"um-campeonato-de-jogos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26501","title":{"rendered":"Um campeonato de jogos"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26501' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26501' class='GTTabs_curr'><a  id=\"26501_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26501' ><a  id=\"26501_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_26501'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A turma do Rafael organizou um campeonato de jogos na sua escola. Neste campeonato, os pais participaram em algumas competi\u00e7\u00f5es. O Rafael registou o tempo (em segundos) gasto, pelos pais e pelos alunos, a terminar um jogo de computador.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26503\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26503\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1.png\" data-orig-size=\"934,188\" 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_Pag223-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1.png\" class=\"aligncenter wp-image-26503\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1-300x60.png\" alt=\"\" width=\"640\" height=\"129\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1-300x60.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1-768x155.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1.png 934w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/p>\n<ol>\n<li>Organiza os dados num diagrama de caule-e-folhas para cada uma das distribui\u00e7\u00f5es.<\/li>\n<li>Calcula a m\u00e9dia dos tempos obtidos pelos pais e pelos alunos.<\/li>\n<li>Determina a mediana e os quartis para cada conjunto de dados.<\/li>\n<li>Constr\u00f3i paralelamente os diagramas de extremos e quartis para cada conjunto de dados.<\/li>\n<li>Compara e comenta os resultados obtidos pelos dois grupos.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26501' onClick='GTTabs_show(1,26501)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26501'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>A turma do Rafael organizou um campeonato de jogos na sua escola. Neste campeonato, os pais participaram em algumas competi\u00e7\u00f5es. O Rafael registou o tempo (em segundos) gasto, pelos pais e pelos alunos, a terminar um jogo de computador.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26503\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26503\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1.png\" data-orig-size=\"934,188\" 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_Pag223-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1.png\" class=\"aligncenter wp-image-26503\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1-300x60.png\" alt=\"\" width=\"640\" height=\"129\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1-300x60.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1-768x155.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1.png 934w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/a><\/p>\n<p>\u00a0<\/p>\n<ol>\n<li>Apresenta-se seguidamente os dados organizados num diagrama de caule-e-folhas, para cada uma das distribui\u00e7\u00f5es.<br \/><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-C-F.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26508\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26508\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-C-F.png\" data-orig-size=\"1300,498\" 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_Pag223-1_Diag-C-F\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-C-F-1024x392.png\" class=\"aligncenter wp-image-26508\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-C-F.png\" alt=\"\" width=\"520\" height=\"199\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-C-F.png 1300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-C-F-300x115.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-C-F-1024x392.png 1024w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-C-F-768x294.png 768w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/a><\/li>\n<li>As m\u00e9dia dos tempos (em segundos) obtidos pelos pais e pelos alunos s\u00e3o as seguintes:<br \/>\\({{\\bar x}_P} = \\frac{{320 + \\ldots + 321}}{{18}} = \\frac{{6135}}{{18}} \\approx 341\\) e \\({{\\bar x}_A} = \\frac{{280 + \\ldots + 306}}{{18}} = \\frac{{5462}}{{18}} \\approx 303\\).<br \/><br \/><\/li>\n<li>Considerando a ordena\u00e7\u00e3o dos dados presente nos diagramas de caule-e-folhas acima, comecemos por registar os extremos e os quartis da distribui\u00e7\u00e3o dos tempos gastos pelos pais e pelos alunos.<br \/>(Escreve as listas completas e confirma os valores indicados a seguir.)<br \/>\n<table style=\"border-collapse: collapse;\">\n<tbody>\n<tr>\n<td>\u00a0<\/td>\n<td>M\u00ednimo<\/td>\n<td>1.\u00ba quartil<\/td>\n<td>Mediana<\/td>\n<td>3.\u00ba quartil<\/td>\n<td>M\u00e1ximo<\/td>\n<\/tr>\n<tr>\n<td>Pais<\/td>\n<td>\\[{{x_1} = 320}\\]<\/td>\n<td>\\[{{x_5} = 335}\\]<\/td>\n<td>\\[\\frac{{{x_9} + {x_{10}}}}{2} = \\frac{{340 + 341}}{2} = 340,5\\]<\/td>\n<td>\\[{{x_{14}} = 352}\\]<\/td>\n<td>\\[{{x_{18}} = 364}\\]<\/td>\n<\/tr>\n<tr>\n<td>Alunos<\/td>\n<td>\\[{{x_1} = 280}\\]<\/td>\n<td>\\[{{x_5} = 293}\\]<\/td>\n<td>\\[\\frac{{{x_9} + {x_{10}}}}{2} = \\frac{{305 + 305}}{2} = 305\\]<\/td>\n<td>\\[{{x_{14}} = 314}\\]<\/td>\n<td>\\[{{x_{18}} = 323}\\]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Seguem os diagramas de extremos e quartis para cada conjunto de dados.<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-E-Q.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26523\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26523\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-E-Q.png\" data-orig-size=\"1223,287\" 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_Pag223-1_Diag-E-Q\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-E-Q-1024x240.png\" class=\"aligncenter wp-image-26523 size-full\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-E-Q.png\" alt=\"\" width=\"1223\" height=\"287\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-E-Q.png 1223w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-E-Q-300x70.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-E-Q-1024x240.png 1024w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_Diag-E-Q-768x180.png 768w\" sizes=\"auto, (max-width: 1223px) 100vw, 1223px\" \/><\/a><\/li>\n<li>Ainda que em ambos os grupos a amplitude dos dados seja id\u00eantica (44 e 43 segundos), o grupo dos pais \u00e9 mais lento, pois demora a terminar o jogo de computador cerca de mais 38 segundos do que o grupo dos alunos.<br \/>No entanto, o grupo dos pais apresenta uma maior concentra\u00e7\u00e3o dos 50% dos tempos mais centrais, pois a amplitude interquartil deste grupo \u00e9 de 17 segundos, enquanto no grupo dos alunos essa amplitude \u00e9 4 segundos mais extensa.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26501' onClick='GTTabs_show(0,26501)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A turma do Rafael organizou um campeonato de jogos na sua escola. Neste campeonato, os pais participaram em algumas competi\u00e7\u00f5es. O Rafael registou o tempo (em segundos) gasto, pelos pais e&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":26504,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,717],"tags":[424,718,219,716,115],"series":[],"class_list":["post-26501","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-mediana"],"views":125,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag223-1_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26501","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=26501"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26501\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/26504"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26501"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26501"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26501"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26501"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}