{"id":762,"date":"2025-07-29T16:29:02","date_gmt":"2025-07-29T20:29:02","guid":{"rendered":"https:\/\/literaciadigital.ufms.br\/?page_id=762"},"modified":"2025-10-11T15:42:05","modified_gmt":"2025-10-11T19:42:05","slug":"14-4","status":"publish","type":"page","link":"https:\/\/literaciadigital.ufms.br\/en\/data8\/14-0\/14-4\/","title":{"rendered":"Cap\u00edtulo 14.4"},"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 math\r\nimport numpy as np\r\nfrom scipy import stats<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">colors = Table.read_table(path_data + 'roulette_wheel.csv').column('Color')\r\npockets = make_array('0','00')\r\nfor i in np.arange(1, 37):\r\n    pockets = np.append(pockets, str(i))\r\n\r\nwheel = Table().with_columns(\r\n    'Pocket', pockets,\r\n    'Color', colors\r\n)<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<h1 id=\"o-teorema-central-do-limite\" style=\"text-align: center\">O Teorema Central do Limite<\/h1>\n<p style=\"text-align: justify\">Muito poucos dos histogramas de dados que vimos neste curso t\u00eam forma de sino. Quando encontramos uma distribui\u00e7\u00e3o em forma de sino, ela quase invariavelmente tem sido um histograma emp\u00edrico de uma estat\u00edstica baseada em uma amostra aleat\u00f3ria.<\/p>\n<p style=\"text-align: justify\">Os exemplos abaixo mostram duas situa\u00e7\u00f5es muito diferentes nas quais uma forma aproximada de sino aparece em tais histogramas.<\/p>\n<h2 id=\"ganho-l-quido-na-roleta\" style=\"text-align: justify\">Ganho L\u00edquido na Roleta<\/h2>\n<p style=\"text-align: justify\">Em uma se\u00e7\u00e3o anterior, a forma de sino apareceu como a forma aproximada do valor total de dinheiro que ganhar\u00edamos se fiz\u00e9ssemos a mesma aposta repetidamente em diferentes giros de uma roleta.<\/p>\n<pre><code><span style=\"color: black\">wheel<\/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\">Pocket<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Color<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">green<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">00<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">green<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">red<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">black<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">red<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">4<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">black<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">red<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">6<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">black<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">7<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">red<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">8<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">black<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Lembre-se de que a aposta no vermelho paga o mesmo valor, 1 para 1. Definimos a fun\u00e7\u00e3o <code>red_winnings<\/code> que retorna os ganhos l\u00edquidos em uma aposta de $1 no vermelho. Especificamente, a fun\u00e7\u00e3o usa uma cor como argumento e retorna 1 se a cor \u00e9 vermelha. Para todas as outras cores retorna -1.<\/p>\n<pre><code><span style=\"color: black\">def red_winnings(color):\r\n    if color == 'red':\r\n        return 1\r\n    else:\r\n        return -1<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">red = wheel.with_column(\r\n    'Winnings: Red', wheel.apply(red_winnings, 'Color')\r\n    )\r\nred<\/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\">Pocket<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Color<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Winnings: Red<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">green<\/td>\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\">00<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">green<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-1<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">red<\/td>\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\">2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">black<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-1<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">red<\/td>\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\">4<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">black<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-1<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">red<\/td>\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\">6<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">black<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-1<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">7<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">red<\/td>\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\">8<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">black<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Seu ganho l\u00edquido em uma aposta \u00e9 um sorteio aleat\u00f3rio da coluna <code>Winnings: Red<\/code>. H\u00e1 uma chance de 18\/38 de ganhar 1 e uma chance de 20\/38 de ganhar -1. Esta distribui\u00e7\u00e3o de probabilidade \u00e9 mostrada no histograma abaixo.<\/p>\n<pre><code><span style=\"color: black\">red.select('Winnings: Red').hist(bins=np.arange(-1.5, 1.6, 1))<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-764\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-1.png\" alt=\"\" width=\"433\" height=\"284\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-1.png 433w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-1-300x197.png 300w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p style=\"text-align: justify\">Agora suponha que voc\u00ea aposte muitas vezes no vermelho. Seus ganhos l\u00edquidos ser\u00e3o a soma de muitos sorteios feitos aleatoriamente com reposi\u00e7\u00e3o da distribui\u00e7\u00e3o acima.<\/p>\n<p style=\"text-align: justify\">Ser\u00e1 preciso um pouco de matem\u00e1tica para listar todos os valores poss\u00edveis de seus ganhos l\u00edquidos junto com todas as suas chances. N\u00e3o faremos isso; em vez disso, aproximaremos a distribui\u00e7\u00e3o de probabilidade por simula\u00e7\u00e3o, como fizemos ao longo deste curso.<\/p>\n<p style=\"text-align: justify\">O c\u00f3digo abaixo simula seu ganho l\u00edquido se voc\u00ea apostar $1 no vermelho em 400 giros diferentes da roleta.<\/p>\n<pre><code><span style=\"color: black\">num_bets = 400\r\nrepetitions = 10000\r\n\r\nnet_gain_red = make_array()\r\n\r\nfor i in np.arange(repetitions):\r\n    spins = red.sample(num_bets)\r\n    new_net_gain_red = spins.column('Winnings: Red').sum()\r\n    net_gain_red = np.append(net_gain_red, new_net_gain_red)\r\n\r\n\r\nresults = Table().with_column(\r\n    'Net Gain on Red', net_gain_red\r\n    )<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">results.hist(bins=np.arange(-80, 50, 6))<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-765\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-2.png\" alt=\"\" width=\"437\" height=\"284\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-2.png 437w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-2-300x195.png 300w\" sizes=\"(max-width: 437px) 100vw, 437px\" \/><\/p>\n<p style=\"text-align: justify\">Esse \u00e9 um histograma em formato de sino, embora a distribui\u00e7\u00e3o que estamos desenhando n\u00e3o esteja nem perto do formato de sino.<\/p>\n<p style=\"text-align: justify\"><strong>Centro.<\/strong> A distribui\u00e7\u00e3o est\u00e1 centrada perto de -20 d\u00f3lares, aproximadamente. Para ver o porqu\u00ea, observe que seus ganhos ser\u00e3o 1 em cerca de 18\/38 das apostas e -1 nos 20\/38 restantes. Portanto, seus ganhos m\u00e9dios por d\u00f3lar apostado ser\u00e3o de aproximadamente -5,26 centavos:<\/p>\n<pre><code><span style=\"color: black\">average_per_bet = 1*(18\/38) + (-1)*(20\/38)\r\naverage_per_bet<\/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\">-0.05263157894736842<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Ent\u00e3o, em 400 apostas voc\u00ea espera que seu ganho l\u00edquido seja de cerca de -$21:<\/p>\n<pre><code><span style=\"color: black\">400 * average_per_bet<\/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\">-21.052631578947366<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Para confirma\u00e7\u00e3o, podemos calcular a m\u00e9dia dos 10.000 ganhos l\u00edquidos simulados:<\/p>\n<pre><code><span style=\"color: black\">np.mean(results.column(0))<\/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\">-20.9586<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong>Dispers\u00e3o.<\/strong> Passe o olho ao longo da curva come\u00e7ando no centro e observe que o ponto de inflex\u00e3o est\u00e1 pr\u00f3ximo de 0. Em uma curva em forma de sino, o SD \u00e9 a dist\u00e2ncia do centro a um ponto de inflex\u00e3o. O centro \u00e9 aproximadamente -$20, o que significa que o SD da distribui\u00e7\u00e3o est\u00e1 em torno de $20.<\/p>\n<p style=\"text-align: justify\">Na pr\u00f3xima se\u00e7\u00e3o veremos de onde vem o $20. Por enquanto, vamos confirmar nossa observa\u00e7\u00e3o simplesmente calculando o DP dos 10.000 ganhos l\u00edquidos simulados:<\/p>\n<pre><code><span style=\"color: black\">np.std(results.column(0))<\/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\">20.029115957525438<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong>Resumo.<\/strong> O ganho l\u00edquido em 400 apostas \u00e9 a soma dos 400 valores ganhos em cada aposta individual. A distribui\u00e7\u00e3o de probabilidade dessa soma \u00e9 aproximadamente normal, com uma m\u00e9dia e um SD que podemos aproximar.<\/p>\n<h2 id=\"atraso-m-dio-de-voo\" style=\"text-align: justify\">Atraso m\u00e9dio de voo<\/h2>\n<p style=\"text-align: justify\">A tabela <code>united<\/code> cont\u00e9m dados sobre atrasos nas partidas de 13.825 voos dom\u00e9sticos da United Airlines saindo do aeroporto de S\u00e3o Francisco no ver\u00e3o de 2015. Como vimos antes, a distribui\u00e7\u00e3o dos atrasos tem uma longa cauda \u00e0 direita.<\/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\">united.select('Delay').hist(bins=np.arange(-20, 300, 10))<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-766\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-3.png\" alt=\"\" width=\"445\" height=\"284\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-3.png 445w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-3-300x191.png 300w\" sizes=\"(max-width: 445px) 100vw, 445px\" \/><\/p>\n<p style=\"text-align: justify\">O atraso m\u00e9dio foi de cerca de 16,6 minutos e o SD foi de cerca de 39,5 minutos. Observe como o SD \u00e9 grande, comparado \u00e0 m\u00e9dia. Esses grandes desvios \u00e0 direita t\u00eam um efeito, embora sejam uma propor\u00e7\u00e3o muito pequena dos dados.<\/p>\n<pre><code><span style=\"color: black\">mean_delay = np.mean(united.column('Delay'))\r\nsd_delay = np.std(united.column('Delay'))\r\n\r\nmean_delay, sd_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\">(16.658155515370705, 39.480199851609314)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Agora, suponha que amostramos 400 atrasos aleatoriamente com reposi\u00e7\u00e3o. Voc\u00ea poderia fazer uma amostragem sem reposi\u00e7\u00e3o, se quiser, mas os resultados seriam muito semelhantes aos da amostragem com reposi\u00e7\u00e3o. Se voc\u00ea amostrar algumas centenas de 13.825 sem reposi\u00e7\u00e3o, dificilmente alterar\u00e1 a popula\u00e7\u00e3o cada vez que voc\u00ea extrai um valor.<\/p>\n<p style=\"text-align: justify\">Na amostra, qual poderia ser o atraso m\u00e9dio? Esperamos que seja em torno de 16 ou 17, porque essa \u00e9 a m\u00e9dia da popula\u00e7\u00e3o; mas \u00e9 prov\u00e1vel que esteja um pouco errado. Vamos ver o que obtemos por amostragem. Trabalharemos com a tabela <code>delay<\/code> que cont\u00e9m apenas a coluna de atrasos.<\/p>\n<pre><code><span style=\"color: black\">delay = united.select('Delay')<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">np.mean(delay.sample(400).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[6]:<\/td>\n<td style=\"text-align: left\">15.59<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">A m\u00e9dia amostral varia de acordo com o resultado da amostra, ent\u00e3o vamos simular o processo de amostragem repetidamente e desenhar o histograma emp\u00edrico da m\u00e9dia amostral. Isso ser\u00e1 uma aproxima\u00e7\u00e3o do histograma de probabilidade da m\u00e9dia amostral.<\/p>\n<pre><code><span style=\"color: black\">sample_size = 400\r\nrepetitions = 10000\r\n\r\nmeans = make_array()\r\n\r\nfor i in np.arange(repetitions):\r\n    sample = delay.sample(sample_size)\r\n    new_mean = np.mean(sample.column('Delay'))\r\n    means = np.append(means, new_mean)\r\n\r\nresults = Table().with_column(\r\n    'Sample Mean', means\r\n)<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">results.hist(bins=np.arange(10, 25, 0.5))<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-767\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-4.png\" alt=\"\" width=\"433\" height=\"284\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-4.png 433w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-4-300x197.png 300w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p style=\"text-align: justify\">Mais uma vez, vemos um formato de sino aproximado, embora estejamos partindo de uma distribui\u00e7\u00e3o muito distorcida. O sino est\u00e1 centralizado em algum lugar entre 16 e 17, como esperamos.<\/p>\n<h2 id=\"teorema-central-do-limite\" style=\"text-align: justify\">Teorema Central do Limite<\/h2>\n<p style=\"text-align: justify\">A raz\u00e3o pela qual a forma de sino aparece em tais configura\u00e7\u00f5es \u00e9 um resultado not\u00e1vel da teoria da probabilidade chamado de <strong>Teorema Central do Limite<\/strong>.<\/p>\n<p style=\"text-align: justify\"><strong>O Teorema Central do Limite diz que a distribui\u00e7\u00e3o de probabilidade da soma ou m\u00e9dia de uma grande amostra aleat\u00f3ria retirada com reposi\u00e7\u00e3o ser\u00e1 aproximadamente normal, <em>independentemente da distribui\u00e7\u00e3o da popula\u00e7\u00e3o da qual a amostra \u00e9 retirada<\/em>.<\/strong><\/p>\n<p style=\"text-align: justify\">Como observamos quando est\u00e1vamos estudando os limites de Chebychev, resultados que podem ser aplicados a amostras aleat\u00f3rias <em>independentemente da distribui\u00e7\u00e3o da popula\u00e7\u00e3o<\/em> s\u00e3o muito poderosos, porque em ci\u00eancia de dados raramente conhecemos a distribui\u00e7\u00e3o da popula\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify\">O Teorema Central do Limite torna poss\u00edvel fazer infer\u00eancias com muito pouco conhecimento sobre a popula\u00e7\u00e3o, desde que tenhamos uma grande amostra aleat\u00f3ria. Por isso, ele \u00e9 central para o campo da infer\u00eancia estat\u00edstica.<\/p>\n<h2 id=\"propor-o-de-flores-roxas\" style=\"text-align: justify\">Propor\u00e7\u00e3o de Flores Roxas<\/h2>\n<p style=\"text-align: justify\">Relembre o modelo de probabilidade de Mendel para as cores das flores de uma esp\u00e9cie de planta de ervilha. O modelo diz que as cores das flores das plantas s\u00e3o como retiradas aleat\u00f3rias com reposi\u00e7\u00e3o de {Roxa, Roxa, Roxa, Branca}.<\/p>\n<p style=\"text-align: justify\">Em uma grande amostra de plantas, qual propor\u00e7\u00e3o ter\u00e1 flores roxas? Esperar\u00edamos que a resposta fosse cerca de 0,75, a propor\u00e7\u00e3o de roxo no modelo. E, como propor\u00e7\u00f5es s\u00e3o m\u00e9dias, o Teorema Central do Limite diz que a distribui\u00e7\u00e3o da propor\u00e7\u00e3o amostral de plantas roxas \u00e9 aproximadamente normal.<\/p>\n<p style=\"text-align: justify\">Podemos confirmar isso por simula\u00e7\u00e3o. Vamos simular a propor\u00e7\u00e3o de plantas com flores roxas em uma amostra de 200 plantas.<\/p>\n<pre><code><span style=\"color: black\">colors = make_array('Purple', 'Purple', 'Purple', 'White')\r\n\r\nmodel = Table().with_column('Color', colors)\r\n\r\nmodel<\/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\">Color<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Purple<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Purple<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Purple<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">White<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">props = make_array()\r\n\r\nnum_plants = 200\r\nrepetitions = 10000\r\n\r\nfor i in np.arange(repetitions):\r\n    sample = model.sample(num_plants)\r\n    new_prop = np.count_nonzero(sample.column('Color') == 'Purple')\/num_plants\r\n    props = np.append(props, new_prop)\r\n\r\nresults = Table().with_column('Sample Proportion: 200', props)<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">results.hist(bins=np.arange(0.65, 0.85, 0.01))<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-768\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-5.png\" alt=\"\" width=\"451\" height=\"284\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-5.png 451w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-5-300x189.png 300w\" sizes=\"(max-width: 451px) 100vw, 451px\" \/><\/p>\n<p style=\"text-align: justify\">H\u00e1 aquela curva normal novamente, conforme previsto pelo Teorema do Limite Central, centrada em torno de 0,75, exatamente como seria de esperar.<\/p>\n<p style=\"text-align: justify\">Como essa distribui\u00e7\u00e3o mudaria se aument\u00e1ssemos o tamanho da amostra? Vamos executar o c\u00f3digo novamente com um tamanho de amostra de 800 e coletar os resultados das simula\u00e7\u00f5es na mesma tabela em que coletamos simula\u00e7\u00f5es com base em um tamanho de amostra de 200. Iremos manter o n\u00famero de <code>repetitions<\/code> igual ao anterior para que as duas colunas tenham o mesmo comprimento.<\/p>\n<pre><code><span style=\"color: black\">props2 = make_array()\r\n\r\nnum_plants = 800\r\n\r\nfor i in np.arange(repetitions):\r\n    sample = model.sample(num_plants)\r\n    new_prop = np.count_nonzero(sample.column('Color') == 'Purple')\/num_plants\r\n    props2 = np.append(props2, new_prop)\r\n\r\nresults = results.with_column('Sample Proportion: 800', props2)<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">results.hist(bins=np.arange(0.65, 0.85, 0.01))<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-769\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-6.png\" alt=\"\" width=\"693\" height=\"265\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-6.png 693w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/14-4-6-300x115.png 300w\" sizes=\"(max-width: 693px) 100vw, 693px\" \/><\/p>\n<p style=\"text-align: justify\">Ambas as distribui\u00e7\u00f5es s\u00e3o aproximadamente normais, mas uma \u00e9 mais estreita do que a outra. As propor\u00e7\u00f5es baseadas em um tamanho de amostra de 800 est\u00e3o mais agrupadas em torno de 0,75 do que aquelas de um tamanho de amostra de 200. Aumentar o tamanho da amostra reduziu a variabilidade na propor\u00e7\u00e3o da amostra.<\/p>\n<p style=\"text-align: justify\">Isso n\u00e3o deveria ser surpreendente. Muitas vezes, confiamos na intui\u00e7\u00e3o de que um tamanho de amostra maior geralmente reduz a variabilidade de uma estat\u00edstica. No entanto, no caso de uma m\u00e9dia amostral, podemos <em>quantificar<\/em> a rela\u00e7\u00e3o entre o tamanho da amostra e a variabilidade.<\/p>\n<p style=\"text-align: justify\">Exatamente como o tamanho da amostra afeta a variabilidade de uma m\u00e9dia amostral ou propor\u00e7\u00e3o? Essa \u00e9 a pergunta que examinaremos na pr\u00f3xima se\u00e7\u00e3o.<\/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\/14-3\/\">\u2190 Cap\u00edtulo 14.3 &#8211; DP e a Curva Normal<\/a><\/td>\n<td align=\"right\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-5\/\">Cap\u00edtulo 14.5 &#8211; Variabilidade da M\u00e9dia da 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-762","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/762","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=762"}],"version-history":[{"count":9,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/762\/revisions"}],"predecessor-version":[{"id":1068,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/762\/revisions\/1068"}],"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=762"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/coauthors?post=762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}