{"id":724,"date":"2025-07-29T15:50:45","date_gmt":"2025-07-29T19:50:45","guid":{"rendered":"https:\/\/literaciadigital.ufms.br\/?page_id=724"},"modified":"2025-10-11T10:32:01","modified_gmt":"2025-10-11T14:32:01","slug":"14-1","status":"publish","type":"page","link":"https:\/\/literaciadigital.ufms.br\/en\/data8\/14-0\/14-1\/","title":{"rendered":"Cap\u00edtulo 14.1"},"content":{"rendered":"<div style=\"position: relative\">\n<div style=\"float: left;width: 300px;background-color: #f5f5f5;border: 1px solid #ddd;border-radius: 5px;padding: 15px;margin-right: 20px;margin-bottom: 5px;overflow: hidden\">\n<h3 style=\"margin: 0 0 10px 0;padding-bottom: 8px;border-bottom: 1px solid #ddd\">\u00cdndice<\/h3>\n<ol style=\"margin: 0;padding-left: 0;list-style-type: none\">\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/\">1. O que \u00e9 Ci\u00eancia de Dados?<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-1\/\">1.1. Introdu\u00e7\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-1\/1-1\/\">1.1.1. Ferramentas Computacionais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-1\/1-2\/\">1.1.2. T\u00e9cnicas Estat\u00edsticas<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-2\/\">1.2. Por que Ci\u00eancia de Dados?<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-3\/\">1.3. Tra\u00e7ando os Cl\u00e1ssicos<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-3\/3-1\/\">1.3.1. Personagens Liter\u00e1rios<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-3\/3-2\/\">1.3.2. Outro Tipo de Personagem<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/\">2. Causalidade e Experimentos<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-1\/\">2.1. John Snow e a Bomba da Broad Street<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-2\/\">2.2. O &#8220;Grande Experimento&#8221; de Snow<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-3\/\">2.3. Estabelecendo Causalidade<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-4\/\">2.4. Randomiza\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-5\/\">2.5. Notas Finais<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/\">3. Progamando em Python<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-1\/\">3.1. Express\u00f5es<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-2\/\">3.2. Nomes<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-2\/2-1\/\">3.2.1. Exemplo: Taxas de Crescimento<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-3\/\">3.3. Chamadas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-4\/\">3.4. Introdu\u00e7\u00e3o \u00e0s Tabelas<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/\">4. Tipos de Dados<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-1\/\">4.1. N\u00fameros<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-2\/\">4.2. Strings<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-2\/2-1\/\">4.2.1. M\u00e9todos de Strings<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-3\/\">4.3. Compara\u00e7\u00f5es<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/\">5. Sequ\u00eancias<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/5-1\/\">5.1. Arrays<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/5-2\/\">5.2. Ranges<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/5-3\/\">5.3. Mais sobre Arrays<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/\">6. Tabelas<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-1\/\">6.1. Ordenando Linhas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-2\/\">6.2. Selecionando Linhas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-3\/\">6.3. Exemplo: Tend\u00eancias Populacionais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-4\/\">6.4. Examplo: Propor\u00e7\u00f5es de Sexos<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/\">7. Visualiza\u00e7\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/7-1\/\">7.1. Visualizando Distribui\u00e7\u00f5es<br \/>\nCateg\u00f3ricas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/7-2\/\">7.2. Visualizando Distribui\u00e7\u00f5es Num\u00e9ricas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/7-3\/\">7.3. Gr\u00e1ficos Sobrepostos<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/\">8. Fun\u00e7\u00f5es e Tabelas<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-1\/\">8.1. Aplicando Fun\u00e7\u00e3o a uma Coluna<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-2\/\">8.2. Classificando por uma Vari\u00e1vel<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-3\/\">8.3. Classifica\u00e7\u00e3o Cruzada<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-4\/\">8.4. Unindo Tabelas por Colunas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-5\/\">8.5. Compartilhamento de Bicicletas<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/\">9. Aleatoriedade<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-1\/\">9.1. Declara\u00e7\u00f5es Condicionais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-2\/\">9.2. Itera\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-3\/\">9.3. Simula\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-4\/\">9.4. O Problema de Monty Hall<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-5\/\">9.5. Encontrando Probabilidades<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/\">10. Amostragem e Distribui\u00e7\u00f5es Emp\u00edricas<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-1\/\">10.1. Distribui\u00e7\u00f5es Emp\u00edricas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-2\/\">10.2. Amostragem de uma Popula\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-3\/\">10.3. Distribui\u00e7\u00e3o Emp\u00edrica de uma<br \/>\nEstat\u00edstica<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-4\/\">10.4. Amostragem Aleat\u00f3ria em Python <\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/\">11. Testando Hip\u00f3teses<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-1\/\">11.1. Avaliando um Modelo<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-2\/\">11.2. M\u00faltiplas Categorias<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-3\/\">11.3. Decis\u00f5es e Incertezas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-4\/\">11.4. Probabilidades de Erro<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/\">12. Comparando Duas Amostras<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-1\/\">12.1. Teste A\/B<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-2\/\">12.2. Causalidade<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-3\/\">12.3. Esvaziar<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/\">13. Estima\u00e7\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-1\/\">13.1. Percentis<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-2\/\">13.2. O Bootstrap<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-3\/\">13.3. Intervalos de Confian\u00e7a<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-4\/\">13.4. Usando Intervalos de Confian\u00e7a<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/\">14. Por que a M\u00e9dia \u00e9 Importante<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-1\/\">14.1. Propriedades da M\u00e9dia<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-2\/\">14.2. Variabilidade<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-3\/\">14.3. O DP e a Curva Normal<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-4\/\">14.4. Teorema Central do Limite<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-5\/\">14.5. Variabilidade da M\u00e9dia da Amostra<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-6\/\">14.6. Escolhendo um Tamanho de Amostra<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/\">15. Previs\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-1\/\">15.1. Correla\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-2\/\">15.2. Linha de Regress\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-3\/\">15.3. M\u00e9todo dos M\u00ednimos Quadrados<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-4\/\">15.4. Regress\u00e3o de M\u00ednimos Quadrados<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-5\/\">15.5. Diagn\u00f3sticos Visuais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-6\/\">15.6. Diagn\u00f3stico Num\u00e9rico<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<p><!-- Main Content --><\/p>\n<div style=\"overflow: hidden\">\n<p><!--###########################################################################################################################################################--><\/p>\n<pre><code><span style=\"color: black\">from datascience import *\r\n%matplotlib inline\r\npath_data = '..\/..\/..\/assets\/data\/'\r\nimport matplotlib.pyplot as plots\r\nplots.style.use('fivethirtyeight')\r\nimport pylab as pl\r\nimport numpy as np<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<h1 id=\"propriedades-da-m-dia\" style=\"text-align: center\">Propriedades da M\u00e9dia<\/h1>\n<p style=\"text-align: justify\">Neste curso, temos usado as palavras &#8220;m\u00e9dia&#8221; e &#8220;m\u00e9dia aritm\u00e9tica&#8221; de forma intercambi\u00e1vel e continuaremos a faz\u00ea-lo. A defini\u00e7\u00e3o de m\u00e9dia ser\u00e1 familiar para voc\u00ea desde os tempos de escola ou at\u00e9 antes.<\/p>\n<p style=\"text-align: justify\"><strong>Defini\u00e7\u00e3o.<\/strong> A <em>m\u00e9dia<\/em> ou <em>m\u00e9dia aritm\u00e9tica<\/em> de uma cole\u00e7\u00e3o de n\u00fameros \u00e9 a soma de todos os elementos da cole\u00e7\u00e3o, dividida pelo n\u00famero de elementos na cole\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify\">Os m\u00e9todos <code>np.average<\/code> e <code>np.mean<\/code> retornam a m\u00e9dia de um array.<\/p>\n<pre><code><span style=\"color: black\">not_symmetric = make_array(2, 3, 3, 9)<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">np.average(not_symmetric)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[1]:<\/td>\n<td style=\"text-align: left\">4.25<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">np.mean(not_symmetric)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[2]:<\/td>\n<td style=\"text-align: left\">4.25<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h2 id=\"propriedades-b-sicas\" style=\"text-align: justify\">Propriedades B\u00e1sicas<\/h2>\n<p style=\"text-align: justify\">A defini\u00e7\u00e3o e o exemplo acima apontam algumas propriedades da m\u00e9dia.<\/p>\n<ul style=\"text-align: justify\">\n<li>Ela n\u00e3o precisa ser um elemento da cole\u00e7\u00e3o.<\/li>\n<li>Ela n\u00e3o precisa ser um n\u00famero inteiro, mesmo que todos os elementos da cole\u00e7\u00e3o sejam inteiros.<\/li>\n<li>Ela est\u00e1 entre os menores e maiores valores da cole\u00e7\u00e3o.<\/li>\n<li>N\u00e3o precisa estar na metade entre os dois extremos; n\u00e3o \u00e9 geralmente verdade que metade dos elementos de uma cole\u00e7\u00e3o est\u00e3o acima da m\u00e9dia.<\/li>\n<li>Se a cole\u00e7\u00e3o consiste em valores de uma vari\u00e1vel medida em unidades especificadas, ent\u00e3o a m\u00e9dia tem as mesmas unidades tamb\u00e9m.<\/li>\n<\/ul>\n<p style=\"text-align: justify\">Agora estudaremos outras propriedades que s\u00e3o \u00fateis para entender a m\u00e9dia e sua rela\u00e7\u00e3o com outras estat\u00edsticas.<\/p>\n<h2 id=\"a-m-dia-um-suavizador-\" style=\"text-align: justify\">A M\u00e9dia \u00e9 um &#8220;Suavizador&#8221;<\/h2>\n<p style=\"text-align: justify\">Voc\u00ea pode pensar em calcular a m\u00e9dia como uma opera\u00e7\u00e3o de &#8220;equaliza\u00e7\u00e3o&#8221; ou &#8220;suaviza\u00e7\u00e3o&#8221;. Por exemplo, imagine os valores em <code>not_symmetric<\/code> acima como d\u00f3lares nos bolsos de quatro pessoas diferentes. Para obter a m\u00e9dia, voc\u00ea primeiro coloca todo o dinheiro em um grande pote e depois divide igualmente entre as quatro pessoas. Elas come\u00e7aram com diferentes quantias de dinheiro em seus bolsos ($2, $3, $3, e $9), mas agora cada pessoa tem $4,25, o valor m\u00e9dio.<\/p>\n<h2 id=\"propor-es-s-o-m-dias\" style=\"text-align: justify\">Propor\u00e7\u00f5es s\u00e3o M\u00e9dias<\/h2>\n<p style=\"text-align: justify\">Se uma cole\u00e7\u00e3o consiste apenas em uns e zeros, ent\u00e3o a soma da cole\u00e7\u00e3o \u00e9 o n\u00famero de uns nela, e a m\u00e9dia da cole\u00e7\u00e3o \u00e9 a propor\u00e7\u00e3o de uns.<\/p>\n<pre><code><span style=\"color: black\">zero_one = make_array(1, 1, 1, 0)\r\nsum(zero_one)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[3]:<\/td>\n<td style=\"text-align: left\">3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">np.mean(zero_one)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[4]:<\/td>\n<td style=\"text-align: left\">0.75<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Voc\u00ea pode substituir 1 pelo booleano <code>True<\/code> e 0 por <code>False<\/code>:<\/p>\n<pre><code><span style=\"color: black\">np.mean(make_array(True, True, True, False))<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[5]:<\/td>\n<td style=\"text-align: left\">0.75<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Como as propor\u00e7\u00f5es s\u00e3o um caso especial de m\u00e9dias, os resultados sobre m\u00e9dias de amostras aleat\u00f3rias tamb\u00e9m se aplicam a propor\u00e7\u00f5es de amostras aleat\u00f3rias.<\/p>\n<h2 id=\"a-media-e-o-histograma-\" style=\"text-align: justify\">A M\u00e9dia e o Histograma<\/h2>\n<p style=\"text-align: justify\">A m\u00e9dia da cole\u00e7\u00e3o <code>{2, 3, 3, 9}<\/code> \u00e9 4.25, que n\u00e3o \u00e9 o &#8220;ponto m\u00e9dio&#8221; dos dados. Ent\u00e3o, o que a m\u00e9dia mede?<\/p>\n<p style=\"text-align: justify\">Para ver isso, observe que a m\u00e9dia pode ser calculada de diferentes maneiras.<\/p>\n<div style=\"font-family: serif;font-size: 1.6em;text-align: center\">\n<p><span style=\"font-size: 14pt\">m\u00e9dia = 4.25<\/span><\/p>\n<p><span style=\"font-size: 14pt\">= <sup>(2 + 3 + 3 + 9)<\/sup>\u2044<sub>4<\/sub><\/span><\/p>\n<p><span style=\"font-size: 14pt\">= 2 \u22c5 <sup>1<\/sup>\u2044<sub>4<\/sub> + 3 \u22c5 <sup>1<\/sup>\u2044<sub>4<\/sub> + 3 \u22c5 <sup>1<\/sup>\u2044<sub>4<\/sub> + 9 \u22c5 <sup>1<\/sup>\u2044<sub>4<\/sub><\/span><\/p>\n<p><span style=\"font-size: 14pt\">= 2 \u22c5 <sup>1<\/sup>\u2044<sub>4<\/sub> + 3 \u22c5 <sup>2<\/sup>\u2044<sub>4<\/sub> + 9 \u22c5 <sup>1<\/sup>\u2044<sub>4<\/sub><\/span><\/p>\n<p><span style=\"font-size: 14pt\">= 2 \u22c5 0.25 + 3 \u22c5 0.5 + 9 \u22c5 0.25<\/span><\/p>\n<\/div>\n<p style=\"text-align: justify\">A \u00faltima express\u00e3o \u00e9 um exemplo de um fato geral: quando calculamos a m\u00e9dia, cada valor distinto na cole\u00e7\u00e3o \u00e9 <em>ponderado<\/em> pela propor\u00e7\u00e3o de vezes que ele aparece na cole\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify\">Isso tem uma consequ\u00eancia importante. A m\u00e9dia de uma cole\u00e7\u00e3o depende apenas dos valores distintos e suas propor\u00e7\u00f5es, n\u00e3o do n\u00famero de elementos na cole\u00e7\u00e3o. Em outras palavras, a m\u00e9dia de uma cole\u00e7\u00e3o depende apenas da distribui\u00e7\u00e3o dos valores na cole\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify\">Portanto, <strong>se duas cole\u00e7\u00f5es t\u00eam a mesma distribui\u00e7\u00e3o, ent\u00e3o elas t\u00eam a mesma m\u00e9dia.<\/strong><\/p>\n<p style=\"text-align: justify\">Por exemplo, aqui est\u00e1 outra cole\u00e7\u00e3o que tem a mesma distribui\u00e7\u00e3o que <code>not_symmetric<\/code> e, portanto, a mesma m\u00e9dia.<\/p>\n<pre><code><span style=\"color: black\">not_symmetric<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[6]:<\/td>\n<td style=\"text-align: left\">array([2, 3, 3, 9])<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">same_distribution = make_array(2, 2, 3, 3, 3, 3, 9, 9)\r\nnp.mean(same_distribution)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[7]:<\/td>\n<td style=\"text-align: left\">4.25<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">A m\u00e9dia \u00e9 um atributo f\u00edsico do histograma da distribui\u00e7\u00e3o. Aqui est\u00e1 o histograma da distribui\u00e7\u00e3o de <code>not_symmetric<\/code>ou equivalentemente a distribui\u00e7\u00e3o de <code>same_distribution<\/code>.<\/p>\n<pre><code><span style=\"color: black\">t1 = Table().with_columns('not symmetric', not_symmetric)\r\nt1.hist(bins=np.arange(1.5, 9.6, 1))<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-725\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-1.png\" alt=\"\" width=\"433\" height=\"284\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-1.png 433w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-1-300x197.png 300w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p style=\"text-align: justify\">Imagine o histograma como uma figura feita de papel\u00e3o presa a um fio que corre ao longo do eixo horizontal, e imagine as barras como pesos presos nos valores 2, 3 e 9. Suponha que voc\u00ea tente equilibrar esta figura em um ponto no fio. Se o ponto estiver pr\u00f3ximo de 2, a figura vai tombar para a direita. Se o ponto estiver pr\u00f3ximo de 9, a figura vai tombar para a esquerda. Em algum lugar entre est\u00e1 o ponto onde a figura vai se equilibrar; esse ponto \u00e9 o 4,25, a m\u00e9dia.<\/p>\n<p style=\"text-align: justify\"><strong>A m\u00e9dia \u00e9 o centro de gravidade ou ponto de equil\u00edbrio do histograma.<\/strong><\/p>\n<p style=\"text-align: justify\">Para entender por que isso \u00e9 verdade, \u00e9 \u00fatil conhecer um pouco de f\u00edsica. O centro de gravidade \u00e9 calculado exatamente como calculamos a m\u00e9dia, usando os valores distintos ponderados por suas propor\u00e7\u00f5es.<\/p>\n<p style=\"text-align: justify\">Por ser um ponto de equil\u00edbrio, a m\u00e9dia \u00e0s vezes \u00e9 exibida como um <em>fulcro<\/em> ou tri\u00e2ngulo na base do histograma.<\/p>\n<pre><code><span style=\"color: black\">mean_ns = np.mean(not_symmetric)\r\nt1.hist(bins=np.arange(1.5, 9.6, 1))\r\nplots.scatter(mean_ns, -0.009, marker='^', color='darkblue', s=60)\r\nplots.plot([1.5, 9.5], [0, 0], color='grey')\r\nplots.ylim(-0.05, 0.5);<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-726\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-2.png\" alt=\"\" width=\"433\" height=\"289\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-2.png 433w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-2-300x200.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-2-350x233.png 350w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<h2 id=\"a-m-dia-e-a-mediana\" style=\"text-align: justify\">A M\u00e9dia e a Mediana<\/h2>\n<p style=\"text-align: justify\">Se a nota de um aluno em um teste est\u00e1 abaixo da m\u00e9dia, isso implica que o aluno est\u00e1 na metade inferior da turma nesse teste?<\/p>\n<p style=\"text-align: justify\">Felizmente para o aluno, a resposta \u00e9: &#8220;N\u00e3o necessariamente.&#8221; O motivo est\u00e1 relacionado \u00e0 rela\u00e7\u00e3o entre a m\u00e9dia, que \u00e9 o ponto de equil\u00edbrio do histograma, e a mediana, que \u00e9 o &#8220;ponto m\u00e9dio&#8221; dos dados.<\/p>\n<p style=\"text-align: justify\">A rela\u00e7\u00e3o \u00e9 f\u00e1cil de ver em um exemplo simples. Aqui est\u00e1 o histograma da cole\u00e7\u00e3o {2, 3, 3, 4}, que est\u00e1 no array <code>symmetric<\/code>. A distribui\u00e7\u00e3o \u00e9 sim\u00e9trica em torno de 3. A m\u00e9dia e a mediana s\u00e3o ambas iguais a 3.<\/p>\n<pre><code><span style=\"color: black\">symmetric = make_array(2, 3, 3, 4)<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">t2 = Table().with_columns('symmetric', symmetric)\r\nmean_s = np.mean(symmetric)\r\n\r\nt2.hist(bins=np.arange(1.5, 4.6, 1))\r\nplots.scatter(mean_s, -0.009, marker='^', color='darkblue', s=60)\r\nplots.xlim(1, 10)\r\nplots.ylim(-0.05, 0.5);<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-727\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-3.png\" alt=\"\" width=\"442\" height=\"289\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-3.png 442w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-3-300x196.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">np.mean(symmetric)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[8]:<\/td>\n<td style=\"text-align: left\">3.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">percentile(50, symmetric)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[9]:<\/td>\n<td style=\"text-align: left\">3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Em geral, <strong>para distribui\u00e7\u00f5es sim\u00e9tricas, a m\u00e9dia e a mediana s\u00e3o iguais.<\/strong><\/p>\n<p style=\"text-align: justify\">E se a distribui\u00e7\u00e3o n\u00e3o for sim\u00e9trica? Vamos comparar <code>symmetric<\/code> e <code>not_symmetric<\/code>.<\/p>\n<pre><code><span style=\"color: black\">t3 = t2.with_column(\r\n        'not_symmetric', not_symmetric\r\n)\r\n\r\nt3.hist(bins=np.arange(1.5, 9.6, 1))\r\nplots.scatter(mean_s, -0.009, marker='^', color='darkblue', s=60)\r\nplots.scatter(mean_ns, -0.009, marker='^', color='gold', s=60)\r\nplots.ylim(-0.05, 0.5);<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-728\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-4.png\" alt=\"\" width=\"613\" height=\"270\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-4.png 613w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-4-300x132.png 300w\" sizes=\"(max-width: 613px) 100vw, 613px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">O histograma azul representa a distribui\u00e7\u00e3o original <code>symmetric<\/code>. O histograma dourado de <code>not_symmetric<\/code> come\u00e7a da mesma forma que o azul na extremidade esquerda, mas sua barra mais \u00e0 direita deslocou-se para o valor 9. A parte marrom \u00e9 onde os dois histogramas se sobrep\u00f5em.<\/p>\n<p style=\"text-align: justify\">A mediana e a m\u00e9dia da distribui\u00e7\u00e3o azul s\u00e3o ambas iguais a 3. A mediana da distribui\u00e7\u00e3o dourada tamb\u00e9m \u00e9 igual a 3, embora a metade direita esteja distribu\u00edda de forma diferente da metade esquerda.<\/p>\n<p style=\"text-align: justify\">Mas a m\u00e9dia da distribui\u00e7\u00e3o dourada n\u00e3o \u00e9 3: o histograma dourado n\u00e3o se equilibraria em 3. O ponto de equil\u00edbrio deslocou-se para a direita, para 4,25.<\/p>\n<p style=\"text-align: justify\">Na distribui\u00e7\u00e3o dourada, 3 em cada 4 entradas (75%) est\u00e3o abaixo da m\u00e9dia. O estudante com uma nota abaixo da m\u00e9dia pode, portanto, se alegrar. Ele ou ela pode estar na maioria da classe.<\/p>\n<p style=\"text-align: justify\">Em geral, <strong>se o histograma tem uma cauda em um lado (o termo formal \u00e9 &#8220;skewed&#8221;), ent\u00e3o a m\u00e9dia \u00e9 puxada para longe da mediana na dire\u00e7\u00e3o da cauda.<\/strong><\/p>\n<h3 id=\"exemplo\" style=\"text-align: justify\">Exemplo<\/h3>\n<p style=\"text-align: justify\">A tabela <code>sf2015<\/code> cont\u00e9m dados salariais e de benef\u00edcios dos funcion\u00e1rios da cidade de S\u00e3o Francisco em 2015. Como antes, restringiremos nossa an\u00e1lise aos que tiveram o equivalente a pelo menos meio per\u00edodo de trabalho durante o ano.<\/p>\n<pre><code><span style=\"color: black\">sf2015 = Table.read_table(path_data + 'san_francisco_2015.csv').where('Salaries', are.above(10000))<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[10]:<\/td>\n<td style=\"text-align: left\">Como vimos anteriormente, a remunera\u00e7\u00e3o mais alta estava acima de $600.000, mas a grande maioria dos funcion\u00e1rios tinha remunera\u00e7\u00f5es abaixo de $300.000.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">sf2015.select('Total Compensation').hist(bins = np.arange(10000, 700000, 25000))<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-729\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-5.png\" alt=\"\" width=\"464\" height=\"323\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-5.png 464w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-5-300x209.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-1-5-460x320.png 460w\" sizes=\"(max-width: 464px) 100vw, 464px\" \/><\/p>\n<p style=\"text-align: justify\">Este histograma est\u00e1 inclinado para a direita; tem uma cauda para a direita.<\/p>\n<p style=\"text-align: justify\">A m\u00e9dia \u00e9 afastada da mediana em dire\u00e7\u00e3o \u00e0 cauda. Portanto, esperamos que a compensa\u00e7\u00e3o m\u00e9dia seja maior que a mediana, e esse \u00e9 realmente o caso.<\/p>\n<pre><code><span style=\"color: black\">compensation = sf2015.column('Total Compensation')\r\npercentile(50, compensation)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[11]:<\/td>\n<td style=\"text-align: left\">110305.79<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">np.mean(compensation)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[12]:<\/td>\n<td style=\"text-align: left\">114725.98411824222<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">As distribui\u00e7\u00f5es de rendimentos de grandes popula\u00e7\u00f5es tendem a ser distorcidas para a direita. Quando a maior parte da popula\u00e7\u00e3o tem rendimentos m\u00e9dios a baixos, mas uma propor\u00e7\u00e3o muito pequena tem rendimentos muito elevados, o histograma tem uma cauda longa e fina para a direita.<\/p>\n<p style=\"text-align: justify\">A renda m\u00e9dia \u00e9 afetada por esta cauda: quanto mais a cauda se estende para a direita, maior se torna a m\u00e9dia. Mas a mediana n\u00e3o \u00e9 afetada pelos valores nos extremos da distribui\u00e7\u00e3o. \u00c9 por isso que os economistas muitas vezes resumem as distribui\u00e7\u00f5es de renda pela mediana em vez da m\u00e9dia.<\/p>\n<p>&nbsp;<\/p>\n<p><!--###########################################################################################################################################################--><\/p>\n<table width=\"100%\">\n<tbody>\n<tr>\n<td align=\"left\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/\">\u2190 Cap\u00edtulo 14 &#8211; Por que a M\u00e9dia Importa<\/a><\/td>\n<td align=\"right\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-2\/\">Cap\u00edtulo 14.2 &#8211; Variabilidade \u2192<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><!--###########################################################################################################################################################--><\/p>\n<\/div>\n<\/div>\n<div style=\"clear: both;height: 1px;margin-top: -1px\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u00cdndice 1. O que \u00e9 Ci\u00eancia de Dados? 1.1. Introdu\u00e7\u00e3o 1.1.1. Ferramentas Computacionais 1.1.2. T\u00e9cnicas Estat\u00edsticas 1.2. Por que Ci\u00eancia de Dados? 1.3. Tra\u00e7ando os Cl\u00e1ssicos 1.3.1. Personagens Liter\u00e1rios 1.3.2. Outro Tipo de Personagem 2. Causalidade e Experimentos 2.1. John Snow e a Bomba da Broad Street 2.2. O &#8220;Grande Experimento&#8221; de Snow 2.3. Estabelecendo [&hellip;]<\/p>\n","protected":false},"author":21894,"featured_media":0,"parent":722,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-templates\/full-width.php","meta":{"footnotes":""},"coauthors":[14],"class_list":["post-724","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/724","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/users\/21894"}],"replies":[{"embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/comments?post=724"}],"version-history":[{"count":10,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/724\/revisions"}],"predecessor-version":[{"id":1054,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/724\/revisions\/1054"}],"up":[{"embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/722"}],"wp:attachment":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/media?parent=724"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/coauthors?post=724"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}