{"id":136,"date":"2023-08-05T02:21:20","date_gmt":"2023-08-05T02:21:20","guid":{"rendered":"https:\/\/statorials.org\/id\/teorema-chebyshev\/"},"modified":"2023-08-05T02:21:20","modified_gmt":"2023-08-05T02:21:20","slug":"teorema-chebyshev","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/teorema-chebyshev\/","title":{"rendered":"Teorema chebyshev"},"content":{"rendered":"<p>Artikel ini menjelaskan apa itu teorema Chebyshev. Di sini Anda akan menemukan rumus teorema Chebyshev, latihan yang diselesaikan, dan, sebagai tambahan, kalkulator teorema Chebyshev online. Terakhir, ini menunjukkan perbedaan antara teorema Chebyshev dan aturan empiris. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-teorema-de-chebyshev\"><\/span> Apa teorema Chebyshev?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Teorema Chebyshev<\/strong> , juga dikenal sebagai <strong>pertidaksamaan Chebyshev<\/strong> , adalah aturan statistik yang digunakan untuk menghitung probabilitas suatu nilai variabel acak berada dalam jarak tertentu dari meannya.<\/p>\n<p> Dengan kata lain, dalam statistik, teorema Chebyshev digunakan untuk menentukan probabilitas suatu nilai berada dalam interval kepercayaan.<\/p>\n<p> Selain itu, teorema Chebyshev juga digunakan untuk membuktikan teorema statistik lainnya, seperti hukum bilangan besar.<\/p>\n<p> Meskipun teorema Chebyshev pertama kali dirumuskan oleh orang Prancis Ir\u00e9n\u00e9e-Jules Bienaym\u00e9, teorema ini dinamakan demikian karena berasal dari Pafnuty Chebushev dari Rusia pada tahun 1867.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-teorema-de-chebyshev\"><\/span> Rumus teorema Chebyshev<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Teorema Chebyshev mengatakan bahwa probabilitas suatu nilai sama <em>dengan k<\/em> standar deviasi dari mean lebih besar atau sama dengan satu dikurangi rasio satu dibagi <em>k<\/em> kuadrat.<\/p>\n<p> Oleh karena itu, <strong>rumus teorema Chebyshev<\/strong> adalah sebagai berikut:<\/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-f13ff7c0d76ea2442ecd978dbfc457a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(\\mu-k\\sigma\\leq X \\leq \\mu+k\\sigma)\\geq 1 -\\frac{1}{k^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"271\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Emas<\/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> adalah nilai variabel acak,<\/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> <a href=\"https:\/\/statorials.org\/id\/rata-rata-aritmatika\/\">mean aritmatika<\/a> dari variabel,<\/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> <a href=\"https:\/\/statorials.org\/id\/simpangan-baku-atau-simpangan-baku\/\">deviasi standarnya<\/a> dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> jumlah deviasi standar dari mean yang akan digunakan untuk menghitung probabilitas.<\/p>\n<p> Perlu diperhatikan bahwa rumus ini hanya dapat digunakan jika jumlah simpangan baku yang dilakukan penghitungan lebih besar dari 1, atau dengan kata lain jika <em>k<\/em> lebih besar dari 1.<\/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-76b1d6dbe5ee35b66ff33156e238ad73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;41&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<p> \ud83d\udc49 <u style=\"text-decoration-color:#FF8A05;\">Anda dapat menggunakan kalkulator Teorema Chebyshev online di bawah ini untuk menghitung probabilitas.<\/u><\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-teorema-de-chebyshev\"><\/span> Contoh teorema Chebyshev<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita melihat definisi teorema Chebyshev dan rumusnya, berikut adalah contoh penyelesaian teorema statistika untuk lebih memahami konsep tersebut.<\/p>\n<ul>\n<li> Jika nilai yang diperoleh dalam statistik mata kuliah suatu universitas ditentukan oleh distribusi dengan rata-rata 65 dan deviasi standar 10, berapa persentase siswa yang memperoleh nilai antara 50 dan 80?<\/li>\n<\/ul>\n<p> Untuk menyelesaikan masalah ini, kita perlu menerapkan rumus teorema Chebyshev. Namun kita harus menentukan terlebih dahulu berapa standar deviasi nilai 50 dan 80 dari mean variabel tersebut, untuk itu kita hanya perlu melakukan perhitungan sebagai berikut: <\/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-23a555d6493c0a0be742097fe319932d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{\\text{valor}-\\text{media}}{\\text{desviaci\\'on t\\'ipica}}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"165\" style=\"vertical-align: -16px;\"><\/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-edee4613c11e3eebd7e1158ad7f7b5c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{50-65}{10}=-1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"155\" style=\"vertical-align: -12px;\"><\/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-7668ffc75752b84a5fdfe4de807efe0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{80-65}{10}=1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"141\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, nilai 50 dan 80 masing-masing sesuai dengan 1,5 standar deviasi dari mean bawah dan atas. Oleh karena itu kami menggunakan rumus teorema Chebysheva dengan k=1,5: <\/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-6dede501857215fec033905b64a01431_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(\\mu-k\\sigma\\leq X \\leq \\mu+k\\sigma)\\leq 1 -\\frac{1}{k^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"271\" style=\"vertical-align: -12px;\"><\/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-ace95ab1310d82dc6a6275b123556c07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(\\mu-1,5\\sigma\\leq X \\leq \\mu+1,5\\sigma)\\leq 1 -\\frac{1}{1,5^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"319\" style=\"vertical-align: -16px;\"><\/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-aa011250591257ffebf651292398d016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(50\\leq X \\leq 80)\\leq 0,5556\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"203\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dengan demikian, setidaknya 55,56% siswa memperoleh nilai antara 50 dan 80. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-del-teorema-de-chebyshev\"><\/span> Kalkulator Teorema Chebyshev<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Masukkan jumlah simpangan baku antara nilai yang dimaksud dengan mean <em>(k)<\/em> , lalu klik \u201cHitung\u201d. Kalkulator kemudian akan mengembalikan probabilitas minimum dari interval kepercayaan.<\/p>\n<p> Anda harus memasukkan jumlah simpangan baku menggunakan titik sebagai pemisah desimal. <\/p>\n<form action=\"\" method=\"post\">\n<ul style=\"color:#1C2C92;\">\n<li style=\"margin-bottom:15px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f4c08f6419fa469da3aa1c832f5c6b2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k = \" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: 0px;\"><\/p>\n<p><input name=\"datos\" style=\"border:1.5px solid #1C2C92; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" placeholder=\"1.5\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el n\u00famero total de datos aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/span><\/li>\n<\/ul>\n<div style=\"text-align:center\"><input align=\"center\" style=\"font-size:105%; border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"Menghitung\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"el-teorema-de-chebyshev-y-la-regla-empirica\"><\/span> Teorema dan aturan praktis Chebyshev<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dua konsep yang berkaitan erat dalam statistik adalah teorema Chebyshev dan aturan empiris, karena keduanya digunakan untuk menghitung probabilitas interval kepercayaan.<\/p>\n<p> <strong>Perbedaan teorema Chebyshev dengan kaidah empiris<\/strong> adalah teorema Chebyshev dapat digunakan pada semua jenis distribusi, sedangkan kaidah empiris hanya berlaku untuk distribusi normal.<\/p>\n<p> Oleh karena itu, penggunaan teorema Chebyshev lebih luas, tetapi aturan empiris memberikan hasil yang lebih tepat untuk distribusi normal.<\/p>\n<p> Klik di sini untuk melihat aturan praktisnya: <\/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>Lihat:<\/strong> <a href=\"https:\/\/statorials.org\/id\/aturan-praktis\/\">aturan umum<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Artikel ini menjelaskan apa itu teorema Chebyshev. Di sini Anda akan menemukan rumus teorema Chebyshev, latihan yang diselesaikan, dan, sebagai tambahan, kalkulator teorema Chebyshev online. Terakhir, ini menunjukkan perbedaan antara teorema Chebyshev dan aturan empiris. Apa teorema Chebyshev? Teorema Chebyshev , juga dikenal sebagai pertidaksamaan Chebyshev , adalah aturan statistik yang digunakan untuk menghitung probabilitas [&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":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Teorema Chebyshev: rumus, contoh dan kalkulator<\/title>\n<meta name=\"description\" content=\"Di sini Anda akan menemukan teorema Chebyshev (atau pertidaksamaan Chebyshev), rumusnya, contoh konkret, dan kalkulator teorema Chebyshev.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/id\/teorema-chebyshev\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Teorema Chebyshev: rumus, contoh dan kalkulator\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan teorema Chebyshev (atau pertidaksamaan Chebyshev), rumusnya, contoh konkret, dan kalkulator teorema Chebyshev.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/teorema-chebyshev\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-05T02:21:20+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f13ff7c0d76ea2442ecd978dbfc457a4_l3.png\" \/>\n<meta name=\"author\" content=\"Benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/teorema-chebyshev\/\",\"url\":\"https:\/\/statorials.org\/id\/teorema-chebyshev\/\",\"name\":\"\u25b7 Teorema Chebyshev: rumus, contoh dan kalkulator\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-08-05T02:21:20+00:00\",\"dateModified\":\"2023-08-05T02:21:20+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Di sini Anda akan menemukan teorema Chebyshev (atau pertidaksamaan Chebyshev), rumusnya, contoh konkret, dan kalkulator teorema Chebyshev.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/teorema-chebyshev\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/teorema-chebyshev\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/teorema-chebyshev\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Teorema chebyshev\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/id\/#website\",\"url\":\"https:\/\/statorials.org\/id\/\",\"name\":\"Statorials\",\"description\":\"Panduan anda untuk kompetensi statistik!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\",\"name\":\"Benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin anderson\"},\"description\":\"Halo, saya Benjamin, pensiunan profesor statistika yang menjadi guru Statorial yang berdedikasi. 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