{"id":132,"date":"2023-08-05T02:39:38","date_gmt":"2023-08-05T02:39:38","guid":{"rendered":"https:\/\/statorials.org\/pl\/praktyczna-zasada\/"},"modified":"2023-08-05T02:39:38","modified_gmt":"2023-08-05T02:39:38","slug":"praktyczna-zasada","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/praktyczna-zasada\/","title":{"rendered":"G\u0142\u00f3wna zasada"},"content":{"rendered":"<p>W tym artykule dowiesz si\u0119, jaka jest praktyczna zasada w statystyce i jaki jest jej wz\u00f3r. Dodatkowo b\u0119dziesz m\u00f3g\u0142 zobaczy\u0107 rozwi\u0105zane \u0107wiczenie krok po kroku na zasadzie praktycznej. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-regla-empirica\"><\/span> Jaka jest og\u00f3lna zasada?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> W statystyce praktyczna <strong>zasada<\/strong> , zwana tak\u017ce <strong>regu\u0142\u0105 68-95-99,7<\/strong> , to regu\u0142a okre\u015blaj\u0105ca procent warto\u015bci w rozk\u0142adzie normalnym mieszcz\u0105cych si\u0119 w granicach trzech odchyle\u0144 standardowych od \u015bredniej.<\/p>\n<p> Og\u00f3lna zasada m\u00f3wi wi\u0119c, \u017ce:<\/p>\n<ul>\n<li> 68% warto\u015bci mie\u015bci si\u0119 w granicach jednego odchylenia standardowego \u015bredniej.<\/li>\n<li> 95% warto\u015bci mie\u015bci si\u0119 w granicach dw\u00f3ch odchyle\u0144 standardowych od \u015bredniej.<\/li>\n<li> 99,7% warto\u015bci mie\u015bci si\u0119 w granicach trzech odchyle\u0144 standardowych od \u015bredniej. <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/regle-empirique.png\" alt=\"g\u0142\u00f3wna zasada\" class=\"wp-image-2764\" width=\"530\" height=\"435\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-regla-empirica\"><\/span> Zasada kciuka<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Praktyczn\u0105 zasad\u0119 mo\u017cna r\u00f3wnie\u017c wyrazi\u0107 za pomoc\u0105 nast\u0119puj\u0105cych wzor\u00f3w: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e92eaf9290bcca728ecc254cc4db66f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\mu-1\\sigma\\leq X \\leq \\mu+1\\sigma)\\approx 0,6827\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"271\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3e71dd42960bbc41b7e7422a76e2c09c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\mu-2\\sigma\\leq X \\leq \\mu+2\\sigma)\\approx 0,9545\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"270\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e746a83d35dd0de33d187c4b2c901e04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\mu-3\\sigma\\leq X \\leq \\mu+3\\sigma)\\approx 0,9973\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"271\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Z\u0142oto<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-996ff7036e644e89f8ac379fa58d0cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"><\/p>\n<p> jest obserwacj\u0105 zmiennej losowej o rozk\u0142adzie normalnym,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> jest \u015bredni\u0105 rozk\u0142adu i<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-eaaf379fee5e67946f3fedf5631047b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> jego odchylenie standardowe. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Zobacz:<\/strong> <a href=\"https:\/\/statorials.org\/pl\/srednia-arytmetyczna\/\">Jaka jest \u015brednia arytmetyczna?<\/a><br \/> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Zobacz:<\/strong> <a href=\"https:\/\/statorials.org\/pl\/odchylenie-standardowe-lub-odchylenie-standardowe\/\">Co to jest odchylenie standardowe?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-regla-empirica\"><\/span> Przyk\u0142adowa zasada<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Teraz, gdy znamy definicj\u0119 regu\u0142y empirycznej i jej wz\u00f3r, zobaczmy konkretny przyk\u0142ad, jak obliczy\u0107 reprezentatywne warto\u015bci regu\u0142y empirycznej rozk\u0142adu normalnego.<\/p>\n<ul>\n<li> Wiemy, \u017ce roczna liczba urodze\u0144 w danej miejscowo\u015bci ma rozk\u0142ad normalny ze \u015bredni\u0105 10 000 i odchyleniem standardowym 1000. Oblicz charakterystyczne przedzia\u0142y empirycznej regu\u0142y tego rozk\u0142adu normalnego.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d09b321949a08b77332ea928d62a8bff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu=10000\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"79\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0135bc054da6b9586f68fb0d8fa10274_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma=1000\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"70\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Jak wyja\u015bniono powy\u017cej, wzory na obliczanie odst\u0119p\u00f3w wed\u0142ug regu\u0142y kciuka s\u0105 nast\u0119puj\u0105ce:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e92eaf9290bcca728ecc254cc4db66f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\mu-1\\sigma\\leq X \\leq \\mu+1\\sigma)\\approx 0,6827\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"271\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3e71dd42960bbc41b7e7422a76e2c09c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\mu-2\\sigma\\leq X \\leq \\mu+2\\sigma)\\approx 0,9545\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"270\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e746a83d35dd0de33d187c4b2c901e04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\mu-3\\sigma\\leq X \\leq \\mu+3\\sigma)\\approx 0,9973\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"271\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>Dlatego podstawiamy dane \u0107wicze\u0144 do wzor\u00f3w: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-071728b8171e6298d5d87844d9a7c435_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(10000-1\\cdot 1000\\leq X \\leq 10000+1\\cdot 1000)\\approx 0,6827\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"414\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-cab8ec3bbd5f0a77239069d42c6d3a6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(10000-2\\cdot 1000\\leq X \\leq 10000+2\\cdot 1000)\\approx 0,9545\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"413\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5b65d82fd46ec1867ef7495209fa55b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(10000-3\\cdot 1000\\leq X \\leq 10000+3\\cdot 1000)\\approx 0,9973\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"414\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Wykonuj\u0105c obliczenia, uzyskane wyniki s\u0105 nast\u0119puj\u0105ce: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e6f922719937bb5efbf52c36cc66012d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(9000\\leq X \\leq 11000)\\approx 0,6827\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"247\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-55c2ae5f287da3e1f9b60aefcf4a792c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(8000\\leq X \\leq 12000)\\approx 0,9545\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"246\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b799f69b8991d29afbaf1ca6da4014ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(7000\\leq X \\leq 13000)\\approx 0,9973\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"247\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Zatem dochodzimy do wniosku, \u017ce istnieje prawdopodobie\u0144stwo 68,27%, \u017ce liczba urodze\u0144 mie\u015bci si\u0119 w przedziale [9000,11000], prawdopodobie\u0144stwo 95,45%, \u017ce jest pomi\u0119dzy [8000,12000] i ostatecznie prawdopodobie\u0144stwo 99,73% \u017ce jest pomi\u0119dzy [7000,13000]. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tabla-de-valores-de-la-regla-empirica\"><\/span> Tabela praktycznych warto\u015bci<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Opr\u00f3cz warto\u015bci 68, 95 i 99,7, za pomoc\u0105 odchylenia standardowego mo\u017cna znale\u017a\u0107 r\u00f3wnie\u017c inne warto\u015bci prawdopodobie\u0144stwa. Poni\u017cej znajduje si\u0119 tabela z prawdopodobie\u0144stwami rozk\u0142adu normalnego: <\/p>\n<figure class=\"wp-block-table is-style-stripes\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\"> Czysty<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\"> Prawdopodobie\u0144stwo<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u03bc \u00b1 0,5\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,382924922548026<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u00b5 \u00b1 1\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,682689492137086<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u03bc \u00b1 1,5\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,866385597462284<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u00b5 \u00b1 2\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,954499736103642<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u00b5 \u00b1 2,5\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,987580669348448<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u00b5 \u00b1 3\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,997300203936740<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u00b5\u00b13,5\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,999534741841929<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u00b5 \u00b1 4\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,999936657516334<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u03bc \u00b1 4,5\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,999993204653751<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u00b5 \u00b1 5\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,999999426696856<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u00b5\u00b15,5\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,999999962020875<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u00b5 \u00b1 6\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,999999998026825<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u00b5\u00b16,5\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,9999999999919680<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u00b5 \u00b1 7\u03c3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 0,999999999997440<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p> Wszystkie te warto\u015bci liczbowe w tabeli pochodz\u0105 ze skumulowanej funkcji prawdopodobie\u0144stwa rozk\u0142adu normalnego.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>W tym artykule dowiesz si\u0119, jaka jest praktyczna zasada w statystyce i jaki jest jej wz\u00f3r. Dodatkowo b\u0119dziesz m\u00f3g\u0142 zobaczy\u0107 rozwi\u0105zane \u0107wiczenie krok po kroku na zasadzie praktycznej. Jaka jest og\u00f3lna zasada? W statystyce praktyczna zasada , zwana tak\u017ce regu\u0142\u0105 68-95-99,7 , to regu\u0142a okre\u015blaj\u0105ca procent warto\u015bci w rozk\u0142adzie normalnym mieszcz\u0105cych si\u0119 w granicach trzech [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-132","post","type-post","status-publish","format-standard","hentry","category-prawdopodobienstwo"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Jaka jest og\u00f3lna zasada? 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