{"id":15712,"date":"2022-04-22T13:14:25","date_gmt":"2022-04-22T12:14:25","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=15712"},"modified":"2022-04-22T14:27:11","modified_gmt":"2022-04-22T13:27:11","slug":"tutoriel-sur-la-moyenne-geometrique-et-harmonique","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/es\/analisis-descriptivo\/tutorial-sobre-la-media-geometrica-y-armonica\/","title":{"rendered":"Tutorial de Media Geom\u00e9trica y Arm\u00f3nicos"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"15712\" class=\"elementor elementor-15712\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d011e01 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d011e01\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5755304\" data-id=\"5755304\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ea2fd87 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"ea2fd87\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/analisis-descriptivo\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">An\u00e1lisis descriptivo<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-804b560\" data-id=\"804b560\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-aa75127 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"aa75127\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/es\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Pagina de inicio<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-21a319e\" data-id=\"21a319e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8e5291b elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"8e5291b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/fr.wikipedia.org\/wiki\/Statistique_descriptive\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">WIki<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-25751ac elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"25751ac\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2008db9\" data-id=\"2008db9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c5483d8 elementor-widget elementor-widget-text-editor\" data-id=\"c5483d8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Esta p\u00e1gina muestra varios ejemplos sobre los casos de uso de los diferentes medios, en particular, la media geom\u00e9trica y la media arm\u00f3nica.<\/p><p><img decoding=\"async\" class=\"aligncenter wp-image-11096 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/cropped-Capture.png\" alt=\"media geom\u00e9trica y media arm\u00f3nica\" width=\"97\" height=\"97\" title=\"\"><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b6767c2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b6767c2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-43a78af\" data-id=\"43a78af\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-aa3c20b elementor-widget elementor-widget-heading\" data-id=\"aa3c20b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contenido<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Tabla de contenido alternativo\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Palanca<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/es\/analisis-descriptivo\/tutorial-sobre-la-media-geometrica-y-armonica\/#Moyenne-arithmetique\" >promedio aritm\u00e9tico<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/complex-systems-ai.com\/es\/analisis-descriptivo\/tutorial-sobre-la-media-geometrica-y-armonica\/#La-moyenne-geometrique\" >la media geometrica<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/complex-systems-ai.com\/es\/analisis-descriptivo\/tutorial-sobre-la-media-geometrica-y-armonica\/#Exemple-de-moyenne-geometrique\" >Ejemplo de media geom\u00e9trica<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/complex-systems-ai.com\/es\/analisis-descriptivo\/tutorial-sobre-la-media-geometrica-y-armonica\/#Moyenne-geometrique-et-changement-dechelle\" >Media geom\u00e9trica y cambio de escala<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/complex-systems-ai.com\/es\/analisis-descriptivo\/tutorial-sobre-la-media-geometrica-y-armonica\/#Et-la-moyenne-harmonique\" >\u00bfY la media arm\u00f3nica?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/complex-systems-ai.com\/es\/analisis-descriptivo\/tutorial-sobre-la-media-geometrica-y-armonica\/#Exemple-de-moyenne-harmonique\" >Ejemplo de media arm\u00f3nica<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Moyenne-arithmetique\"><\/span>promedio aritm\u00e9tico<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a85d084 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a85d084\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e3f56cd\" data-id=\"e3f56cd\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6d9dfe4 elementor-widget elementor-widget-text-editor\" data-id=\"6d9dfe4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p id=\"af2e\" class=\"pw-post-body-paragraph lk ll jd lm b ln lo ke lp lq lr kh ls lt lu lv lw lx ly lz ma mb mc md me mf iw gc\" data-selectable-paragraph=\"\">La media aritm\u00e9tica se nombra apropiadamente: la encontramos sumando todos los n\u00fameros en el conjunto de datos, luego dividiendo por el n\u00famero de n\u00fameros en el conjunto de datos (para reducir la suma a la escala de los n\u00fameros originales).<\/p><blockquote class=\"nd ne nf\"><p id=\"e7a7\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\">3 + 8 + 10 = 21<br \/>21 \u00f7 3 = 7<br \/><strong class=\"lm je\">Significado aritmetico<\/strong>\u00a0=\u00a0<strong class=\"lm je\">7<\/strong><\/code><\/p><\/blockquote><p id=\"68f0\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Observe, lo que b\u00e1sicamente estamos diciendo aqu\u00ed es: si cada n\u00famero en nuestro conjunto de datos fuera el mismo n\u00famero, \u00bfqu\u00e9 n\u00famero tendr\u00eda que ser para tener la misma suma que nuestro conjunto de datos real?<\/p><p id=\"c0bb\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Pero no hay nada particularmente especial en la adici\u00f3n. Es solo una operaci\u00f3n matem\u00e1tica bastante simple. La media aritm\u00e9tica funciona bien para producir un n\u00famero &quot;promedio&quot; de un conjunto de datos cuando existe una relaci\u00f3n aditiva entre los n\u00fameros.<\/p><p class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Tal relaci\u00f3n a menudo se llama &quot;lineal&quot;, porque cuando se grafican en orden ascendente o descendente, los n\u00fameros tienden a caer sobre una l\u00ednea recta o alrededor de ella. Un ejemplo idealizado simple ser\u00eda un conjunto de datos donde cada n\u00famero se produce sumando 3 al n\u00famero anterior:<\/p><blockquote class=\"nd ne nf\"><p id=\"e236\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\">1, 4, 7, 10, 13, 16, 19...<\/code><\/p><\/blockquote><figure class=\"mi mj mk ml gz mm gn go paragraph-image\"><div class=\"gn go xh\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-medium wp-image-15715\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_nr24D4m2hTL7cGjg1uThyw-300x259.png\" alt=\"\" width=\"300\" height=\"259\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_nr24D4m2hTL7cGjg1uThyw-300x259.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_nr24D4m2hTL7cGjg1uThyw-14x12.png 14w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_nr24D4m2hTL7cGjg1uThyw.png 576w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/div><\/figure><p id=\"ea4a\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">La media aritm\u00e9tica por lo tanto nos da un valor mediano perfectamente razonable:<\/p><blockquote class=\"nd ne nf\"><p id=\"ffe7\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\">(1 + 4 + 7 + 10 + 13 + 16 + 19) \u00f7 7 =\u00a0<strong class=\"lm je\">10<\/strong><\/code><\/p><\/blockquote><figure class=\"mi mj mk ml gz mm gn go paragraph-image\"><div class=\"gn go xh\"><img decoding=\"async\" class=\"aligncenter size-medium wp-image-15716\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_iqmOO-Ar-2A9PnkXTQ-wgA-300x259.png\" alt=\"\" width=\"300\" height=\"259\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_iqmOO-Ar-2A9PnkXTQ-wgA-300x259.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_iqmOO-Ar-2A9PnkXTQ-wgA-14x12.png 14w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_iqmOO-Ar-2A9PnkXTQ-wgA.png 576w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/div><\/figure><p id=\"3595\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Pero no todos los conjuntos de datos se describen mejor con esta regresi\u00f3n lineal. Algunos tienen una relaci\u00f3n multiplicativa o exponencial, por ejemplo, si multiplicamos cada n\u00famero consecutivo por 3 en lugar de sumar por 3 como hicimos anteriormente:<\/p><blockquote class=\"nd ne nf\"><p id=\"16a7\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\">1, 3, 9, 27, 81, 243, 729\u2026<\/code><\/p><\/blockquote><p id=\"0590\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Esto produce lo que se llama una serie geom\u00e9trica. Cuando se dibujan en orden, estos n\u00fameros se parecen m\u00e1s a una curva que a una l\u00ednea recta.<\/p><p id=\"bc28\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">En esta situaci\u00f3n, la media aritm\u00e9tica no es adecuada para producir un n\u00famero &quot;promedio&quot; para resumir estos datos.<\/p><blockquote class=\"nd ne nf\"><p id=\"f953\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\">(1 + 3 + 9 + 27 + 81 + 243 + 729) \u00f7 7 =\u00a0<strong class=\"lm je\">156.1<\/strong><\/code><\/p><\/blockquote><figure class=\"mi mj mk ml gz mm gn go paragraph-image\"><div class=\"gn go xh\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-15717\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_3FQYgskPEfwodxSVgrGMlg-300x254.png\" alt=\"\" width=\"300\" height=\"254\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_3FQYgskPEfwodxSVgrGMlg-300x254.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_3FQYgskPEfwodxSVgrGMlg-14x12.png 14w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_3FQYgskPEfwodxSVgrGMlg.png 576w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/div><\/figure><p id=\"4b97\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">156 no est\u00e1 particularmente cerca de la mayor\u00eda de los n\u00fameros en nuestro conjunto de datos. De hecho, es m\u00e1s de 5 veces la mediana (n\u00famero del medio), que es 27.<\/p><p class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">\u00bfQu\u00e9 hacer en este caso?<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bc5dade elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bc5dade\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ad742a5\" data-id=\"ad742a5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ad02b57 elementor-widget elementor-widget-heading\" data-id=\"ad02b57\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"La-moyenne-geometrique\"><\/span>la media geometrica<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7eba54b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7eba54b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-825016e\" data-id=\"825016e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c94a366 elementor-widget elementor-widget-text-editor\" data-id=\"c94a366\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p id=\"1b7b\" class=\"pw-post-body-paragraph lk ll jd lm b ln lo ke lp lq lr kh ls lt lu lv lw lx ly lz ma mb mc md me mf iw gc\" data-selectable-paragraph=\"\">Dado que la relaci\u00f3n es multiplicativa, para encontrar la media geom\u00e9trica multiplicamos en lugar de sumar todos los n\u00fameros. Luego, para escalar el producto al rango del conjunto de datos, necesitamos sacar la ra\u00edz del conteo de elementos, en lugar de simplemente dividir.<\/p><p id=\"f10b\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Por lo tanto, la media geom\u00e9trica de nuestro conjunto de datos es:<\/p><blockquote class=\"nd ne nf\"><p id=\"de57\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\">1 * 3 * 9 * 27 * 81 * 243 * 729 = 10,460,353,203<br \/>s\u00e9ptima ra\u00edz de 10,460,353,203 = 27<br \/><strong class=\"lm je\">significado geometrico<\/strong>\u00a0=\u00a0<strong class=\"lm je\">27<\/strong><\/code><\/p><\/blockquote><figure class=\"mi mj mk ml gz mm gn go paragraph-image\"><div class=\"gn go xh\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-15718\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_7sQflp6iyrOK2IX3Lhg68A-300x254.png\" alt=\"\" width=\"300\" height=\"254\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_7sQflp6iyrOK2IX3Lhg68A-300x254.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_7sQflp6iyrOK2IX3Lhg68A-14x12.png 14w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_7sQflp6iyrOK2IX3Lhg68A.png 576w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/div><\/figure><p id=\"a970\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">En este caso, nuestra media geom\u00e9trica se parece mucho al valor de la mediana de nuestro conjunto de datos. De hecho, es igual a la mediana.<\/p><p id=\"9aa0\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">La media geom\u00e9trica no siempre ser\u00e1 igual a la mediana, solo en los casos en que exista una relaci\u00f3n multiplicativa exacta y consistente entre todos los n\u00fameros (por ejemplo, multiplicando cada n\u00famero anterior por 3, como hemos hecho).<\/p><p class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Los conjuntos de datos del mundo real rara vez contienen relaciones tan exactas, pero para aquellos que se aproximan a este tipo de relaci\u00f3n multiplicativa, la media geom\u00e9trica producir\u00e1 un &quot;n\u00famero mediano&quot; m\u00e1s cercano que la media aritm\u00e9tica.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a981dab elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a981dab\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4d6b871\" data-id=\"4d6b871\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-54b5336 elementor-widget elementor-widget-heading\" data-id=\"54b5336\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exemple-de-moyenne-geometrique\"><\/span>Ejemplo de media geom\u00e9trica<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-371315d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"371315d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1800c94\" data-id=\"1800c94\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-080f1c4 elementor-widget elementor-widget-text-editor\" data-id=\"080f1c4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p id=\"2bf6\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Supongamos que tenemos 100.000 $ que genera una tasa de inter\u00e9s variable cada a\u00f1o durante 5 a\u00f1os:<\/p><blockquote class=\"nd ne nf\"><p id=\"bcb4\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\">tipos de inter\u00e9s anuales: 1%, 9%, 6%, 2%, 15%<\/code><\/p><\/blockquote><p id=\"7d7a\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Nos gustar\u00eda tomar un atajo para encontrar nuestra tasa de inter\u00e9s anual promedio y, por lo tanto, nuestra cantidad total de dinero despu\u00e9s de 5 a\u00f1os, por lo que tratamos de &quot;promediar&quot; estas tasas:<\/p><blockquote class=\"nd ne nf\"><p id=\"75a6\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\">(.01 + .09 + .06 + .02 + .15) \u00f7 5 = .066 =\u00a0<strong class=\"lm je\">6.6%<\/strong><\/code><\/p><\/blockquote><p id=\"21af\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">A continuaci\u00f3n, insertamos este porcentaje promedio en una f\u00f3rmula de inter\u00e9s compuesto:<\/p><blockquote class=\"nd ne nf\"><p id=\"5801\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\">Inter\u00e9s total devengado = $100.000 * (1,066\u2075 - 1) = $37.653,11<br \/>Inter\u00e9s + principal = $37.653,11 + 100.000 = $137.653,11<br \/><strong class=\"lm je\">suma final<\/strong>\u00a0=\u00a0<strong class=\"lm je\">$137,653.11<\/strong><\/code><\/p><\/blockquote><p id=\"1c43\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Comparemos los resultados:<\/p><blockquote class=\"nd ne nf\"><p id=\"900c\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\"><strong class=\"lm je\">A\u00f1o 1<\/strong>: 100,000 + (100,000 * .01) = 100,000 * 1.01 = $101,000<\/code><br \/><code class=\"fr xd xe xf xg b\"><strong class=\"lm je\">A\u00f1o 2<\/strong>: 101,000 * 1.09 = $110,090<\/code><br \/><code class=\"fr xd xe xf xg b\"><strong class=\"lm je\">a\u00f1o 3<\/strong>: 110,090 * 1.06 = $116,695.40<\/code><br \/><code class=\"fr xd xe xf xg b\"><strong class=\"lm je\">a\u00f1o 4<\/strong>: 116,695.40 * 1.02 = $119,029.31<\/code><br \/><code class=\"fr xd xe xf xg b\"><strong class=\"lm je\">a\u00f1o 5<\/strong>: 119,029.31 * 1.15 = $136,883.70<\/code><br \/><code class=\"fr xd xe xf xg b\"><strong class=\"lm je\">Total final real<\/strong>\u00a0=\u00a0<strong class=\"lm je\">$136,883.70<\/strong><\/code><\/p><\/blockquote><p id=\"ef3e\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Nuestro atajo sobrestim\u00f3 nuestras ganancias reales en casi 1000 $.<\/p><p>Cometimos un error com\u00fan: aplicamos una operaci\u00f3n aditiva a un proceso multiplicativo y obtuvimos un resultado inexacto.<\/p><p>Probemos de nuevo con la media geom\u00e9trica:<\/p><blockquote class=\"nd ne nf\"><p id=\"9685\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\">1.01 * 1.09 * 1.06 * 1.02 * 1.15 = 1.368837042<br \/>Quinta ra\u00edz de 1.368837042 = 1.064805657<br \/><strong class=\"lm je\">significado geometrico<\/strong>\u00a0=\u00a0<strong class=\"lm je\">1.064805657<\/strong><\/code><\/p><\/blockquote><p id=\"e8d8\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Introduzca la media geom\u00e9trica de las tasas de inter\u00e9s en nuestra f\u00f3rmula de inter\u00e9s compuesto:<\/p><blockquote class=\"nd ne nf\"><p id=\"9eed\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\">Inter\u00e9s total devengado = $100.000 * (1,0648\u2075 - 1) = $36.883,70<br \/>Inter\u00e9s + principal = $36.883,70 + 100.000 = $136.883,70<br \/><strong class=\"lm je\">suma final<\/strong>\u00a0=\u00a0<strong class=\"lm je\">$136,883.70\u00a0<\/strong>exactamente lo mismo que el m\u00e9todo largo anterior<\/code><\/p><\/blockquote><p id=\"8ba9\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">\u00a1Lo que corresponde a la realidad!<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f1546d4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f1546d4\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c9e620c\" data-id=\"c9e620c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d7b52fd elementor-widget elementor-widget-heading\" data-id=\"d7b52fd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Moyenne-geometrique-et-changement-dechelle\"><\/span>Media geom\u00e9trica y cambio de escala<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ef865cc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ef865cc\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0caa537\" data-id=\"0caa537\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-edf0dc1 elementor-widget elementor-widget-text-editor\" data-id=\"edf0dc1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p id=\"bfc0\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Una caracter\u00edstica interesante de la media geom\u00e9trica es que en realidad puedes promediar n\u00fameros en escalas completamente diferentes.<\/p><p id=\"b7c7\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Por ejemplo, queremos comparar las calificaciones en l\u00ednea de dos cafeter\u00edas usando dos fuentes diferentes. El problema es que la fuente 1 usa una escala de 5 estrellas y la fuente 2 usa una escala de 100 puntos:<\/p><blockquote class=\"nd ne nf\"><p id=\"3d3b\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><strong class=\"lm je\"><em class=\"jd\">Cafeter\u00eda A<\/em><\/strong><em class=\"jd\"><br \/><\/em><code class=\"fr xd xe xf xg b\"><em class=\"jd\">fuente 1<\/em><\/code><em class=\"jd\">\u00a0clasificaci\u00f3n:\u00a0<\/em><code class=\"fr xd xe xf xg b\"><em class=\"jd\">4.5<\/em><\/code><em class=\"jd\"><br \/><\/em><code class=\"fr xd xe xf xg b\"><em class=\"jd\">primavera 2<\/em><\/code><em class=\"jd\">\u00a0clasificaci\u00f3n:\u00a0<\/em><code class=\"fr xd xe xf xg b\"><em class=\"jd\">68<\/em><\/code><\/p><p id=\"3306\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><strong class=\"lm je\"><em class=\"jd\">Cafeter\u00eda B<\/em><\/strong><em class=\"jd\"><br \/><\/em><code class=\"fr xd xe xf xg b\"><em class=\"jd\">fuente 1<\/em><\/code><strong class=\"lm je\"><em class=\"jd\">\u00a0<\/em><\/strong><em class=\"jd\">clasificaci\u00f3n:\u00a0<\/em><code class=\"fr xd xe xf xg b\"><em class=\"jd\">3<\/em><\/code><em class=\"jd\"><br \/><\/em><code class=\"fr xd xe xf xg b\"><em class=\"jd\">primavera 2<\/em><\/code><strong class=\"lm je\"><em class=\"jd\">\u00a0<\/em><\/strong><em class=\"jd\">clasificaci\u00f3n:\u00a0<\/em><code class=\"fr xd xe xf xg b\"><em class=\"jd\">75<\/em><\/code><\/p><\/blockquote><p id=\"7eac\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Si tomamos ingenuamente la media aritm\u00e9tica de las puntuaciones brutas de cada cafeter\u00eda:<\/p><blockquote class=\"nd ne nf\"><p id=\"a745\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><strong class=\"lm je\"><em class=\"jd\">Cafeter\u00eda A =<\/em>\u00a0<\/strong><code class=\"fr xd xe xf xg b\">(4.5 + 68)\u00a0<em class=\"jd\">\u00f7<\/em>\u00a02<strong class=\"lm je\">\u00a0= 36.25<br \/><\/strong><\/code><strong class=\"lm je\"><em class=\"jd\">Cafeter\u00eda B =<\/em><\/strong>\u00a0<code class=\"fr xd xe xf xg b\">(3 + 75)\u00a0<em class=\"jd\">\u00f7<\/em>\u00a02 =<strong class=\"lm je\">\u00a039<\/strong><\/code><\/p><\/blockquote><p id=\"cbbd\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Concluir\u00edamos que Coffeeshop B fue el ganador.<\/p><p id=\"dc0f\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Si conoci\u00e9ramos un poco mejor los n\u00fameros, sabr\u00edamos que necesitamos normalizar nuestros valores en la misma escala antes de promediarlos con la media aritm\u00e9tica, para obtener un resultado preciso. As\u00ed que multiplicamos las calificaciones de la Fuente 1 por 20 para escalarlas de una escala de 5 estrellas a una escala de 100 estrellas de la Fuente 2:<\/p><blockquote class=\"nd ne nf\"><p id=\"c1cb\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><strong class=\"lm je\"><em class=\"jd\">Cafeter\u00eda A<\/em><br \/><\/strong><code class=\"fr xd xe xf xg b\">4.5 * 20 = 90<br \/>(90 + 68) \u00f7 2 =\u00a0<strong class=\"lm je\">79<\/strong><\/code><\/p><p id=\"3ef7\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><strong class=\"lm je\"><em class=\"jd\">Cafeter\u00eda B<br \/><\/em><\/strong><code class=\"fr xd xe xf xg b\">3 * 20 = 60<br \/>(60 + 75) \u00f7 2 =\u00a0<strong class=\"lm je\">67.5<\/strong><\/code><\/p><\/blockquote><p id=\"7108\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Entonces encontramos que Coffeeshop A es el verdadero ganador, a diferencia de la aplicaci\u00f3n ingenua de la media aritm\u00e9tica anterior.<\/p><p id=\"d995\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">La media geom\u00e9trica, sin embargo, nos permite llegar a la misma conclusi\u00f3n sin tener que preocuparnos por la escala o las unidades de medida:<\/p><blockquote class=\"nd ne nf\"><p id=\"37be\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><strong class=\"lm je\"><em class=\"jd\">Cafeter\u00eda A<\/em><\/strong><em class=\"jd\">\u00a0=\u00a0<\/em><code class=\"fr xd xe xf xg b\"><em class=\"jd\">ra\u00edz cuadrada de (4.5 * 68) =\u00a0<\/em><strong class=\"lm je\"><em class=\"jd\">17.5<br \/><\/em><\/strong><\/code><strong class=\"lm je\"><em class=\"jd\">Cafeter\u00eda B<\/em><\/strong><em class=\"jd\">\u00a0=\u00a0<\/em><code class=\"fr xd xe xf xg b\"><em class=\"jd\">ra\u00edz cuadrada de (3 * 75) =\u00a0<\/em><strong class=\"lm je\"><em class=\"jd\">15<\/em><\/strong><\/code><\/p><\/blockquote><p id=\"f12a\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">\u00a1Y ah\u00ed lo tienes!<\/p><p id=\"84ed\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">La media aritm\u00e9tica est\u00e1 dominada por n\u00fameros de mayor escala, lo que nos hace pensar que Coffeeshop B es la tienda mejor calificada. Esto se debe a que la media aritm\u00e9tica espera una relaci\u00f3n aditiva entre n\u00fameros e ignora escalas y proporciones. De ah\u00ed la necesidad de poner los n\u00fameros en la misma escala antes de aplicar la media aritm\u00e9tica.<\/p><p id=\"a004\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">La media geom\u00e9trica, por otro lado, puede manejar f\u00e1cilmente proporciones variables, debido a su naturaleza multiplicativa. Esta es una propiedad extremadamente \u00fatil, pero observe lo que estamos perdiendo: no tenemos ninguna escala interpretable. La media geom\u00e9trica no tiene unidades en tales situaciones.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-54d1d04 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"54d1d04\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6065fc3\" data-id=\"6065fc3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3bbc901 elementor-widget elementor-widget-heading\" data-id=\"3bbc901\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Et-la-moyenne-harmonique\"><\/span>\u00bfY la media arm\u00f3nica?<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ceac652 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ceac652\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9d22746\" data-id=\"9d22746\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-81ab43a elementor-widget elementor-widget-text-editor\" data-id=\"81ab43a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p id=\"68a1\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Mientras que la media aritm\u00e9tica requiere la suma y la media geom\u00e9trica utiliza la multiplicaci\u00f3n, la media arm\u00f3nica utiliza inversas.<\/p><p id=\"dc37\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Como recordar\u00e1s, el inverso de un n\u00famero n es simplemente 1\/n. (por ejemplo, el rec\u00edproco de 5 es 1\/5). Para n\u00fameros que ya son fracciones, esto significa que simplemente puedes &quot;voltear&quot; el numerador y el denominador: inverso de 4\/5 = 5\/4. Esto es cierto porque 1 dividido por una fracci\u00f3n da el inverso de esa fracci\u00f3n, p. 1 \u00f7 (4\/5) = 5\/4.<\/p><p id=\"5516\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">As\u00ed, la media arm\u00f3nica se puede describir con palabras: la inversa de la media aritm\u00e9tica de las inversas del conjunto de datos.<\/p><p id=\"91ab\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">En realidad son solo unos simples pasos:<\/p><blockquote class=\"nd ne nf\"><p id=\"77a8\" class=\"lk ll mg lm b ln my ke lp lq mz kh ls ng na lv lw nh nb lz ma ni nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\"><em class=\"jd\">1. Tome el rec\u00edproco de todos los n\u00fameros en el conjunto de datos<br \/>2. Encuentra la media aritm\u00e9tica de esos rec\u00edprocos<br \/>3. Toma el rec\u00edproco de ese n\u00famero<\/em><\/code><\/p><\/blockquote><p id=\"a4a3\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">En notaci\u00f3n matem\u00e1tica, esto se ve as\u00ed:<\/p><figure class=\"mi mj mk ml gz mm gn go paragraph-image\"><div class=\"gn go yc\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-15719 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_Q4U3tTSsNKPNp2weVxa93Q.png\" alt=\"\" width=\"700\" height=\"207\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_Q4U3tTSsNKPNp2weVxa93Q.png 700w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_Q4U3tTSsNKPNp2weVxa93Q-300x89.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_Q4U3tTSsNKPNp2weVxa93Q-18x5.png 18w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2022\/04\/1_Q4U3tTSsNKPNp2weVxa93Q-600x177.png 600w\" sizes=\"(max-width: 700px) 100vw, 700px\" \/><\/div><\/figure><p id=\"5c33\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">La media arm\u00f3nica de 1, 4 y 4 es 2.<\/p><p id=\"b0ac\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Nota: Debido a que 0 no tiene inversa (nada se puede multiplicar por 0 para = 1), la media arm\u00f3nica tampoco puede manejar conjuntos de datos que contienen 0, como la media geom\u00e9trica.<\/p><p id=\"ecf9\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">\u00bfPero para qu\u00e9 es eso?<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7807de7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7807de7\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-99bcc10\" data-id=\"99bcc10\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cc8a925 elementor-widget elementor-widget-heading\" data-id=\"cc8a925\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Exemple-de-moyenne-harmonique\"><\/span>Ejemplo de media arm\u00f3nica<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b943552 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b943552\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3a7340c\" data-id=\"3a7340c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-edab0ad elementor-widget elementor-widget-text-editor\" data-id=\"edab0ad\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p id=\"acfa\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Nuevamente, similar al uso de la media geom\u00e9trica como la contraparte de la media aritm\u00e9tica para relaciones multiplicativas o no lineales, la media arm\u00f3nica nos ayuda a encontrar relaciones de multiplicaci\u00f3n\/divisi\u00f3n entre fracciones sin preocuparnos por los denominadores comunes.<\/p><p id=\"c50e\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Como tal, la media arm\u00f3nica acepta naturalmente otra capa de multiplicaci\u00f3n\/divisi\u00f3n encima de la media geom\u00e9trica. Por lo tanto, es \u00fatil cuando se trata de conjuntos de datos de tasas o razones (es decir, fracciones) durante diferentes per\u00edodos de tiempo.<\/p><div class=\"o dz\"><div class=\"eo cf fc fd fe ff fg fh fi fj fk\"><article class=\"meteredContent\"><div class=\"l\"><div class=\"l\"><section><div class=\"iw ix iy iz ja\"><p id=\"070a\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">El ejemplo can\u00f3nico de usar medios arm\u00f3nicos en el mundo real implica viajar a trav\u00e9s del espacio f\u00edsico a diferentes velocidades, es decir, velocidades.<\/p><p>Considere un viaje de ida y vuelta al supermercado:<\/p><ul><li>En el camino, manejaste a 30 mph todo el camino<\/li><li>En el camino de regreso, el tr\u00e1fico era lento y manejaste a 16 km\/h todo el camino.<\/li><li>Tomaste la misma ruta y cubriste la misma cantidad de terreno (5 millas) en cada sentido.<\/li><\/ul><p>\u00bfCu\u00e1l fue su velocidad promedio durante toda la duraci\u00f3n de este viaje?<\/p><p>Una vez m\u00e1s, podr\u00edamos aplicar ingenuamente la media aritm\u00e9tica a 30 mph y 10 mph, y declarar con orgullo &quot;\u00a120 mph!&quot; \u00bb<\/p><p id=\"f81e\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Debido a que viaj\u00f3 m\u00e1s r\u00e1pido en una direcci\u00f3n, viaj\u00f3 8 km m\u00e1s r\u00e1pido y pas\u00f3 menos tiempo viajando a esa velocidad, por lo que su velocidad de viaje promedio durante toda la duraci\u00f3n de su viaje n No es el punto medio entre 30 mph y 10 mph, deber\u00eda ser m\u00e1s cerca de 10 mph porque ha pasado m\u00e1s tiempo conduciendo a esa velocidad.<\/p><p id=\"c765\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Para aplicar correctamente la media aritm\u00e9tica aqu\u00ed, necesitamos determinar el tiempo empleado en viajar en cada tarifa y luego ponderar nuestro c\u00e1lculo de la media aritm\u00e9tica de manera adecuada:<\/p><p id=\"ca80\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\"><strong class=\"lm je\">Viaje all\u00ed: (a 30 mph)<\/strong><code class=\"fr xd xe xf xg b\"><br \/>30 millas por 60 minutos = 1 milla cada 2 minutos = 1\/2 milla cada minuto<br \/>5 millas a 1\/2 milla por minuto = 5 \u00f7 1\/2 = 10 minutos<br \/><strong class=\"lm je\">Tiempo de &quot;viaje all\u00ed&quot;<\/strong>\u00a0=\u00a0<strong class=\"lm je\">10 minutos<\/strong><\/code><\/p><p id=\"8f97\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\"><strong class=\"lm je\">Viaje de regreso: (a 10 mph)<\/strong><code class=\"fr xd xe xf xg b\"><br \/>10 millas por 60 minutos = 1 milla cada 6 minutos = 1\/6 de milla cada minuto<br \/>5 millas a 1\/6 de milla por minuto = 5 \u00f7 1\/6 = 30 minutos<br \/><strong class=\"lm je\">Tiempo de &quot;viaje de regreso&quot;<\/strong>\u00a0=\u00a0<strong class=\"lm je\">30 minutos<\/strong><\/code><\/p><p id=\"4a69\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\"><strong class=\"lm je\">Tiempo total de viaje<\/strong>\u00a0= 10 + 30 =\u00a0<strong class=\"lm je\">40 minutos<\/strong><\/code><\/p><p id=\"e9f5\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\"><strong class=\"lm je\">\u201cViaje All\u00ed\u201d % del viaje total<\/strong>\u00a0= 10 \/ 40 minutos = .25 = 25%<br \/><strong class=\"lm je\">\u201cTrip Back\u201d % de viaje total<\/strong>\u00a0= 30 \/ 40 minutos = .75 = 75%<\/code><\/p><p id=\"589c\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\"><strong class=\"lm je\">Media aritm\u00e9tica ponderada<\/strong>\u00a0= (30 mph * 0,25) + (10 mph * 0,75) = 7,5 + 7,5 = 15<br \/><strong class=\"lm je\">Tasa promedio de viaje = 15 mph<\/strong><\/code><\/p><p id=\"43c2\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">As\u00ed que vemos que nuestra verdadera velocidad promedio de viaje fue de 15 mph, que es 5 mph (o 25 %) menos que nuestra afirmaci\u00f3n ingenua de 20 mph usando una media aritm\u00e9tica no ponderada.<\/p><p id=\"2116\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">Intentemos nuevamente usando la media arm\u00f3nica.<\/p><p id=\"5169\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\"><code class=\"fr xd xe xf xg b\"><strong class=\"lm je\">Significado armonico<\/strong>\u00a0de 30 y 10 = ...<br \/><strong class=\"lm je\">Significado aritmetico<\/strong>\u00a0de\u00a0<strong class=\"lm je\">rec\u00edprocos<\/strong>\u00a0= 1\/30 + 1\/10 = 4\/30 \u00f7 2 = 4\/60 = 1\/15<br \/><strong class=\"lm je\">Rec\u00edproco<\/strong>\u00a0de\u00a0<strong class=\"lm je\">significado aritmetico<\/strong>\u00a0= 1 \u00f7 1\/15 = 15\/1 =\u00a0<strong class=\"lm je\">15<\/strong><\/code><\/p><p id=\"561f\" class=\"pw-post-body-paragraph lk ll jd lm b ln my ke lp lq mz kh ls lt na lv lw lx nb lz ma mb nc md me mf iw gc\" data-selectable-paragraph=\"\">\u00a1Y ah\u00ed lo tienes!<\/p><\/div><\/section><\/div><\/div><\/article><\/div><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>An\u00e1lisis descriptivo P\u00e1gina de inicio de WIki Esta p\u00e1gina muestra varios ejemplos sobre los casos de uso de los diferentes medios, en particular, la media geom\u00e9trica y la media arm\u00f3nica. \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":15506,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-15712","page","type-page","status-publish","hentry"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/15712","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/comments?post=15712"}],"version-history":[{"count":3,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/15712\/revisions"}],"predecessor-version":[{"id":15722,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/15712\/revisions\/15722"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/pages\/15506"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/es\/wp-json\/wp\/v2\/media?parent=15712"}],"curies":[{"name":"gracias","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}