{"id":628,"date":"2025-07-28T15:51:16","date_gmt":"2025-07-28T19:51:16","guid":{"rendered":"https:\/\/literaciadigital.ufms.br\/?page_id=628"},"modified":"2025-10-09T17:49:24","modified_gmt":"2025-10-09T21:49:24","slug":"10-3","status":"publish","type":"page","link":"https:\/\/literaciadigital.ufms.br\/en\/data8\/10-0\/10-3\/","title":{"rendered":"Cap\u00edtulo 10.3"},"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\npath_data = '..\/..\/..\/assets\/data\/'\r\nimport matplotlib\r\nmatplotlib.use('Agg')\r\n%matplotlib inline\r\nimport matplotlib.pyplot as plots\r\nplots.style.use('fivethirtyeight')\r\nimport numpy as np<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<h1 id=\"distribui\u00e7\u00e3o-emp\u00edrica-de-uma-estat\u00edstica\" style=\"text-align: center\">Distribui\u00e7\u00e3o Emp\u00edrica de uma Estat\u00edstica<\/h1>\n<p style=\"text-align: justify\">A Lei das M\u00e9dias implica que, com alta probabilidade, a distribui\u00e7\u00e3o emp\u00edrica de uma grande amostra aleat\u00f3ria se assemelhar\u00e1 \u00e0 distribui\u00e7\u00e3o da popula\u00e7\u00e3o da qual a amostra foi extra\u00edda.<\/p>\n<p style=\"text-align: justify\">A semelhan\u00e7a \u00e9 vis\u00edvel em dois histogramas: o histograma emp\u00edrico de uma grande amostra aleat\u00f3ria provavelmente se assemelha ao histograma da popula\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify\">Como lembrete, aqui est\u00e1 o histograma dos atrasos de todos os voos em <code>united<\/code>, e um histograma emp\u00edrico dos atrasos de uma amostra aleat\u00f3ria de 1.000 desses voos.<\/p>\n<pre><code><span style=\"color: black\">united = Table.read_table(path_data + 'united_summer2015.csv')<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">delay_bins = np.arange(-20, 201, 10)\r\nunited.hist('Delay', bins = delay_bins, unit = 'minute')\r\nplots.title('Population');<\/span><\/code><\/pre>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-630\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/10-3-1.png\" alt=\"\" width=\"437\" height=\"305\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/10-3-1.png 437w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/10-3-1-300x209.png 300w\" sizes=\"(max-width: 437px) 100vw, 437px\" \/><\/p>\n<pre><code><span style=\"color: black\">sample_1000 = united.sample(1000)\r\nsample_1000.hist('Delay', bins = delay_bins, unit = 'minute')\r\nplots.title('Sample of Size 1000');<\/span><\/code><\/pre>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-631\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/10-3-2.png\" alt=\"\" width=\"437\" height=\"305\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/10-3-2.png 437w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/10-3-2-300x209.png 300w\" sizes=\"(max-width: 437px) 100vw, 437px\" \/><\/p>\n<p style=\"text-align: justify\">Os dois histogramas claramente se assemelham, embora n\u00e3o sejam id\u00eanticos.<\/p>\n<h2>Par\u00e2metro<\/h2>\n<p style=\"text-align: justify\">Frequentemente, estamos interessados em quantidades num\u00e9ricas associadas a uma popula\u00e7\u00e3o.<\/p>\n<ul>\n<li>Em uma popula\u00e7\u00e3o de eleitores, qual percentual votar\u00e1 no Candidato A?<\/li>\n<li>Em uma popula\u00e7\u00e3o de usu\u00e1rios do Facebook, qual \u00e9 o maior n\u00famero de amigos no Facebook que os usu\u00e1rios t\u00eam?<\/li>\n<li>Em uma popula\u00e7\u00e3o de voos da United, qual \u00e9 o atraso de partida mediano?<\/li>\n<\/ul>\n<p style=\"text-align: justify\">Quantidades num\u00e9ricas associadas a uma popula\u00e7\u00e3o s\u00e3o chamadas de <em>par\u00e2metros<\/em>. Para a popula\u00e7\u00e3o de voos em <code>united<\/code>, sabemos o valor do par\u00e2metro &#8220;atraso mediano&#8221;:<\/p>\n<pre><code><span style=\"color: black\">np.median(united.column('Delay'))<\/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\">2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">A fun\u00e7\u00e3o <code>NumPy<\/code> <code>median<\/code> retorna a mediana (ponto intermedi\u00e1rio) de um array. Entre todos os voos em <code>united<\/code>, o atraso m\u00e9dio foi de 2 minutos. Ou seja, cerca de 50% dos voos da popula\u00e7\u00e3o tiveram atrasos de 2 minutos ou menos:<\/p>\n<pre><code><span style=\"color: black\">united.where('Delay', are.below_or_equal_to(2)).num_rows \/ united.num_rows<\/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\">0.5017720795297<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Metade de todos os voos partiram no m\u00e1ximo 2 minutos ap\u00f3s o hor\u00e1rio de partida programado. Isso \u00e9 um atraso muito curto!<\/p>\n<p style=\"text-align: justify\"><strong>Nota.<\/strong> A porcentagem n\u00e3o \u00e9 exatamente 50% por causa dos &#8220;empates&#8221;, ou seja, voos que tiveram atrasos de exatamente 2 minutos. Houve 480 desses voos. Empates s\u00e3o bastante comuns em conjuntos de dados e n\u00e3o nos preocuparemos com eles neste curso.<\/p>\n<pre><code><span style=\"color: black\">united.where('Delay', are.equal_to(2)).num_rows<\/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\">480<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h2>Estat\u00edstica<\/h2>\n<p style=\"text-align: justify\">Em muitas situa\u00e7\u00f5es, estaremos interessados em descobrir o valor de um par\u00e2metro desconhecido. Para isso, vamos depender de dados de uma grande amostra aleat\u00f3ria retirada da popula\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify\">Uma <em>estat\u00edstica<\/em> (note o singular!) \u00e9 qualquer n\u00famero calculado usando os dados de uma amostra. Portanto, a mediana da amostra \u00e9 uma estat\u00edstica.<\/p>\n<p style=\"text-align: justify\">Lembre-se de que <code>sample_1000<\/code> cont\u00e9m uma amostra aleat\u00f3ria de 1000 voos da <code>united<\/code>. O valor observado da mediana da amostra \u00e9:<\/p>\n<pre><code><span style=\"color: black\">np.median(sample_1000.column('Delay'))<\/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\">2.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Nosso exemplo &#8211; um conjunto de 1.000 voos &#8211; nos forneceu um valor observado da estat\u00edstica. Isso levanta um problema importante de infer\u00eancia:<\/p>\n<p style=\"text-align: justify\"><strong>A estat\u00edstica poderia ter sido diferente.<\/strong><br \/>\nUma considera\u00e7\u00e3o fundamental ao usar qualquer estat\u00edstica baseada em uma amostra aleat\u00f3ria \u00e9 que <em>a amostra poderia ter sido diferente<\/em> e, portanto, a estat\u00edstica tamb\u00e9m poderia ter sido diferente.<\/p>\n<pre><code><span style=\"color: black\">np.median(united.sample(1000).column('Delay'))<\/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\">3.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Execute a c\u00e9lula acima algumas vezes para ver como a resposta varia. Muitas vezes \u00e9 igual a 2, o mesmo valor do par\u00e2metro populacional. Mas \u00e0s vezes \u00e9 diferente.<\/p>\n<p style=\"text-align: justify\"><strong>Qu\u00e3o diferente a estat\u00edstica poderia ter sido?<\/strong> Uma maneira de responder a isso \u00e9 simular a estat\u00edstica muitas vezes e anotar os valores. Um histograma desses valores nos informar\u00e1 sobre a distribui\u00e7\u00e3o da estat\u00edstica.<\/p>\n<p style=\"text-align: justify\">Vamos relembrar as principais etapas de uma simula\u00e7\u00e3o.<\/p>\n<h2>Simulando uma Estat\u00edstica<\/h2>\n<p style=\"text-align: justify\">Vamos simular a mediana da amostra usando os passos que configuramos em um cap\u00edtulo anterior quando come\u00e7amos a estudar simula\u00e7\u00e3o. Voc\u00ea pode substituir o tamanho da amostra de 1000 por qualquer outro tamanho de amostra, e a mediana da amostra por qualquer outra estat\u00edstica.<\/p>\n<p style=\"text-align: justify\"><strong>Passo 1: Decida qual estat\u00edstica simular.<\/strong> J\u00e1 decidimos isso: vamos simular a mediana de uma amostra aleat\u00f3ria de tamanho 1000 retirada da popula\u00e7\u00e3o de atrasos de voos.<\/p>\n<p style=\"text-align: justify\"><strong>Passo 2: Defina uma fun\u00e7\u00e3o que retorne um valor simulado da estat\u00edstica.<\/strong> Extraia uma amostra aleat\u00f3ria de tamanho 1000 e calcule a mediana da amostra. Fizemos isso na c\u00e9lula de c\u00f3digo acima. Aqui est\u00e1 novamente, encapsulado em uma fun\u00e7\u00e3o.<\/p>\n<pre><code><span style=\"color: black\">def random_sample_median():\r\n    return np.median(united.sample(1000).column('Delay'))<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong>Passo 3: Decidir quantos valores simulados gerar.<\/strong> Vamos fazer 5.000 repeti\u00e7\u00f5es.<\/p>\n<p style=\"text-align: justify\"><strong>Passo 4: Usar um loop <code>for<\/code> para gerar um array de valores simulados.<\/strong> Como de costume, come\u00e7aremos criando um array vazio para coletar nossos resultados. Em seguida, configuraremos um loop <code>for<\/code> para gerar todos os valores simulados. O corpo do loop consistir\u00e1 em gerar um valor simulado da mediana da amostra e adicion\u00e1-lo ao nosso array de resultados.<\/p>\n<p style=\"text-align: justify\">A simula\u00e7\u00e3o leva um tempo percept\u00edvel para ser executada. Isso ocorre porque ela est\u00e1 realizando 5.000 repeti\u00e7\u00f5es do processo de amostragem de tamanho 1.000 e computando sua mediana. Isso significa muita amostragem e repeti\u00e7\u00e3o!<\/p>\n<pre><code><span style=\"color: black\">medians = make_array()\r\n\r\nfor i in np.arange(5000):\r\n    medians = np.append(medians, random_sample_median())<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">A simula\u00e7\u00e3o est\u00e1 conclu\u00edda. Todas as 5.000 medianas de amostras simuladas foram coletadas no array <code>medians<\/code>. Agora \u00e9 hora de visualizar os resultados.<\/p>\n<h2>Visualiza\u00e7\u00e3o<\/h2>\n<p style=\"text-align: justify\">Aqui est\u00e3o as medianas de amostras aleat\u00f3rias simuladas exibidas na tabela <code>simulated_medians<\/code>.<\/p>\n<pre><code><span style=\"color: black\">simulated_medians = Table().with_column('Sample Median', medians)\r\nsimulated_medians<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-collapse: collapse;width: auto;margin-left: 1em\" border=\"1\">\n<thead>\n<tr style=\"background-color: #f0f0f0;border-bottom: 2px solid #ddd\">\n<th style=\"text-align: left;padding: 4px 8px\">Sample Median<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.5<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Tamb\u00e9m podemos visualizar os dados simulados usando um histograma. O histograma \u00e9 chamado de <em>histograma emp\u00edrico da estat\u00edstica<\/em>. Ele exibe a <em>distribui\u00e7\u00e3o emp\u00edrica<\/em> da estat\u00edstica. Lembre-se de que <em>emp\u00edrico<\/em> significa <em>observado<\/em>.<\/p>\n<pre><code><span style=\"color: black\">simulated_medians.hist(bins=np.arange(0.5, 5, 1))<\/span><\/code><\/pre>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-632\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/10-3-3.png\" alt=\"\" width=\"433\" height=\"284\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/10-3-3.png 433w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/10-3-3-300x197.png 300w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Voc\u00ea pode ver que a mediana da amostra \u00e9 muito provavelmente cerca de 2, que foi o valor da mediana da popula\u00e7\u00e3o. Como amostras de 1000 atrasos de voo tendem a se assemelhar \u00e0 popula\u00e7\u00e3o de atrasos, n\u00e3o \u00e9 surpreendente que as medianas dos atrasos dessas amostras estejam pr\u00f3ximas \u00e0 mediana do atraso na popula\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify\">Este \u00e9 um exemplo de como uma estat\u00edstica pode fornecer uma boa estimativa de um par\u00e2metro.<\/p>\n<h2>O Poder da Simula\u00e7\u00e3o<\/h2>\n<p style=\"text-align: justify\">Se pud\u00e9ssemos gerar todas as poss\u00edveis amostras aleat\u00f3rias de tamanho 1000, conhecer\u00edamos todos os valores poss\u00edveis da estat\u00edstica (a mediana da amostra), bem como as probabilidades de todos esses valores. Poder\u00edamos visualizar todos os valores e probabilidades no histograma de probabilidade da estat\u00edstica.<\/p>\n<p style=\"text-align: justify\">Mas em muitas situa\u00e7\u00f5es, incluindo esta, o n\u00famero de todas as amostras poss\u00edveis \u00e9 grande o suficiente para exceder a capacidade do computador, e c\u00e1lculos puramente matem\u00e1ticos das probabilidades podem ser dificilmente trat\u00e1veis.<\/p>\n<p style=\"text-align: justify\">\u00c9 aqui que entram os histogramas emp\u00edricos.<\/p>\n<p style=\"text-align: justify\">Sabemos que, pela Lei dos Grandes N\u00fameros, o histograma emp\u00edrico da estat\u00edstica provavelmente se assemelhar\u00e1 ao histograma de probabilidade da estat\u00edstica, se o tamanho da amostra for grande e se voc\u00ea repetir o processo de amostragem aleat\u00f3ria v\u00e1rias vezes.<\/p>\n<p style=\"text-align: justify\">Isso significa que simular processos aleat\u00f3rios repetidamente \u00e9 uma maneira de aproximar distribui\u00e7\u00f5es de probabilidade <em>sem calcular as probabilidades matematicamente ou gerar todas as poss\u00edveis amostras aleat\u00f3rias<\/em>. Assim, as simula\u00e7\u00f5es computacionais se tornam uma ferramenta poderosa na ci\u00eancia de dados. Elas podem ajudar os cientistas de dados a entender as propriedades de quantidades aleat\u00f3rias que seriam complicadas de analisar de outras maneiras.<\/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\/10-0\/10-2\/\">\u2190 Cap\u00edtulo 10.2 &#8211; Amostragem de uma Popula\u00e7\u00e3o<\/a><\/td>\n<td align=\"right\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-4\/\">Cap\u00edtulo 10.4 &#8211; Amostragem Aleat\u00f3ria em Python \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":611,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-templates\/full-width.php","meta":{"footnotes":""},"coauthors":[14],"class_list":["post-628","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/628","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=628"}],"version-history":[{"count":5,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/628\/revisions"}],"predecessor-version":[{"id":997,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/628\/revisions\/997"}],"up":[{"embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/611"}],"wp:attachment":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/media?parent=628"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/coauthors?post=628"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}