{"id":134,"date":"2023-08-05T02:39:38","date_gmt":"2023-08-05T02:39:38","guid":{"rendered":"https:\/\/statorials.org\/nl\/vuistregel\/"},"modified":"2023-08-05T02:39:38","modified_gmt":"2023-08-05T02:39:38","slug":"vuistregel","status":"publish","type":"post","link":"https:\/\/statorials.org\/nl\/vuistregel\/","title":{"rendered":"Algemene regel"},"content":{"rendered":"<p>In dit artikel ontdek je wat de vuistregel in de statistiek is en wat de formule ervan is. Bovendien kunt u een opgeloste stap-voor-stap-oefening op de vuistregel zien. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-regla-empirica\"><\/span> Wat is de vuistregel?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> In de statistiek is de <strong>vuistregel<\/strong> , ook wel <strong>de 68-95-99.7-regel<\/strong> genoemd, een regel die het percentage waarden in een normale verdeling definieert dat binnen drie standaarddeviaties van het gemiddelde valt.<\/p>\n<p> De algemene regel luidt dus:<\/p>\n<ul>\n<li> 68% van de waarden ligt binnen \u00e9\u00e9n standaardafwijking van het gemiddelde.<\/li>\n<li> 95% van de waarden ligt binnen twee standaarddeviaties van het gemiddelde.<\/li>\n<li> 99,7% van de waarden ligt binnen drie standaarddeviaties van het gemiddelde. <\/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=\"algemene regel\" 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> Vuistregelformule<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> De vuistregel kan ook worden uitgedrukt met de volgende formules: <\/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> Goud<\/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> is een observatie van een willekeurige variabele die wordt beheerst door een normale verdeling,<\/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> is het gemiddelde van de verdeling en<\/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> zijn standaarddeviatie. <\/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>Zie:<\/strong> <a href=\"https:\/\/statorials.org\/nl\/rekenkundig-gemiddelde\/\">Wat is het rekenkundig gemiddelde?<\/a><br \/> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Zie:<\/strong> <a href=\"https:\/\/statorials.org\/nl\/standaardafwijking-of-standaardafwijking\/\">Wat is standaarddeviatie?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-regla-empirica\"><\/span> Voorbeeld vuistregel<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Nu we de definitie van de empirische regel kennen en wat de formule ervan is, laten we een concreet voorbeeld bekijken van hoe we de representatieve waarden van de empirische regel van een normale verdeling kunnen berekenen.<\/p>\n<ul>\n<li> We weten dat het jaarlijkse aantal geboorten op een bepaalde plaats een normale verdeling volgt met een gemiddelde van 10.000 en een standaarddeviatie van 1.000. Bereken de karakteristieke intervallen van de empirische regel van deze normale verdeling.<\/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> Zoals hierboven uitgelegd, zijn de formules voor het berekenen van de vuistregelintervallen:<\/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>Daarom vervangen we de trainingsgegevens in de formules: <\/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> En door de berekeningen uit te voeren, zijn de verkregen resultaten: <\/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\"> We concluderen dus dat er een waarschijnlijkheid is van 68,27% dat het aantal geboorten in het interval [9000,11000] ligt, een waarschijnlijkheid van 95,45% dat het tussen [8000,12000] ligt en, ten slotte, een waarschijnlijkheid van 99,73%. dat het tussen [7000,13000] ligt. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tabla-de-valores-de-la-regla-empirica\"><\/span> Tabel met vuistregelwaarden<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Naast de waarden 68, 95 en 99,7 zijn er ook andere waarschijnlijkheidswaarden te vinden met behulp van de standaarddeviatie. Hieronder zie je een tabel met de kansen voor een normale verdeling: <\/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\"> Netjes<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\"> Waarschijnlijkheid<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> \u00b5 \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\"> \u00b5 \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\"> \u00b5 \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\"> 0,9999999999997440<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p> Al deze numerieke waarden in de tabel zijn afkomstig van de cumulatieve waarschijnlijkheidsfunctie van de normale verdeling.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In dit artikel ontdek je wat de vuistregel in de statistiek is en wat de formule ervan is. Bovendien kunt u een opgeloste stap-voor-stap-oefening op de vuistregel zien. Wat is de vuistregel? In de statistiek is de vuistregel , ook wel de 68-95-99.7-regel genoemd, een regel die het percentage waarden in een normale verdeling definieert [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-134","post","type-post","status-publish","format-standard","hentry","category-waarschijnlijkheid"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Wat is de vuistregel? 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