{"id":407,"date":"2023-07-30T16:50:52","date_gmt":"2023-07-30T16:50:52","guid":{"rendered":"https:\/\/statorials.org\/pt\/mede-a-tendencia-central\/"},"modified":"2023-07-30T16:50:52","modified_gmt":"2023-07-30T16:50:52","slug":"mede-a-tendencia-central","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/mede-a-tendencia-central\/","title":{"rendered":"Medidas de tend\u00eancia central: defini\u00e7\u00e3o e exemplos"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Uma <strong>medida de tend\u00eancia central<\/strong> \u00e9 um valor \u00fanico que representa o ponto central de um conjunto de dados. Este valor tamb\u00e9m pode ser chamado de \u201clocaliza\u00e7\u00e3o central\u201d de um conjunto de dados.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Nas estat\u00edsticas, existem tr\u00eas medidas comuns de tend\u00eancia central:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>A m\u00e9dia<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>A mediana<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><b>A moda<\/b><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Cada uma dessas medidas encontra a localiza\u00e7\u00e3o central de um conjunto de dados usando m\u00e9todos diferentes.<\/span> <span style=\"color: #000000;\">Dependendo do tipo de dados que voc\u00ea est\u00e1 analisando, pode ser melhor usar uma dessas tr\u00eas m\u00e9tricas em vez das outras duas.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Neste artigo, veremos como calcular cada uma das tr\u00eas medidas de tend\u00eancia central e tamb\u00e9m como determinar qual medida \u00e9 melhor usar com base em seus dados.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Por que as medidas de tend\u00eancia central s\u00e3o \u00fateis?<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Antes de vermos como calcular a m\u00e9dia, a mediana e a moda, \u00e9 \u00fatil entender <em>por que<\/em> essas medidas s\u00e3o realmente \u00fateis.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Considere o seguinte cen\u00e1rio:<\/span><\/p>\n<blockquote>\n<p> <span style=\"color: #000000;\">Um jovem casal est\u00e1 tentando decidir onde comprar sua primeira casa em uma nova cidade e o m\u00e1ximo que podem gastar \u00e9 US$ 150 mil. Algumas \u00e1reas da cidade t\u00eam casas caras, algumas t\u00eam casas baratas e algumas t\u00eam casas de pre\u00e7o m\u00e9dio. Eles desejam restringir facilmente sua pesquisa a bairros espec\u00edficos que cabem em seu or\u00e7amento.<\/span><\/p>\n<\/blockquote>\n<p> <span style=\"color: #000000;\">Se o casal apenas olhasse os pre\u00e7os das casas unifamiliares em cada bairro, poderia ter dificuldade em determinar quais bairros melhor se adaptam ao seu or\u00e7amento, porque poderia ver algo assim:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pre\u00e7os das casas no bairro <em>A<\/em> :<\/strong> $ 140.000, $ 190.000, $ 265.000, $ 115.000, $ 270.000, $ 240.000, $ 250.000, $ 180.000, $ 160.000, $ 200.000, $ 240.000, $ 280.000,\u2026<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pre\u00e7os das casas no bairro <em>B<\/em> :<\/strong> $ 140.000, $ 290.000, $ 155.000, $ 165.000, $ 280.000, $ 220.000, $ 155.000, $ 185.000, $ 160.000, $ 200.000, $ 190.000, $ 140.000, $ 145,0 0 0,\u2026<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pre\u00e7os das casas no bairro <em>C<\/em> :<\/strong> $ 140.000, $ 130.000, $ 165.000, $ 115.000, $ 170.000, $ 100.000, $ 150.000, $ 180.000, $ 190.000, $ 120.000, $ 110.000, $ 130.000, $ 120,0 0 0,\u2026<\/span><\/p>\n<p> <span style=\"color: #000000;\">No entanto, se conhecessem o pre\u00e7o <em>m\u00e9dio<\/em> (por exemplo, uma medida de tend\u00eancia central) das casas em cada bairro, ent\u00e3o poderiam refinar a sua pesquisa muito mais rapidamente porque poderiam identificar mais facilmente qual bairro tem pre\u00e7os de casas que correspondem ao seu or\u00e7amento:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pre\u00e7o m\u00e9dio <em>de uma<\/em> casa no bairro A:<\/strong> US$ 220 mil<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pre\u00e7o m\u00e9dio de uma casa no bairro <em>B<\/em> :<\/strong> $ 190.000<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pre\u00e7o m\u00e9dio de uma casa no bairro <em>C<\/em> :<\/strong> $ 140.000<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ao conhecer o pre\u00e7o m\u00e9dio das casas em cada bairro, eles podem ver rapidamente que o Bairro <em>C<\/em> provavelmente ter\u00e1 o maior n\u00famero de casas dispon\u00edveis dentro do seu or\u00e7amento.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Este \u00e9 o benef\u00edcio de usar uma medida de tend\u00eancia central: ajuda a entender o valor central de um conjunto de dados, que tende a descrever onde geralmente est\u00e3o os valores dos dados. Neste exemplo espec\u00edfico, ajuda o jovem casal a compreender o pre\u00e7o t\u00edpico de uma casa em cada bairro.<\/span><\/p>\n<blockquote>\n<p> <span style=\"color: #000000;\"><strong>Conclus\u00e3o:<\/strong> uma medida de tend\u00eancia central \u00e9 \u00fatil porque nos fornece um valor \u00fanico que descreve o \u201ccentro\u201d de um conjunto de dados. Isso nos ajuda a entender um conjunto de dados com muito mais rapidez do que apenas observar todos os valores individuais no conjunto de dados.<\/span><\/p>\n<\/blockquote>\n<h2> <strong><span style=\"color: #000000;\">Significar<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">A medida de tend\u00eancia central mais comumente usada \u00e9 <strong>a m\u00e9dia<\/strong> . Para calcular a m\u00e9dia de um conjunto de dados, basta somar todos os valores individuais e dividir pelo n\u00famero total de valores.<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">M\u00e9dia = (soma de todos os valores) \/ (n\u00famero total de valores)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Por exemplo, suponha que temos o seguinte conjunto de dados que mostra o n\u00famero de home runs rebatidos por 10 jogadores de beisebol do mesmo time durante uma temporada:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Jogador<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#1<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#2<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#3<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#4<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#5<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#6<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#7<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#8<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#9<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#dez<\/span><\/strong><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Home runs<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">8<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">15<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">22<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">21<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">12<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">9<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">11<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">27<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">14<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">13<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">O n\u00famero m\u00e9dio de home runs rebatidos por jogador pode ser calculado da seguinte forma:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">M\u00e9dia = (8+15+22+21+12+9+11+27+14+13) \/ 10 = <strong>15,2<\/strong> <strong>circuitos<\/strong> .<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">Mediana<\/span><\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A <strong>mediana<\/strong> \u00e9 o valor m\u00e9dio de um conjunto de dados. Voc\u00ea pode encontrar a mediana ordenando todos os valores individuais em um conjunto de dados do menor para o maior e encontrando o valor mediano. Se houver um n\u00famero \u00edmpar de valores, a mediana \u00e9 o valor do meio. Se houver um n\u00famero par de valores, a mediana ser\u00e1 a m\u00e9dia dos dois valores intermedi\u00e1rios.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Por exemplo, para encontrar o n\u00famero m\u00e9dio de home runs rebatidos pelos 10 jogadores de beisebol do exemplo anterior, podemos classificar os jogadores em ordem decrescente do n\u00famero de home runs rebatidos:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Jogador<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#1<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#6<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#7<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#5<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#dez<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#9<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#2<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#4<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#3<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#8<\/span><\/strong><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Home runs<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">8<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">9<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">11<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">12<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>13<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>14<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">15<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">21<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">22<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">27<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">Como temos um n\u00famero par de valores, a mediana \u00e9 simplesmente a m\u00e9dia dos dois valores intermedi\u00e1rios: <strong>13,5<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Em vez disso, considere se tiv\u00e9ssemos nove jogadores:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Jogador<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#1<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#6<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#7<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#5<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#9<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#2<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#4<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#3<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#8<\/span><\/strong><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Home runs<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">8<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">9<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">11<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">12<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>14<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">15<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">21<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">22<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">27<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">Neste caso, como temos um n\u00famero \u00edmpar de valores, a mediana \u00e9 simplesmente o valor do meio: <strong>14<\/strong> .<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>A moda<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A <strong>moda<\/strong> \u00e9 o valor que aparece com mais frequ\u00eancia em um conjunto de dados. Um conjunto de dados n\u00e3o pode ter modos (se nenhum valor se repetir), um modo ou v\u00e1rios modos.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Por exemplo, o seguinte conjunto de dados n\u00e3o tem moda:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Jogador<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#1<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#2<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#3<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#4<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#5<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#6<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#7<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#8<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#9<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#dez<\/span><\/strong><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Home runs<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">8<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">9<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">11<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">12<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">13<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">14<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">15<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">21<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">22<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">27<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">O seguinte conjunto de dados possui uma moda: <strong>15<\/strong> . Este \u00e9 o valor que aparece com mais frequ\u00eancia.<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Jogador<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#1<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#2<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#3<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#4<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#5<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#6<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#7<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#8<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#9<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#dez<\/span><\/strong><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Home runs<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">8<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">9<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">11<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">12<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">13<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>15<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>15<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">21<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">22<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">27<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">O conjunto de dados a seguir possui tr\u00eas modos: <strong>8, 15, 19<\/strong> . Estes s\u00e3o os valores que aparecem com mais frequ\u00eancia.<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Jogador<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#1<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#2<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#3<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#4<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#5<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#6<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#7<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#8<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#9<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#dez<\/span><\/strong><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Home runs<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>8<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>8<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">11<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">12<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>15<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>15<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">17<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>19<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>19<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">27<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">A moda pode ser uma medida de tend\u00eancia central particularmente \u00fatil quando se trabalha com dados categ\u00f3ricos, porque nos diz qual categoria aparece com mais frequ\u00eancia. Por exemplo, considere o seguinte gr\u00e1fico de barras que mostra os resultados de uma pesquisa sobre a cor favorita das pessoas:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-4775 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/mode_bar_chart.jpg\" alt=\"\" width=\"512\" height=\"396\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">A <strong>moda<\/strong> , ou a resposta que ocorreu com mais frequ\u00eancia, foi azul.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Em cen\u00e1rios onde os dados s\u00e3o categ\u00f3ricos (como o acima), nem \u00e9 poss\u00edvel calcular a mediana ou m\u00e9dia, portanto a moda \u00e9 a \u00fanica medida de tend\u00eancia central que podemos utilizar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">O modo tamb\u00e9m pode ser usado para dados num\u00e9ricos, como vimos no exemplo acima com jogadores de beisebol. No entanto, a moda tende a ser menos \u00fatil para responder \u00e0 pergunta <em>\u201cQual \u00e9 um valor t\u00edpico para este conjunto de dados?\u201d \u00bb<\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\">Por exemplo, suponha que queiramos saber o n\u00famero t\u00edpico de home runs rebatidos por um jogador de beisebol deste time:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Jogador<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#1<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#2<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#3<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#4<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#5<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#6<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#7<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#8<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#9<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#dez<\/span><\/strong><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Home runs<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">8<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">8<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">11<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">12<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">15<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">15<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">17<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">19<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">19<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">27<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">A moda para este conjunto de dados \u00e9 8, 15 e 19 porque estes s\u00e3o os valores mais frequentes. No entanto, estes n\u00e3o s\u00e3o muito \u00fateis para compreender o n\u00famero t\u00edpico de home runs rebatidos por um jogador da equipa. Uma melhor medida de tend\u00eancia central neste caso seria a mediana (15) ou a m\u00e9dia (tamb\u00e9m 15).<\/span><\/p>\n<p> <span style=\"color: #000000;\">A moda tamb\u00e9m \u00e9 uma medida pobre de tend\u00eancia central quando \u00e9 um n\u00famero distante do restante dos valores. Por exemplo, o modo do conjunto de dados a seguir \u00e9 30, mas na verdade n\u00e3o representa o n\u00famero &#8220;t\u00edpico&#8221; de home runs por jogador do time:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Jogador<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#1<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#2<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#3<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#4<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#5<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#6<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#7<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#8<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#9<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">#dez<\/span><\/strong><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">Home runs<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">5<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">6<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">7<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">dez<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">11<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">12<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">13<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">15<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">30<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">30<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p> <span style=\"color: #000000;\">Novamente, a m\u00e9dia ou mediana descreveria melhor a localiza\u00e7\u00e3o central deste conjunto de dados.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Quando usar m\u00e9dia, mediana e modo<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Vimos que a m\u00e9dia, a mediana e a moda medem a localiza\u00e7\u00e3o central, ou \u201cvalor t\u00edpico\u201d, de um conjunto de dados de maneiras muito diferentes:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>M\u00e9dia:<\/strong> Encontra o valor m\u00e9dio em um conjunto de dados.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Mediana:<\/strong> Encontra o valor mediano em um conjunto de dados.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Modo:<\/strong> Encontra o valor mais frequente em um conjunto de dados.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Aqui est\u00e3o os cen\u00e1rios em que certas medidas de tend\u00eancia central s\u00e3o melhores para usar do que outras:<\/span><\/p>\n<h3> <strong>Quando usar a m\u00e9dia<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u00c9 melhor usar a m\u00e9dia quando a distribui\u00e7\u00e3o dos dados for bastante sim\u00e9trica e n\u00e3o houver valores discrepantes.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Por exemplo, suponha que temos a seguinte distribui\u00e7\u00e3o que mostra os sal\u00e1rios dos indiv\u00edduos em uma determinada cidade:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-4776 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyenne_dist.jpg\" alt=\"\" width=\"468\" height=\"445\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Dado que esta distribui\u00e7\u00e3o \u00e9 bastante sim\u00e9trica (ou seja, se a dividirmos ao meio, cada metade parecer\u00e1 aproximadamente igual) e n\u00e3o existem valores discrepantes (ou seja, (digamos, n\u00e3o h\u00e1 sal\u00e1rios extremamente elevados), a m\u00e9dia far\u00e1 um bom trabalho ao descrever este conjunto de dados.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A m\u00e9dia acaba sendo de US$ 63.000, que fica aproximadamente no centro da distribui\u00e7\u00e3o:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-4777 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyenne_dist2.jpg\" alt=\"\" width=\"476\" height=\"450\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Quando usar a mediana<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u00c9 melhor usar a mediana quando a distribui\u00e7\u00e3o dos dados \u00e9 distorcida ou quando h\u00e1 valores discrepantes.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Dados tendenciosos:<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Quando a distribui\u00e7\u00e3o \u00e9 distorcida, a mediana ainda consegue capturar a localiza\u00e7\u00e3o central. Por exemplo, considere a seguinte distribui\u00e7\u00e3o de sal\u00e1rios de indiv\u00edduos em uma determinada cidade:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-4778 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/mediane_diste.jpg\" alt=\"\" width=\"473\" height=\"439\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">A mediana reflete melhor o sal\u00e1rio \u201ct\u00edpico\u201d de um indiv\u00edduo do que a m\u00e9dia. Isso ocorre porque valores grandes na cauda de uma distribui\u00e7\u00e3o tendem a afastar a m\u00e9dia do centro e em dire\u00e7\u00e3o \u00e0 cauda longa.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Neste exemplo espec\u00edfico, a m\u00e9dia diz-nos que um indiv\u00edduo t\u00edpico ganha cerca de 47.000 d\u00f3lares por ano nesta cidade, enquanto a mediana diz-nos que o indiv\u00edduo t\u00edpico ganha apenas cerca de 32.000 d\u00f3lares por ano, o que \u00e9 muito mais representativo do indiv\u00edduo t\u00edpico.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">Valores discrepantes:<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A mediana tamb\u00e9m ajuda a capturar melhor a localiza\u00e7\u00e3o central de uma distribui\u00e7\u00e3o quando h\u00e1 valores discrepantes nos dados. Por exemplo, considere o gr\u00e1fico a seguir que mostra a metragem quadrada das casas em uma determinada rua:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-4779 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyenne_dist3.jpg\" alt=\"\" width=\"478\" height=\"416\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">A m\u00e9dia \u00e9 fortemente influenciada por algumas casas extremamente grandes, enquanto a mediana n\u00e3o. Assim, a mediana captura melhor a metragem quadrada \u201ct\u00edpica\u201d de uma casa naquela rua do que a m\u00e9dia.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Quando usar o modo<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Este modo \u00e9 melhor usado quando voc\u00ea est\u00e1 trabalhando com dados categ\u00f3ricos e deseja saber qual categoria aparece com mais frequ\u00eancia. aqui est\u00e3o alguns exemplos:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Voc\u00ea est\u00e1 realizando uma pesquisa sobre as cores favoritas das pessoas e quer saber qual cor aparece com mais frequ\u00eancia nas respostas.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Voc\u00ea est\u00e1 conduzindo uma pesquisa sobre as prefer\u00eancias das pessoas entre tr\u00eas op\u00e7\u00f5es de design de site e deseja saber qual design as pessoas preferem mais.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Conforme mencionado anteriormente, se voc\u00ea estiver trabalhando com dados categ\u00f3ricos, nem \u00e9 poss\u00edvel calcular a mediana ou m\u00e9dia, o que deixa a moda como a \u00fanica medida de tend\u00eancia central.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Em geral, se voc\u00ea estiver trabalhando com dados num\u00e9ricos, como metragem quadrada de casas, n\u00famero de home runs rebatidos por jogador, sal\u00e1rio por indiv\u00edduo, etc., geralmente \u00e9 melhor usar a mediana ou m\u00e9dia para descrever o valor \u201ct\u00edpico\u201d em o conjunto de dados.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Nota:<\/strong> \u00c9 importante observar que se um conjunto de dados for <em>perfeitamente<\/em> distribu\u00eddo normalmente, ent\u00e3o a m\u00e9dia, a mediana e a moda ter\u00e3o todos o mesmo valor.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Uma medida de tend\u00eancia central \u00e9 um valor \u00fanico que representa o ponto central de um conjunto de dados. Este valor tamb\u00e9m pode ser chamado de \u201clocaliza\u00e7\u00e3o central\u201d de um conjunto de dados. Nas estat\u00edsticas, existem tr\u00eas medidas comuns de tend\u00eancia central: A m\u00e9dia A mediana A moda Cada uma dessas medidas encontra a localiza\u00e7\u00e3o [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-407","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Medidas de tend\u00eancia central: defini\u00e7\u00e3o e exemplos - Statorials<\/title>\n<meta name=\"description\" content=\"Uma explica\u00e7\u00e3o simples das medidas de tend\u00eancia central nas estat\u00edsticas, incluindo v\u00e1rios exemplos.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pt\/mede-a-tendencia-central\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Medidas de tend\u00eancia central: defini\u00e7\u00e3o e exemplos - Statorials\" \/>\n<meta property=\"og:description\" content=\"Uma explica\u00e7\u00e3o simples das medidas de tend\u00eancia central nas estat\u00edsticas, incluindo v\u00e1rios exemplos.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/mede-a-tendencia-central\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-30T16:50:52+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/mode_bar_chart.jpg\" \/>\n<meta name=\"author\" content=\"Dr. benjamim anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. benjamim anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo estimado de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"9 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/mede-a-tendencia-central\/\",\"url\":\"https:\/\/statorials.org\/pt\/mede-a-tendencia-central\/\",\"name\":\"Medidas de tend\u00eancia central: defini\u00e7\u00e3o e exemplos - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-30T16:50:52+00:00\",\"dateModified\":\"2023-07-30T16:50:52+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Uma explica\u00e7\u00e3o simples das medidas de tend\u00eancia central nas estat\u00edsticas, incluindo v\u00e1rios exemplos.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/mede-a-tendencia-central\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/mede-a-tendencia-central\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/mede-a-tendencia-central\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Medidas de tend\u00eancia central: defini\u00e7\u00e3o e exemplos\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pt\/#website\",\"url\":\"https:\/\/statorials.org\/pt\/\",\"name\":\"Statorials\",\"description\":\"O seu guia para a literacia estat\u00edstica!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-PT\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\",\"name\":\"Dr. benjamim anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-PT\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr. benjamim anderson\"},\"description\":\"Ol\u00e1, sou Benjamin, um professor aposentado de estat\u00edstica que se tornou professor dedicado na Statorials. 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