{"id":690,"date":"2025-07-28T20:10:02","date_gmt":"2025-07-29T00:10:02","guid":{"rendered":"https:\/\/literaciadigital.ufms.br\/?page_id=690"},"modified":"2025-10-11T02:40:40","modified_gmt":"2025-10-11T06:40:40","slug":"13-1","status":"publish","type":"page","link":"https:\/\/literaciadigital.ufms.br\/en\/data8\/13-0\/13-1\/","title":{"rendered":"Cap\u00edtulo 13.1"},"content":{"rendered":"<div style=\"position: relative\">\n<div style=\"float: left;width: 300px;background-color: #f5f5f5;border: 1px solid #ddd;border-radius: 5px;padding: 15px;margin-right: 20px;margin-bottom: 5px;overflow: hidden\">\n<h3 style=\"margin: 0 0 10px 0;padding-bottom: 8px;border-bottom: 1px solid #ddd\">\u00cdndice<\/h3>\n<ol style=\"margin: 0;padding-left: 0;list-style-type: none\">\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/\">1. O que \u00e9 Ci\u00eancia de Dados?<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-1\/\">1.1. Introdu\u00e7\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-1\/1-1\/\">1.1.1. Ferramentas Computacionais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-1\/1-2\/\">1.1.2. T\u00e9cnicas Estat\u00edsticas<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-2\/\">1.2. Por que Ci\u00eancia de Dados?<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-3\/\">1.3. Tra\u00e7ando os Cl\u00e1ssicos<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-3\/3-1\/\">1.3.1. Personagens Liter\u00e1rios<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-3\/3-2\/\">1.3.2. Outro Tipo de Personagem<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/\">2. Causalidade e Experimentos<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-1\/\">2.1. John Snow e a Bomba da Broad Street<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-2\/\">2.2. O &#8220;Grande Experimento&#8221; de Snow<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-3\/\">2.3. Estabelecendo Causalidade<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-4\/\">2.4. Randomiza\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-5\/\">2.5. Notas Finais<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/\">3. Progamando em Python<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-1\/\">3.1. Express\u00f5es<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-2\/\">3.2. Nomes<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-2\/2-1\/\">3.2.1. Exemplo: Taxas de Crescimento<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-3\/\">3.3. Chamadas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-4\/\">3.4. Introdu\u00e7\u00e3o \u00e0s Tabelas<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/\">4. Tipos de Dados<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-1\/\">4.1. N\u00fameros<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-2\/\">4.2. Strings<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-2\/2-1\/\">4.2.1. M\u00e9todos de Strings<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-3\/\">4.3. Compara\u00e7\u00f5es<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/\">5. Sequ\u00eancias<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/5-1\/\">5.1. Arrays<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/5-2\/\">5.2. Ranges<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/5-3\/\">5.3. Mais sobre Arrays<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/\">6. Tabelas<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-1\/\">6.1. Ordenando Linhas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-2\/\">6.2. Selecionando Linhas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-3\/\">6.3. Exemplo: Tend\u00eancias Populacionais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-4\/\">6.4. Examplo: Propor\u00e7\u00f5es de Sexos<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/\">7. Visualiza\u00e7\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/7-1\/\">7.1. Visualizando Distribui\u00e7\u00f5es<br \/>\nCateg\u00f3ricas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/7-2\/\">7.2. Visualizando Distribui\u00e7\u00f5es Num\u00e9ricas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/7-3\/\">7.3. Gr\u00e1ficos Sobrepostos<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/\">8. Fun\u00e7\u00f5es e Tabelas<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-1\/\">8.1. Aplicando Fun\u00e7\u00e3o a uma Coluna<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-2\/\">8.2. Classificando por uma Vari\u00e1vel<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-3\/\">8.3. Classifica\u00e7\u00e3o Cruzada<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-4\/\">8.4. Unindo Tabelas por Colunas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-5\/\">8.5. Compartilhamento de Bicicletas<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/\">9. Aleatoriedade<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-1\/\">9.1. Declara\u00e7\u00f5es Condicionais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-2\/\">9.2. Itera\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-3\/\">9.3. Simula\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-4\/\">9.4. O Problema de Monty Hall<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-5\/\">9.5. Encontrando Probabilidades<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/\">10. Amostragem e Distribui\u00e7\u00f5es Emp\u00edricas<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-1\/\">10.1. Distribui\u00e7\u00f5es Emp\u00edricas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-2\/\">10.2. Amostragem de uma Popula\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-3\/\">10.3. Distribui\u00e7\u00e3o Emp\u00edrica de uma<br \/>\nEstat\u00edstica<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-4\/\">10.4. Amostragem Aleat\u00f3ria em Python <\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/\">11. Testando Hip\u00f3teses<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-1\/\">11.1. Avaliando um Modelo<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-2\/\">11.2. M\u00faltiplas Categorias<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-3\/\">11.3. Decis\u00f5es e Incertezas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-4\/\">11.4. Probabilidades de Erro<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/\">12. Comparando Duas Amostras<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-1\/\">12.1. Teste A\/B<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-2\/\">12.2. Causalidade<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-3\/\">12.3. Esvaziar<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/\">13. Estima\u00e7\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-1\/\">13.1. Percentis<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-2\/\">13.2. O Bootstrap<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-3\/\">13.3. Intervalos de Confian\u00e7a<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-4\/\">13.4. Usando Intervalos de Confian\u00e7a<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/\">14. Por que a M\u00e9dia \u00e9 Importante<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-1\/\">14.1. Propriedades da M\u00e9dia<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-2\/\">14.2. Variabilidade<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-3\/\">14.3. O DP e a Curva Normal<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-4\/\">14.4. Teorema Central do Limite<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-5\/\">14.5. Variabilidade da M\u00e9dia da Amostra<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-6\/\">14.6. Escolhendo um Tamanho de Amostra<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/\">15. Previs\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-1\/\">15.1. Correla\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-2\/\">15.2. Linha de Regress\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-3\/\">15.3. M\u00e9todo dos M\u00ednimos Quadrados<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-4\/\">15.4. Regress\u00e3o de M\u00ednimos Quadrados<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-5\/\">15.5. Diagn\u00f3sticos Visuais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-6\/\">15.6. Diagn\u00f3stico Num\u00e9rico<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<p><!-- Main Content --><\/p>\n<div style=\"overflow: hidden\">\n<p><!--###########################################################################################################################################################--><\/p>\n<pre><code><span style=\"color: black\">from datascience import *\r\n%matplotlib inline\r\npath_data = '..\/..\/..\/assets\/data\/'\r\nimport matplotlib.pyplot as plt\r\nplt.style.use('fivethirtyeight')\r\nimport numpy as np<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<h1 id=\"percentis\" style=\"text-align: center\">Percentis<\/h1>\n<p style=\"text-align: justify\">Dados num\u00e9ricos podem ser classificados em ordem crescente ou decrescente. Assim, os valores de um conjunto de dados num\u00e9ricos t\u00eam uma <em>ordem de classifica\u00e7\u00e3o<\/em>. Um percentil \u00e9 o valor em uma posi\u00e7\u00e3o espec\u00edfica dessa ordem.<\/p>\n<p style=\"text-align: justify\">Por exemplo, se sua pontua\u00e7\u00e3o em um teste est\u00e1 no 95\u00ba percentil, uma interpreta\u00e7\u00e3o comum \u00e9 que apenas 5% das pontua\u00e7\u00f5es foram superiores \u00e0 sua. A mediana \u00e9 o 50\u00ba percentil; \u00e9 comumente assumido que 50% dos valores em um conjunto de dados est\u00e3o acima da mediana.<\/p>\n<p style=\"text-align: justify\">Mas algum cuidado \u00e9 necess\u00e1rio para dar aos percentis uma defini\u00e7\u00e3o precisa que funcione para todos os rankings e todas as listas. Para entender por que isso \u00e9 importante, considere um exemplo extremo em que todos os estudantes de uma classe obt\u00eam 75 em um teste. Ent\u00e3o, 75 \u00e9 um candidato natural para a mediana, mas n\u00e3o \u00e9 verdade que 50% das pontua\u00e7\u00f5es est\u00e3o acima de 75. Al\u00e9m disso, 75 \u00e9 um candidato igualmente natural para o 95\u00ba percentil, o 25\u00ba ou qualquer outro percentil. Empates &#8211; ou seja, valores de dados iguais &#8211; precisam ser levados em conta ao definir percentis.<\/p>\n<p style=\"text-align: justify\">Tamb\u00e9m \u00e9 necess\u00e1rio ter cuidado quanto \u00e0 posi\u00e7\u00e3o exata na lista ao calcular percentis quando o \u00edndice relevante n\u00e3o est\u00e1 claro. Por exemplo, qual deveria ser o 87\u00ba percentil de uma cole\u00e7\u00e3o de 10 valores? O 8\u00ba valor da cole\u00e7\u00e3o ordenada, ou o 9\u00ba, ou em algum lugar entre eles?<\/p>\n<p style=\"text-align: justify\">Nesta se\u00e7\u00e3o, daremos uma defini\u00e7\u00e3o que funcione consistentemente para todos os rankings e todas as listas.<\/p>\n<h2 id=\"um-exemplo-num-rico\" style=\"text-align: justify\">Um Exemplo Num\u00e9rico<\/h2>\n<p style=\"text-align: justify\">Antes de darmos uma defini\u00e7\u00e3o geral de todos os percentis, vamos definir o 80\u00ba percentil de uma cole\u00e7\u00e3o de valores como o menor valor na cole\u00e7\u00e3o que \u00e9 pelo menos t\u00e3o grande quanto 80% de todos os valores.<\/p>\n<p style=\"text-align: justify\">Por exemplo, vamos considerar os tamanhos dos cinco maiores continentes &#8211; \u00c1frica, Ant\u00e1rtica, \u00c1sia, Am\u00e9rica do Norte e Am\u00e9rica do Sul &#8211; arredondados para o milh\u00e3o mais pr\u00f3ximo de milhas quadradas.<\/p>\n<pre><code><span style=\"color: black\">sizes = make_array(12, 17, 6, 9, 7)<\/span><\/code><\/pre>\n<p style=\"text-align: justify\">O percentil 80 \u00e9 o menor valor que \u00e9 pelo menos t\u00e3o grande quanto 80% dos elementos de &#8216;tamanhos&#8217;, ou seja, quatro quintos dos cinco elementos. Isso \u00e9 12:<\/p>\n<pre><code><span style=\"color: black\">np.sort(sizes)<\/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\">array([ 6, 7, 9, 12, 17])<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">O 80\u00ba percentil \u00e9 um valor da lista, ou seja, 12. Voc\u00ea pode ver que 80% dos valores s\u00e3o menores ou iguais a ele e que \u00e9 o menor valor da lista para o qual isso \u00e9 verdade.<\/p>\n<p style=\"text-align: justify\">De forma an\u00e1loga, o percentil 70 \u00e9 o menor valor na cole\u00e7\u00e3o que \u00e9 pelo menos t\u00e3o grande quanto 70% dos elementos de <code>sizes<\/code>. Agora, 70% de 5 elementos s\u00e3o &#8220;3,5 elementos&#8221;, ent\u00e3o o percentil 70 \u00e9 o Quarto elemento da lista \u00c9 12, o mesmo que o 80\u00ba percentil para esses dados.<\/p>\n<h2 id=\"a-fun-o-percentile-\" style=\"text-align: justify\">A fun\u00e7\u00e3o <code>percentile<\/code><\/h2>\n<p style=\"text-align: justify\">A fun\u00e7\u00e3o <code>percentil<\/code> leva dois argumentos: uma classifica\u00e7\u00e3o entre 0 e 100 e uma matriz. Ela retorna o percentil correspondente do array.<\/p>\n<pre><code><span style=\"color: black\">percentile(70, sizes)<\/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\">12<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 id=\"a-defini-o-geral\" style=\"text-align: justify\">A Defini\u00e7\u00e3o Geral<\/h3>\n<p style=\"text-align: justify\">Seja <em>p<\/em> um n\u00famero entre 0 e 100. O percentil <em>p<\/em> de uma cole\u00e7\u00e3o \u00e9 o menor valor na cole\u00e7\u00e3o que \u00e9 pelo menos t\u00e3o grande quanto <em>p<\/em>% de todos os valores.<\/p>\n<p style=\"text-align: justify\">Por esta defini\u00e7\u00e3o, qualquer percentil entre 0 e 100 pode ser calculado para qualquer cole\u00e7\u00e3o de valores, e ele sempre \u00e9 um elemento da cole\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify\">Em termos pr\u00e1ticos, suponha que h\u00e1 <em>n<\/em> elementos na cole\u00e7\u00e3o. Para encontrar o percentil <em>p<\/em>:<\/p>\n<ul style=\"text-align: justify\">\n<li>Ordene a cole\u00e7\u00e3o em ordem crescente.<\/li>\n<li>Encontre p% de n: (<em>p<\/em>\/100) \\times <em>n<\/em>. Chame isso de <em>k<\/em>.<\/li>\n<li>Se <em>k<\/em> for um n\u00famero inteiro, pegue o <em>k<\/em>-\u00e9simo elemento da cole\u00e7\u00e3o ordenada.<\/li>\n<li>Se <em>k<\/em> n\u00e3o for um n\u00famero inteiro, arredonde para cima para o pr\u00f3ximo inteiro e pegue esse elemento da cole\u00e7\u00e3o ordenada.<\/li>\n<\/ul>\n<h3 id=\"exemplo\" style=\"text-align: justify\">Exemplo<\/h3>\n<p style=\"text-align: justify\">A tabela <code>scores_and_sections<\/code> cont\u00e9m uma linha para cada estudante em uma turma de 359 alunos. As colunas s\u00e3o a se\u00e7\u00e3o de discuss\u00e3o do aluno e a nota da prova.<\/p>\n<pre><code>scores_and_sections = Table.read_table(path_data + 'scores_by_section.csv')\r\nscores_and_sections <\/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\">Section<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Midterm<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">22<\/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\">12<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">23<\/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\">14<\/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\">20<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">25<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">4<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">19<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">24<\/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\">8<\/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\">14<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<pre><code><span style=\"color: black\">scores_and_sections.select('Midterm').hist(bins=np.arange(-0.5, 25.6, 1))<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-692\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/13-1-1.png\" alt=\"\" width=\"424\" height=\"284\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/13-1-1.png 424w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/13-1-1-300x201.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/13-1-1-350x233.png 350w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><\/p>\n<p style=\"text-align: justify\">Qual foi o percentil 85 das pontua\u00e7\u00f5es? Para usar a fun\u00e7\u00e3o <code>percentile<\/code>, crie um array <code>scores<\/code> contendo as pontua\u00e7\u00f5es intermedi\u00e1rias e encontre o percentil 85:<\/p>\n<pre><code><span style=\"color: black\">scores = scores_and_sections.column(1)<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">percentile(85, scores)<\/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\">22<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">De acordo com a fun\u00e7\u00e3o percentil, o percentil 85 era 22. Para verificar se isso \u00e9 consistente com a nossa nova defini\u00e7\u00e3o, vamos aplicar a defini\u00e7\u00e3o diretamente.<\/p>\n<p style=\"text-align: justify\">Primeiro, coloque as pontua\u00e7\u00f5es em ordem crescente:<\/p>\n<pre><code><span style=\"color: black\">sorted_scores = np.sort(scores_and_sections.column(1))<\/span><\/code><\/pre>\n<p style=\"text-align: justify\">Existem 359 pontua\u00e7\u00f5es no array. A seguir, encontre 85% de 359, que \u00e9 305,15.<\/p>\n<pre><code><span style=\"color: black\">0.85 * 359<\/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\">305.15<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Isso n\u00e3o \u00e9 um n\u00famero inteiro. Pela nossa defini\u00e7\u00e3o, o 85\u00ba percentil \u00e9 o 306\u00ba elemento de <code>sorted_scores<\/code>, que, pela conven\u00e7\u00e3o de indexa\u00e7\u00e3o do Python, \u00e9 o item 305 do array.<\/p>\n<pre><code><span style=\"color: black\"># O 306\u00ba elemento do array classificado\r\n\r\nsorted_scores.item(305)<\/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\">22<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Essa \u00e9 a mesma resposta que obtivemos usando <code>percentile<\/code>. No futuro, usaremos apenas <code>percentile<\/code>.<\/p>\n<h2 id=\"quartis\" style=\"text-align: justify\">Quartis<\/h2>\n<p style=\"text-align: justify\">O <em>primeiro quartil<\/em> de uma cole\u00e7\u00e3o num\u00e9rica \u00e9 o 25\u00ba percentil. A terminologia surge do <em>primeiro quarto<\/em>. O segundo quartil \u00e9 a mediana, e o terceiro quartil \u00e9 o 75\u00ba percentil.<\/p>\n<p style=\"text-align: justify\">Para os dados de <code>scores<\/code>, esses valores s\u00e3o:<\/p>\n<pre><code><span style=\"color: black\">percentile(25, scores)<\/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\">11<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<pre><code><span style=\"color: black\">percentile(50, scores)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[7]:<\/td>\n<td style=\"text-align: left\">16<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<pre><code><span style=\"color: black\">percentile(75, scores)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[8]:<\/td>\n<td style=\"text-align: left\">20<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">As distribui\u00e7\u00f5es das pontua\u00e7\u00f5es \u00e0s vezes s\u00e3o resumidas pelo intervalo de &#8220;50% intermedi\u00e1rios&#8221;, entre o primeiro e o terceiro quartis.<\/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\/13-0\/\">\u2190 Cap\u00edtulo 13 &#8211; Estima\u00e7\u00e3o<\/a><\/td>\n<td align=\"right\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-2\/\">Cap\u00edtulo 13.2 &#8211; Bootstrap \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":687,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-templates\/full-width.php","meta":{"footnotes":""},"coauthors":[14],"class_list":["post-690","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/690","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=690"}],"version-history":[{"count":7,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/690\/revisions"}],"predecessor-version":[{"id":1044,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/690\/revisions\/1044"}],"up":[{"embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/687"}],"wp:attachment":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/media?parent=690"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/coauthors?post=690"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}