{"id":154535,"date":"2022-11-25T16:00:00","date_gmt":"2022-11-25T19:00:00","guid":{"rendered":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/?post_type=eaja&#038;p=154535"},"modified":"2024-05-22T13:38:49","modified_gmt":"2024-05-22T16:38:49","slug":"matematica-media-e-amplitude","status":"publish","type":"eaja","link":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/eaja\/matematica-media-e-amplitude\/","title":{"rendered":"Matem\u00e1tica &#8211; M\u00e9dia Aritm\u00e9tica e Amplitude"},"content":{"rendered":"\n<p class=\"has-text-align-center has-white-background-color has-background has-medium-font-size\"><strong>Esta proposta de atividade de&nbsp;MATEM\u00c1TICA&nbsp;\u00e9 destinada aos estudante do 5\u00ba Per\u00edodo (6\u00aa S\u00e9rie)&nbsp;da Educa\u00e7\u00e3o de Jovens e Adultos \u2013 EJA<\/strong><\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/drive.google.com\/uc?export=douwnload&amp;id=1ItgdbX87-fEvADfzcIKb_P9WutxenIsj\" target=\"_blank\" rel=\"noreferrer noopener\">BAIXE A ATIVIDADE<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/drive.google.com\/uc?export=douwnload&amp;id=1c1xMwhtn23IAh1R39AevP7oZMTeeTpou\" target=\"_blank\" rel=\"noreferrer noopener\">BAIXE OS SLIDES<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/drive.google.com\/uc?export=douwnload&amp;id=1KNWR_i9awe9WlfPtKzbC8l6oI1pZ9zgO\" target=\"_blank\" rel=\"noreferrer noopener\">BAIXE O TEXTO<\/a><\/div>\n<\/div>\n\n\n\n<p><\/p>\n\n\n\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:23% auto\"><figure class=\"wp-block-media-text__media\"><img fetchpriority=\"high\" decoding=\"async\" width=\"241\" height=\"210\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2024\/04\/media.png\" alt=\"\" class=\"wp-image-180451 size-full\"\/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-text-color has-link-color has-medium-font-size wp-elements-b3509aefe47c1c955b933d1f83a8408b\" style=\"color:#0f0488\"><strong>Introdu\u00e7\u00e3o<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Hoje vamos estudar um pouco de um assunto bastante importante e \u00fatil em diversas situa\u00e7\u00f5es da vida cotidiana:&nbsp; <strong>a m\u00e9dia aritm\u00e9tica e a amplitude<\/strong>. Espero que voc\u00ea aproveite.<\/p>\n\n\n\n<p class=\"has-small-font-size\">Imagem: canva.com\/<a href=\"https:\/\/acesse.one\/0RYga\">https:\/\/acesse.one\/0RYga<\/a><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-medium-font-size wp-elements-772d1d36dcdc5881fc275a9fd6279254\" style=\"color:#0f0488\"><strong>M\u00e9dia Aritm\u00e9tica<\/strong><\/p>\n\n\n\n<p class=\"has-vivid-red-color has-text-color has-link-color has-medium-font-size wp-elements-900403f2264bcdb6435df159078614a8\"><strong>Defini\u00e7\u00e3o<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">A <strong>m\u00e9dia aritm\u00e9tica<\/strong> \u00e9 um valor usado para representar um conjunto de dados. Ela \u00e9 calculada <strong>somando<\/strong> todos os n\u00fameros e <strong>dividindo<\/strong> pelo total de n\u00fameros somados.&nbsp;<\/p>\n\n\n\n<p class=\"has-vivid-red-color has-text-color has-link-color has-medium-font-size wp-elements-d7f4ef56b80580875574223c79d63ddb\"><strong>Por exemplo:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">se tivermos os n\u00fameros 10, 15, 20, 25 e 30, a m\u00e9dia aritm\u00e9tica \u00e9 calculada da seguinte forma:\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">(10 + 15 + 20 + 25 + 30) : 5 = 100 : 5 = 20<\/li>\n\n\n\n<li class=\"has-medium-font-size\">Portanto, a m\u00e9dia aritm\u00e9tica desses n\u00fameros \u00e9 20.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li class=\"has-medium-font-size\">se tivermos os n\u00fameros 20, 30 e 40, a m\u00e9dia aritm\u00e9tica \u00e9 calculada da seguinte forma:\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">(20 + 30 + 40) : 3 = 90 : 30 = 30<\/li>\n\n\n\n<li class=\"has-medium-font-size\">Portanto, a m\u00e9dia aritm\u00e9tica desses n\u00fameros \u00e9 30.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-medium-font-size wp-elements-38952428332301d76be43e88de3bc776\" style=\"color:#0f0488\"><strong>M\u00e9dia Aritm\u00e9tica (Significado)<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u00c9 uma maneira simples de resumir um conjunto de n\u00fameros em um \u00fanico valor representativo<\/p>\n\n\n\n<p class=\"has-vivid-red-color has-text-color has-link-color has-medium-font-size wp-elements-d7f4ef56b80580875574223c79d63ddb\"><strong>Por exemplo:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">Suponha que o conjunto de n\u00fameros 10, 20, 30, 40 e 50 represente a idade de um grupo de pessoas, a m\u00e9dia aritm\u00e9tica \u00e9 um \u00fanico valor que possa representar todas essas idades juntas.&nbsp;<\/li>\n\n\n\n<li class=\"has-medium-font-size\">Neste caso a m\u00e9dia aritm\u00e9tica ser\u00e1 (10+20+30+40+50) : 5 = 30.&nbsp;<\/li>\n\n\n\n<li class=\"has-medium-font-size\">Esse n\u00famero significa que, em m\u00e9dia, as pessoas desse grupo t\u00eam cerca de 30 anos de idade.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-medium-font-size wp-elements-3fd1e0ca99fdfcfaed01bfa2cd18bf8b\" style=\"color:#0f0488\"><strong>Exemplos de Aplica\u00e7\u00e3o da M\u00e9dia Aritm\u00e9tica<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">Suponhamos que uma pessoa fa\u00e7a cinco viagens de carro em um m\u00eas, e as dist\u00e2ncias percorridas foram 100 km, 150 km, 200 km, 250 km e 300 km.\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">Para saber a dist\u00e2ncia m\u00e9dia percorrida por viagem, calculamos a m\u00e9dia aritm\u00e9tica desses valores.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li class=\"has-medium-font-size\">Outro exemplo seria calcular a m\u00e9dia das notas de um aluno em cinco provas.\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">Se as notas foram 7, 8, 6, 9 e 5, a m\u00e9dia aritm\u00e9tica dessas notas \u00e9 (7+8+6+9+5):5=7.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-medium-font-size wp-elements-9c8bd4548c178f9ba137f77d375a66b6\" style=\"color:#0f0488\"><strong>Amplitude<\/strong><\/p>\n\n\n\n<p class=\"has-vivid-red-color has-text-color has-link-color has-medium-font-size wp-elements-900403f2264bcdb6435df159078614a8\"><strong>Defini\u00e7\u00e3o<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">A amplitude \u00e9 a <strong>diferen\u00e7a<\/strong> entre o <strong>maior e o meno<\/strong>r valor de um conjunto de dados.&nbsp;<\/p>\n\n\n\n<p class=\"has-vivid-red-color has-text-color has-link-color has-medium-font-size wp-elements-d7f4ef56b80580875574223c79d63ddb\"><strong>Por exemplo:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">Vamos supor que voc\u00ea tenha um conjunto de n\u00fameros que representam a altura de algumas pessoas em cent\u00edmetros: 150, 160, 170, 180 e 190.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-medium-font-size\">Para calcular a amplitude desse conjunto, voc\u00ea precisa encontrar a diferen\u00e7a entre o maior e o menor valor, ou seja, 190 &#8211; 150 = 40. Isso significa que a diferen\u00e7a entre a maior e a menor altura \u00e9 de 40 cent\u00edmetros.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-medium-font-size wp-elements-ecd05447a0218e12f6d7c957686cb6a6\" style=\"color:#0f0488\"><strong>Conclus\u00e3o<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u00c9 importante entender a m\u00e9dia aritm\u00e9tica e a amplitude para interpretar dados de forma eficaz. Esses conceitos podem ser \u00fateis em situa\u00e7\u00f5es do dia a dia. Espero que este texto tenha sido \u00fatil para voc\u00ea compreender melhor esses conceitos matem\u00e1ticos b\u00e1sicos.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">At\u00e9 o pr\u00f3ximo.<\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 01<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Dados os valores num\u00e9ricos de um banco de dados, a m\u00e9dia aritm\u00e9tica representa a m\u00e9dia desses valores obtida pela divis\u00e3o da soma de todos os valores pelo n\u00famero de valores adicionados.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Abaixo temos a informa\u00e7\u00e3o das notas das avalia\u00e7\u00f5es em matem\u00e1tica do IV bimestre dos estudantes Pedro, Paulo e Paula.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"556\" height=\"132\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2022\/11\/1-5-e1669399944369.png\" alt=\"\" class=\"wp-image-154536\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2022\/11\/1-5-e1669399944369.png 556w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2022\/11\/1-5-e1669399944369-300x71.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><figcaption class=\"wp-element-caption\"> canva.com.br <\/figcaption><\/figure><\/div>\n\n\n<p class=\"has-medium-font-size\">A m\u00e9dia para ser aprovado ter\u00e1 que ser maior ou igual a 5,0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">A) Determine a m\u00e9dia aritm\u00e9tica de cada estudante.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">B) Qual estudante obteve a maior m\u00e9dia? Qual \u00e9 esse valor?<\/p>\n\n\n\n<p class=\"has-medium-font-size\">D) Algum estudante n\u00e3o alcan\u00e7ou a m\u00e9dia para aprova\u00e7\u00e3o? Se sim, qual?<\/p>\n\n\n\n<p class=\"has-black-color has-pale-cyan-blue-background-color has-text-color has-background has-link-color has-medium-font-size wp-elements-8d1baed2f47c9670f4e5a8aecf4887b0\"><strong>QUEST\u00c3O 02<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">A m\u00e9dia aritm\u00e9tica \u00e9 ponderada quando os valores t\u00eam pesos diferentes. O c\u00e1lculo \u00e9 feito pelo quociente entre a soma dos produtos de cada valor pelos seus respectivos pesos e a soma dos pesos.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Veja como a professora Marta calculou a m\u00e9dia do IV bimestre da sua aluna Milena.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"505\" height=\"167\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2022\/11\/2-4-e1669400075461.png\" alt=\"\" class=\"wp-image-154537\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2022\/11\/2-4-e1669400075461.png 505w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2022\/11\/2-4-e1669400075461-300x99.png 300w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><figcaption class=\"wp-element-caption\"> canva.com.br <\/figcaption><\/figure><\/div>\n\n\n<p class=\"has-medium-font-size\">Agora \u00e9 com voc\u00ea. Utilizando os mesmos pesos, calcule a m\u00e9dia bimestral dos seguintes estudantes:<\/p>\n\n\n\n<p class=\"has-medium-font-size\">A) Pedro: Tarefas = 4,0 Participa\u00e7\u00e3o = 6,0 Avalia\u00e7\u00e3o escrita = 5,0 e Trabalho = 8,0<\/p>\n\n\n\n<p class=\"has-medium-font-size\">B) J\u00falia: Tarefas = 5,0 Participa\u00e7\u00e3o = 8,0 Avalia\u00e7\u00e3o escrita = 9,0 e Trabalho = 7,0<\/p>\n\n\n\n<p class=\"has-medium-font-size\">C) Gabriel: Tarefas = 5,0 Participa\u00e7\u00e3o = 2,0 Avalia\u00e7\u00e3o escrita = 3,0 e Trabalho = 4,0<\/p>\n\n\n\n<p class=\"has-medium-font-size\">D) Jo\u00e3o: Tarefas = 6,0 Participa\u00e7\u00e3o = 3,0 Avalia\u00e7\u00e3o escrita = 5,0 e Trabalho = 9,0<\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 03<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Patr\u00edcia possui uma loja de vendas de shorts e saias com funcion\u00e1rios que recebem sal\u00e1rios diferenciados. Se o menor sal\u00e1rio dessa loja \u00e9 de 1300 reais e o maior \u00e9 de 2800 reais, podemos afirmar que a amplitude salarial da equipe de Patr\u00edcia \u00e9 de&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(A) 1200 reais.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(B) 1300 reais.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(C) 1400 reais.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(D) 1500 reais.<\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 04<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">O gr\u00e1fico abaixo representa a quantidade de alunos por idade, da 7\u00aa s\u00e9rie de uma escola de Goi\u00e2nia.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"401\" height=\"238\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2022\/11\/4-3.png\" alt=\"\" class=\"wp-image-154539\" style=\"width:309px;height:auto\" srcset=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2022\/11\/4-3.png 401w, https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2022\/11\/4-3-300x178.png 300w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><figcaption class=\"wp-element-caption\"> canva.com.br <\/figcaption><\/figure><\/div>\n\n\n<p class=\"has-medium-font-size\">De acordo com o gr\u00e1fico, podemos afirmar que a m\u00e9dia aritm\u00e9tica das idades desses estudantes \u00e9 de&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(A) Aproximadamente 10 anos.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(B) Aproximadamente 11 anos.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(C) Aproximadamente 12 anos.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(D) Aproximadamente 14 anos.<\/p>\n\n\n\n<p class=\"has-white-color has-text-color has-background has-link-color has-medium-font-size wp-elements-f025b42fbcc42a49a9ff5f0f8253a61b\" style=\"background-color:#0f0488\"><strong>SAIBA MAIS<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Aprenda um pouco mais sobre m\u00e9dia e amplitude assistindo o v\u00eddeo no canal do prof. H\u00e9lio.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<p class=\"responsive-video-wrap clr\"><iframe title=\"M\u00e9dia aritm\u00e9tica simples e ponderada\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/KWcRrGV9vbo?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<\/div><figcaption class=\"wp-element-caption\">canal do prof. H\u00e9lio &lt;YouTube&gt;<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td>Autoria<\/td><td>Professor H\u00e9lio Roberto da Rocha, Mestre em Matem\u00e1tica.<\/td><\/tr><tr><td>Componente Curricular<\/td><td>Objetivos de aprendizagem e desenvolvimento<\/td><\/tr><tr><td>Matem\u00e1tica<\/td><td>(EJAMA0530) Reconhecer e calcular m\u00e9dia aritm\u00e9tica, moda e mediana como medidas de tend\u00eancia central e amplitude como uma medida de dispers\u00e3o de uma pesquisa estat\u00edstica.<\/td><\/tr><tr><td>Refer\u00eancias<\/td><td>SOUZA, Joamir Roberto de: Matem\u00e1tica realidade &amp; tecnologia: 7\u00ba ano: ensino fundamental: anos finais \/Joamir Roberto de Souza. \u2013 1. ed. \u2013 S\u00e3o Paulo: FTD, 2018.<br>GIOVANNI J\u00daNIOR, Jos\u00e9 Ruy &#8211; A conquista da matem\u00e1tica: 7\u00b0 ano: ensino fundamental: anos finais \/ Jos\u00e9 Ruy Giovanni J\u00fanior, Benedicto Castrucci. \u2014 4. ed. \u2014 S\u00e3o Paulo: FTD, 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