{"id":772,"date":"2025-07-29T16:34:45","date_gmt":"2025-07-29T20:34:45","guid":{"rendered":"https:\/\/literaciadigital.ufms.br\/?page_id=772"},"modified":"2025-10-11T16:04:23","modified_gmt":"2025-10-11T20:04:23","slug":"14-5","status":"publish","type":"page","link":"https:\/\/literaciadigital.ufms.br\/en\/data8\/14-0\/14-5\/","title":{"rendered":"Cap\u00edtulo 14.5"},"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\nimport numpy as np\r\npath_data = '..\/..\/..\/assets\/data\/'\r\n%matplotlib inline\r\nimport matplotlib.pyplot as plots\r\nplots.style.use('fivethirtyeight')<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<h1 id=\"a-variabilidade-da-m-dia-da-amostra\" style=\"text-align: center\">A Variabilidade da M\u00e9dia da Amostra<\/h1>\n<p style=\"text-align: justify\">Pelo Teorema Central do Limite, a distribui\u00e7\u00e3o de probabilidade da m\u00e9dia de uma grande amostra aleat\u00f3ria \u00e9 aproximadamente normal. A curva em forma de sino \u00e9 centrada na m\u00e9dia da popula\u00e7\u00e3o. Algumas das m\u00e9dias da amostra s\u00e3o maiores e outras menores, mas os desvios da m\u00e9dia da popula\u00e7\u00e3o s\u00e3o aproximadamente sim\u00e9tricos de ambos os lados, como vimos repetidamente. Formalmente, a teoria da probabilidade mostra que a m\u00e9dia da amostra \u00e9 uma estimativa <em>imparcial<\/em> da m\u00e9dia da<br \/>\npopula\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify\">Em nossas simula\u00e7\u00f5es, tamb\u00e9m observamos que as m\u00e9dias de amostras maiores tendem a se agrupar mais firmemente em torno da m\u00e9dia da popula\u00e7\u00e3o do que as m\u00e9dias de amostras menores. Nesta se\u00e7\u00e3o, quantificaremos a variabilidade da m\u00e9dia da amostra e desenvolveremos uma rela\u00e7\u00e3o entre a variabilidade e o tamanho da amostra.<\/p>\n<p style=\"text-align: justify\">Vamos come\u00e7ar com nossa tabela de atrasos de voo. O atraso m\u00e9dio \u00e9 de aproximadamente 16,7 minutos, e a distribui\u00e7\u00e3o dos atrasos \u00e9 assim\u00e9trica para a direita.<\/p>\n<pre><code><span style=\"color: black\">united = Table.read_table(path_data + 'united_summer2015.csv')\r\ndelay = united.select('Delay')<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">pop_mean = np.mean(delay.column('Delay'))\r\npop_mean<\/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\">16.658155515370705<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<pre><code><span style=\"color: black\">delay.hist(bins=np.arange(-20, 300, 10))\r\nplots.scatter(pop_mean, -0.0008, marker='^', color='darkblue', s=60)\r\nplots.ylim(-0.004, 0.04);<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-774\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-1.png\" alt=\"\" width=\"431\" height=\"289\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-1.png 431w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-1-300x201.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/p>\n<p style=\"text-align: justify\">Agora vamos pegar amostras aleat\u00f3rias e observar a distribui\u00e7\u00e3o de probabilidade da m\u00e9dia amostral. Como de costume, usaremos simula\u00e7\u00e3o para obter uma aproxima\u00e7\u00e3o emp\u00edrica dessa distribui\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify\">Definiremos uma fun\u00e7\u00e3o <code>simulate_sample_mean<\/code> para fazer isso, pois iremos variar o tamanho da amostra posteriormente. Os argumentos s\u00e3o o nome da tabela, o r\u00f3tulo da coluna que cont\u00e9m a vari\u00e1vel, o tamanho da amostra e o n\u00famero de simula\u00e7\u00f5es.<\/p>\n<pre><code><span style=\"color: black\">\"\"\"Distribui\u00e7\u00e3o emp\u00edrica de amostra aleat\u00f3ria significa\"\"\"\r\n\r\ndef simulate_sample_mean(table, label, sample_size, repetitions):\r\n\r\n    means = make_array()\r\n\r\n    for i in range(repetitions):\r\n        new_sample = table.sample(sample_size)\r\n        new_sample_mean = np.mean(new_sample.column(label))\r\n        means = np.append(means, new_sample_mean)\r\n\r\n    sample_means = Table().with_column('Sample Means', means)\r\n\r\n    # Exibir histograma emp\u00edrico e imprimir todas as quantidades relevantes\r\n    sample_means.hist(bins=20)\r\n    plots.xlabel('Sample Means')\r\n    plots.title('Sample Size ' + str(sample_size))\r\n    print(\"Sample size: \", sample_size)\r\n    print(\"Population mean:\", np.mean(table.column(label)))\r\n    print(\"Average of sample means: \", np.mean(means))\r\n    print(\"Population SD:\", np.std(table.column(label)))\r\n    print(\"SD of sample means:\", np.std(means))<\/span><\/code><\/pre>\n<p style=\"text-align: justify\">Vamos simular a m\u00e9dia de uma amostra aleat\u00f3ria de 100 atrasos, depois de 400 atrasos e finalmente de 625 atrasos. Realizaremos 10.000 repeti\u00e7\u00f5es de cada um desses processos. As linhas <code>xlim<\/code> e <code>ylim<\/code> definem os eixos consistentemente em todos os gr\u00e1ficos para facilitar a compara\u00e7\u00e3o. Voc\u00ea pode simplesmente ignorar essas duas linhas de c\u00f3digo em cada c\u00e9lula.<\/p>\n<pre><code><span style=\"color: black\">simulate_sample_mean(delay, 'Delay', 100, 10000)\r\nplots.xlim(5, 35)\r\nplots.ylim(0, 0.25);<\/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\">Sample size: 100<br \/>\nPopulation mean: 16.658155515370705<br \/>\nAverage of sample means: 16.672836<br \/>\nPopulation SD: 39.480199851609314<br \/>\nSD of sample means: 3.92467202924066<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-775\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-2.png\" alt=\"\" width=\"442\" height=\"305\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-2.png 442w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-2-300x207.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<pre><code><span style=\"color: black\">simulate_sample_mean(delay, 'Delay', 400, 10000)\r\nplots.xlim(5, 35)\r\nplots.ylim(0, 0.25);<\/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\">Sample size: 400<br \/>\nPopulation mean: 16.658155515370705<br \/>\nAverage of sample means: 16.678091499999997<br \/>\nPopulation SD: 39.480199851609314<br \/>\nSD of sample means: 1.9474592014668113<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-776\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-3.png\" alt=\"\" width=\"442\" height=\"305\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-3.png 442w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-3-300x207.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<pre><code><span style=\"color: black\">simulate_sample_mean(delay, 'Delay', 625, 10000)\r\nplots.xlim(5, 35)\r\nplots.ylim(0, 0.25);<\/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\">Sample size: 625<br \/>\nPopulation mean: 16.658155515370705<br \/>\nAverage of sample means: 16.649224<br \/>\nPopulation SD: 39.480199851609314<br \/>\nSD of sample means: 1.5883338034053167<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-777\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-4.png\" alt=\"\" width=\"442\" height=\"305\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-4.png 442w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-4-300x207.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p style=\"text-align: justify\">Voc\u00ea pode ver o Teorema Central do Limite em a\u00e7\u00e3o \u2013 os histogramas das m\u00e9dias das amostras s\u00e3o aproximadamente normais, mesmo que o histograma dos atrasos em si esteja longe de ser normal.<\/p>\n<p style=\"text-align: justify\">Voc\u00ea tamb\u00e9m pode ver que cada um dos tr\u00eas histogramas das m\u00e9dias das amostras est\u00e1 centrado muito pr\u00f3ximo da m\u00e9dia da popula\u00e7\u00e3o. Em cada caso, a &#8220;m\u00e9dia das m\u00e9dias das amostras&#8221; \u00e9 muito pr\u00f3xima de 16,66 minutos, a m\u00e9dia da popula\u00e7\u00e3o. Ambos os valores s\u00e3o fornecidos na impress\u00e3o acima de cada histograma. Como esperado, a m\u00e9dia da amostra \u00e9 uma estimativa n\u00e3o tendenciosa da m\u00e9dia da popula\u00e7\u00e3o.<\/p>\n<h2 id=\"o-desvio-padr-o-de-todas-as-m-dias-das-amostras\" style=\"text-align: justify\">O Desvio Padr\u00e3o de Todas as M\u00e9dias das Amostras<\/h2>\n<p style=\"text-align: justify\">Voc\u00ea tamb\u00e9m pode ver que os histogramas ficam mais estreitos e, portanto, mais altos, \u00e0 medida que o tamanho da amostra aumenta. J\u00e1 vimos isso antes, mas agora prestaremos mais aten\u00e7\u00e3o \u00e0 medida de dispers\u00e3o.<\/p>\n<p style=\"text-align: justify\">O desvio padr\u00e3o de toda a popula\u00e7\u00e3o de atrasos \u00e9 de aproximadamente 40 minutos.<\/p>\n<pre><code><span style=\"color: black\">pop_sd = np.std(delay.column('Delay'))\r\npop_sd<\/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\">39.480199851609314<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">D\u00ea uma olhada nos desvios padr\u00e3o (SDs) nos histogramas das m\u00e9dias das amostras acima. Em todos os tr\u00eas, o SD da popula\u00e7\u00e3o de atrasos \u00e9 de cerca de 40 minutos, porque todas as amostras foram retiradas da mesma popula\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify\">Agora, observe o SD de todas as 10.000 m\u00e9dias das amostras, quando o tamanho da amostra \u00e9 100. Esse SD \u00e9 cerca de um d\u00e9cimo do SD da popula\u00e7\u00e3o. Quando o tamanho da amostra \u00e9 400, o SD de todas as m\u00e9dias das amostras \u00e9 cerca de um vig\u00e9simo do SD da popula\u00e7\u00e3o. Quando o tamanho da amostra \u00e9 625, o SD das m\u00e9dias das amostras \u00e9 cerca de um vig\u00e9simo quinto do SD da popula\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify\">Parece uma boa ideia comparar o SD da distribui\u00e7\u00e3o emp\u00edrica das m\u00e9dias das amostras com a quantidade &#8220;SD da popula\u00e7\u00e3o dividido pela raiz quadrada do tamanho da amostra.&#8221;<\/p>\n<p style=\"text-align: justify\">Aqui est\u00e3o os valores num\u00e9ricos. Para cada tamanho de amostra na primeira coluna, foram retiradas 10.000 amostras aleat\u00f3rias desse tamanho, e as 10.000 m\u00e9dias das amostras foram calculadas. A segunda coluna cont\u00e9m o SD dessas 10.000 m\u00e9dias das amostras. A terceira coluna cont\u00e9m o resultado do c\u00e1lculo &#8220;SD da popula\u00e7\u00e3o dividido pela raiz quadrada do tamanho da amostra.&#8221;<\/p>\n<p style=\"text-align: justify\">A c\u00e9lula leva um tempo para ser executada, pois \u00e9 uma simula\u00e7\u00e3o grande. Mas logo voc\u00ea ver\u00e1 que vale a pena esperar.<\/p>\n<pre><code><span style=\"color: black\">repetitions = 10000\r\nsample_sizes = np.arange(25, 626, 25)\r\n\r\nsd_means = make_array()\r\n\r\nfor n in sample_sizes:\r\n    means = make_array()\r\n    for i in np.arange(repetitions):\r\n        means = np.append(means, np.mean(delay.sample(n).column('Delay')))\r\n    sd_means = np.append(sd_means, np.std(means))\r\n\r\nsd_comparison = Table().with_columns(\r\n    'Sample Size n', sample_sizes,\r\n    'SD of 10,000 Sample Means', sd_means,\r\n    'pop_sd\/sqrt(n)', pop_sd\/np.sqrt(sample_sizes)\r\n)<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">sd_comparison<\/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 Size n<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">SD of 10,000 Sample Means<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">pop_sd\/sqrt(n)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">25<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">7.94482<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">7.89604<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">50<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">5.6131<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">5.58334<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">75<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">4.57417<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">4.55878<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">100<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3.98687<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3.94802<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">125<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3.49769<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3.53122<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">150<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3.22776<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3.22354<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">175<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3.00675<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.98442<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">200<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.77764<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.79167<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">225<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.64268<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.63201<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">250<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.49447<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.49695<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Os valores na segunda e terceira colunas s\u00e3o muito pr\u00f3ximos. Se tra\u00e7armos cada uma dessas colunas com o tamanho da amostra no eixo horizontal, os dois gr\u00e1ficos ser\u00e3o essencialmente indistingu\u00edveis.<\/p>\n<pre><code><span style=\"color: black\">sd_comparison.plot('Sample Size n')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-778\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-5.png\" alt=\"\" width=\"677\" height=\"287\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-5.png 677w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-5-5-300x127.png 300w\" sizes=\"(max-width: 677px) 100vw, 677px\" \/><\/p>\n<p style=\"text-align: justify\">Na verdade, h\u00e1 duas curvas ali. Mas elas est\u00e3o t\u00e3o pr\u00f3ximas uma da outra que parece que h\u00e1 apenas uma.<\/p>\n<p style=\"text-align: justify\">O que estamos vendo \u00e9 um exemplo de um resultado geral. Lembre-se de que o gr\u00e1fico acima \u00e9 baseado em 10.000 replicatas para cada tamanho da amostra. Mas h\u00e1 muito mais do que 10.000 amostras de cada tamanho. A distribui\u00e7\u00e3o de probabilidade da m\u00e9dia da amostra \u00e9 baseada nas m\u00e9dias de <em>todas as amostras poss\u00edveis<\/em> de um tamanho fixo.<\/p>\n<p style=\"text-align: justify\"><strong>Fixe um tamanho de amostra.<\/strong> Se as amostras s\u00e3o retiradas aleatoriamente com reposi\u00e7\u00e3o da popula\u00e7\u00e3o, ent\u00e3o<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 1.6em\">SD de todas as m\u00e9dias de amostra poss\u00edveis = <sup>SD da Popula\u00e7\u00e3o<\/sup>\u2044<sub>\u221aTamanho da Amostra<\/sub><\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Este \u00e9 o desvio padr\u00e3o das m\u00e9dias de todas as amostras poss\u00edveis que poderiam ser retiradas. <strong>Isso mede aproximadamente qu\u00e3o distantes as m\u00e9dias das amostras est\u00e3o da m\u00e9dia da popula\u00e7\u00e3o.<\/strong><\/p>\n<h2 id=\"o-teorema-do-limite-central-para-a-m-dia-da-amostra\" style=\"text-align: justify\">O Teorema do Limite Central para a M\u00e9dia da Amostra<\/h2>\n<p style=\"text-align: justify\">Se voc\u00ea retirar uma grande amostra aleat\u00f3ria com reposi\u00e7\u00e3o de uma popula\u00e7\u00e3o, ent\u00e3o, independentemente da distribui\u00e7\u00e3o da popula\u00e7\u00e3o, a distribui\u00e7\u00e3o de probabilidade da m\u00e9dia da amostra \u00e9 aproximadamente normal, centrada na m\u00e9dia da popula\u00e7\u00e3o, com um desvio padr\u00e3o igual ao desvio padr\u00e3o da popula\u00e7\u00e3o dividido pela raiz quadrada do tamanho da amostra.<\/p>\n<h2 id=\"a-precis-o-da-m-dia-da-amostra\" style=\"text-align: justify\">A Precis\u00e3o da M\u00e9dia da Amostra<\/h2>\n<p style=\"text-align: justify\">O desvio padr\u00e3o de todas as m\u00e9dias de amostra poss\u00edveis mede qu\u00e3o vari\u00e1vel pode ser a m\u00e9dia da amostra. Como tal, \u00e9 considerado uma medida da precis\u00e3o da m\u00e9dia da amostra como uma estimativa da m\u00e9dia da popula\u00e7\u00e3o. Quanto menor o desvio padr\u00e3o, mais precisa \u00e9 a estimativa.<\/p>\n<p style=\"text-align: justify\">A f\u00f3rmula mostra que:<\/p>\n<ul style=\"text-align: justify\">\n<li>O tamanho da popula\u00e7\u00e3o n\u00e3o afeta a precis\u00e3o da m\u00e9dia da amostra. O tamanho da popula\u00e7\u00e3o n\u00e3o aparece em nenhum lugar na f\u00f3rmula.<\/li>\n<li>O desvio padr\u00e3o da popula\u00e7\u00e3o \u00e9 uma constante; \u00e9 o mesmo para todas as amostras retiradas da popula\u00e7\u00e3o. O tamanho da amostra pode ser variado. Como o tamanho da amostra aparece no denominador, a variabilidade da m\u00e9dia da amostra <em>diminui<\/em> \u00e0 medida que o tamanho da amostra aumenta, e, portanto, a precis\u00e3o aumenta.<\/li>\n<\/ul>\n<h2 id=\"a-lei-da-raiz-quadrada\" style=\"text-align: justify\">A Lei da Raiz Quadrada<\/h2>\n<p style=\"text-align: justify\">A partir da tabela de compara\u00e7\u00f5es de desvios padr\u00e3o, pode-se ver que o desvio padr\u00e3o das m\u00e9dias de amostras aleat\u00f3rias de 25 atrasos de voo \u00e9 cerca de 8 minutos. Se voc\u00ea multiplicar o tamanho da amostra por 4, obter\u00e1 amostras de tamanho 100. O desvio padr\u00e3o das m\u00e9dias de todas essas amostras \u00e9 cerca de 4 minutos. Isso \u00e9 menor do que 8 minutos, mas n\u00e3o \u00e9 4 vezes menor; \u00e9 apenas 2 vezes menor. Isso ocorre porque o tamanho da amostra no denominador tem uma raiz quadrada sobre ele. O tamanho da amostra aumentou em um fator de 4, mas o desvio padr\u00e3o diminuiu em um fator de 2 = \u221a4. Em outras palavras, a precis\u00e3o aumentou em um fator de 2 = \u221a4.<\/p>\n<p style=\"text-align: justify\">Em geral, quando voc\u00ea multiplica o tamanho da amostra por um fator, a precis\u00e3o da m\u00e9dia da amostra aumenta pela raiz quadrada desse fator.<\/p>\n<p style=\"text-align: justify\">Portanto, para aumentar a precis\u00e3o em um fator de 10, voc\u00ea precisa multiplicar o tamanho da amostra por um fator de 100. Precis\u00e3o n\u00e3o vem barato!<\/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\/14-4\/\">\u2190 Cap\u00edtulo 14.4 &#8211; O Teorema Central do Limite<\/a><\/td>\n<td align=\"right\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-6\/\">Cap\u00edtulo 14.6 &#8211; Escolhendo um Tamanho de Amostra \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-772","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/772","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=772"}],"version-history":[{"count":4,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/772\/revisions"}],"predecessor-version":[{"id":1069,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/772\/revisions\/1069"}],"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=772"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/coauthors?post=772"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}