{"id":26342,"date":"2023-06-07T13:27:31","date_gmt":"2023-06-07T12:27:31","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26342"},"modified":"2023-06-07T22:44:51","modified_gmt":"2023-06-07T21:44:51","slug":"as-classificacoes-do-ultimo-teste","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26342","title":{"rendered":"As classifica\u00e7\u00f5es do \u00faltimo teste"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26342' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26342' class='GTTabs_curr'><a  id=\"26342_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26342' ><a  id=\"26342_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_26342'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>As classifica\u00e7\u00f5es no \u00faltimo teste de Matem\u00e1tica da turma da Marta foram as seguintes.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26348\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26348\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3-b.png\" data-orig-size=\"493,301\" 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_Pag219-T3-b\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3-b.png\" class=\"aligncenter wp-image-26348\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3-b-300x183.png\" alt=\"\" width=\"300\" height=\"183\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3-b-300x183.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3-b.png 493w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<ol>\n<li>Calcula a <strong>m\u00e9dia<\/strong> das classifica\u00e7\u00f5es.<\/li>\n<li>Organiza os dados num diagrama de caule-e-folhas.<\/li>\n<li>Quais s\u00e3o os valores extremos dos dados observados? O que representam?<\/li>\n<li>Escreve os dados por ordem crescente. Determina o valor da <strong>mediana<\/strong> e indica que significado tem esse valor.<\/li>\n<li>Determina o <strong>1.\u00ba quartil<\/strong> e o <strong>3.\u00ba quartil<\/strong>. Que significado t\u00eam esses valores? Determina a diferen\u00e7a entre esses valores e escreve o significado dessa diferen\u00e7a.<\/li>\n<li>Representa esta distribui\u00e7\u00e3o num <strong>diagrama de extremos e quartis<\/strong>.<\/li>\n<li>O Pedro estava doente e faltou no dia do este. F\u00ea-lo no dia seguinte e obteve a classifica\u00e7\u00e3o de 98%.<br>a) Ser\u00e1 que a m\u00e9dia das classifica\u00e7\u00f5es sofre altera\u00e7\u00e3o? Explica a tua resposta.<br>b) Os valores da mediana e do 1.\u00ba e 3.\u00ba quartis alterarm-se? Verifica.<br>c) Quais s\u00e3o os extremos e a amplitude do novo conjunto de dados.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26342' onClick='GTTabs_show(1,26342)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26342'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>As classifica\u00e7\u00f5es no \u00faltimo teste de Matem\u00e1tica da turma da Marta foram as seguintes.<\/p>\n<\/blockquote>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26348\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26348\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3-b.png\" data-orig-size=\"493,301\" 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_Pag219-T3-b\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3-b.png\" class=\"aligncenter wp-image-26348\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3-b-300x183.png\" alt=\"\" width=\"300\" height=\"183\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3-b-300x183.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3-b.png 493w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<ol>\n<li>A <strong>m\u00e9dia<\/strong> das classifica\u00e7\u00f5es \u00e9 \\(\\bar x = \\frac{{52 + 51 + \\ldots + 40 + 62}}{{24}} = \\frac{{1285}}{{24}} \\approx 53,5\\).<br><br><\/li>\n<li>Apresenta-se seguidamente os dados organizados num diagrama de caule-e-folhas:<br><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26353\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26353\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_1.png\" data-orig-size=\"1075,540\" 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_Pag219-T3_Diagramas_1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_1-1024x514.png\" class=\"aligncenter wp-image-26353\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_1-300x151.png\" alt=\"\" width=\"340\" height=\"171\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_1-300x151.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_1-1024x514.png 1024w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_1-768x386.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_1.png 1075w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a><\/li>\n<li>Os valores extremos dos dados observados s\u00e3o \\(37\\) e \\(67\\). Esses valores s\u00e3o, respetivamente, a classifica\u00e7\u00e3o m\u00ednima e a classifica\u00e7\u00e3o m\u00e1xima obtidas neste teste.<br><br><\/li>\n<li>Seguem os dados escritos por ordem crescente: \\[37,39,40,41,42,45,45,48,51,52,52,\\underbrace {52,52,}_{\\tilde x = \\frac{{52 + 52}}{2} = 52}57,59,62,62,63,63,63,63,65,65,67\\] A <strong>mediana<\/strong> \u00e9 \\({\\tilde x = \\frac{{52 + 52}}{2} = 52}\\).<br>Este valor indica que, pelo menos, metade dos alunos obteve classifica\u00e7\u00e3o n\u00e3o superior a 52 pontos.<br>&nbsp;<\/li>\n<li>\\[37,39,40,41,42,\\overbrace {45,45,}^{{Q_1} = \\frac{{45 + 45}}{2} = 45}48,51,52,52,\\underbrace {52,52,}_{\\tilde x = \\frac{{52 + 52}}{2} = 52}57,59,62,62,\\overbrace {63,63,}^{{Q_3} = \\frac{{63 + 63}}{2} = 63}63,63,65,65,67\\] O <strong>1.\u00ba quartil<\/strong> \u00e9 \\({{Q_1} = \\frac{{45 + 45}}{2} = 45}\\) e o <strong>3.\u00ba quartil<\/strong>&nbsp;\u00e9 \\({{Q_3} = \\frac{{63 + 63}}{2} = 63}\\).<br>O 1.\u00ba quartil indica que, aproximadamente, 25% dos alunos obteve classifica\u00e7\u00e3o inferior ou igual a 45 pontos; e o 3.\u00ba quartil indica que, aproximadamente, 75% dos alunos obteve classifica\u00e7\u00e3o inferior ou igual a 63 pontos.<br>Ora, a diferen\u00e7a entre o 3.\u00ba quartil e o 1.\u00ba quartil \u00e9&nbsp; \\({Q_3} &#8211; {Q_1} = 63 &#8211; 45 = 18\\). Esta diferen\u00e7a indica a amplitude do intervalo em que se encontram, aproximadamente, 50% das classifica\u00e7\u00f5es centrais.<br><br><\/li>\n<li>Representa-se seguidamente esta distribui\u00e7\u00e3o num <strong>diagrama de extremos e quartis<\/strong>:<br><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_2a.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26366\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26366\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_2a.png\" data-orig-size=\"2012,507\" 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_Pag219-T3_Diagramas_2a\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_2a-1024x258.png\" class=\"aligncenter wp-image-26366\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_2a-300x76.png\" alt=\"\" width=\"720\" height=\"181\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_2a-300x76.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_2a-1024x258.png 1024w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_2a-768x194.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_2a-1536x387.png 1536w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_Diagramas_2a.png 2012w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><\/a><\/li>\n<li>O Pedro estava doente e faltou no dia do este. F\u00ea-lo no dia seguinte e obteve a classifica\u00e7\u00e3o de 98%.<br>a) Sim, a m\u00e9dia das classifica\u00e7\u00f5es sofre altera\u00e7\u00e3o: aumenta para \\({{\\bar x}_T} = \\frac{{52 + 51 + \\ldots + 40 + 62 + 98}}{{25}} = \\frac{{1285 + 98}}{{25}} = 55,32\\).<br>b) N\u00e3o, n\u00e3o se alteram os valores da mediana e do 1.\u00ba e 3.\u00ba quartis (verificar abaixo).<br>c) Relativamente ao novo conjunto de dados, os extremos s\u00e3o \\(37\\) e \\(98\\), e a amplitude \u00e9 \\(61\\).<br>\\[37,39,40,41,42,\\overbrace {45,45,}^{{Q_1} = \\frac{{45 + 45}}{2} = 45}48,51,52,52,52,\\underbrace {52,}_{\\tilde x = 52}57,59,62,62,63,\\overbrace {63,63,}^{{Q_3} = \\frac{{63 + 63}}{2} = 63}63,65,65,67,98\\]<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26342' onClick='GTTabs_show(0,26342)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado As classifica\u00e7\u00f5es no \u00faltimo teste de Matem\u00e1tica da turma da Marta foram as seguintes. Calcula a m\u00e9dia das classifica\u00e7\u00f5es. Organiza os dados num diagrama de caule-e-folhas. Quais s\u00e3o os valores extremos&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":26347,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,717],"tags":[424,718,716,115],"series":[],"class_list":["post-26342","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-media","tag-mediana"],"views":79,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/06\/8_Pag219-T3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26342","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=26342"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26342\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/26347"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26342"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26342"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26342"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26342"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}