{"id":388,"date":"2023-08-01T08:06:03","date_gmt":"2023-08-01T08:06:03","guid":{"rendered":"https:\/\/statorials.org\/id\/teorema-batas-pusat-2\/"},"modified":"2023-08-01T08:06:03","modified_gmt":"2023-08-01T08:06:03","slug":"teorema-batas-pusat-2","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/teorema-batas-pusat-2\/","title":{"rendered":"Teorema limit pusat"},"content":{"rendered":"<p>Artikel ini menjelaskan apa itu teorema limit pusat (CLT) dan kegunaannya dalam statistik. Anda juga akan menemukan rumus teorema limit pusat dan contoh penerapannya yang diselesaikan langkah demi langkah. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-teorema-central-del-limite\"><\/span> Apa teorema limit pusat?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dalam statistik, <strong>teorema batas pusat<\/strong> , juga disebut <strong>teorema batas pusat<\/strong> , menyatakan bahwa <a href=\"https:\/\/statorials.org\/id\/distribusi-sampling-mean\/\">distribusi rata-rata sampel<\/a> mendekati distribusi normal seiring bertambahnya ukuran sampel, terlepas dari <a href=\"https:\/\/statorials.org\/id\/distribusi-probabilitas-1\/\">distribusi probabilitas<\/a> populasi.<\/p>\n<p> Artinya, teorema limit pusat menyatakan bahwa jika kita mengambil sampel dalam jumlah yang cukup besar, rata-rata sampel tersebut dapat diperkirakan berdistribusi normal.<\/p>\n<p> Selain itu, teorema limit pusat menyatakan bahwa mean sampel akan mendekati nilai mean populasi seiring dengan bertambahnya ukuran sampel. Hal ini memungkinkan kami memperkirakan parameter populasi statistik. Di bawah ini kita akan melihat bagaimana hal ini dilakukan. <\/p>\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\/theoreme-central-limite.png\" alt=\"teorema limit pusat, teorema limit pusat\" class=\"wp-image-8678\" width=\"315\" height=\"315\" srcset=\"\" sizes=\"\"><\/figure>\n<p> Secara umum, untuk menerapkan teorema limit pusat, jumlah sampel harus minimal 30 observasi, meskipun hal ini tergantung pada karakteristik variabel yang diteliti.<\/p>\n<p> Teorema limit pusat memiliki banyak penerapan, karena distribusi normal memungkinkan penghitungan statistik inferensial, seperti pengujian hipotesis atau interval kepercayaan. Misalnya, di bidang keuangan, teorema batas pusat digunakan untuk menganalisis pengembalian dan risiko suatu investasi. <\/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\/distribusi-normal\/\">Apa yang dimaksud dengan distribusi normal?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-teorema-central-del-limite\"><\/span> Contoh teorema limit pusat<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita melihat definisi teorema limit pusat, mari kita lihat contohnya untuk memahami maknanya sepenuhnya.<\/p>\n<p> Contoh teorema limit pusat adalah pelemparan sebuah dadu. Pelemparan dadu mengikuti <a href=\"https:\/\/statorials.org\/id\/distribusi-seragam-yang-diskrit\/\">distribusi seragam yang diskrit<\/a> , karena semua hasil mempunyai peluang yang sama. Namun distribusi jumlah beberapa hasil mendekati distribusi normal. <\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"380\" height=\"456\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-du-theoreme-central-limite.png\" alt=\"contoh teorema limit pusat\" class=\"wp-image-8681\" srcset=\"\" sizes=\"\"><\/figure>\n<p> Dengan demikian, semakin banyak lemparan maka semakin besar kemungkinan bentuk distribusi mean cenderung menyerupai grafik distribusi normal. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-teorema-central-del-limite\"><\/span> Rumus Teorema Limit Pusat<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Teorema limit pusat menyatakan bahwa jika suatu populasi mempunyai mean \u03bc dan simpangan baku \u03c3 dan kita mengambil jumlah sampel yang cukup besar (n\u226530), himpunan mean sampel dapat didekati dengan distribusi normal dengan mean \u03bc dan simpangan baku \u03c3 \/\u221an.<\/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-9bc00b8814e098df988d7c695c66506a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle N\\left(\\mu,\\frac{\\sigma}{\\sqrt{n}}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"90\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> <em>Selanjutnya<\/em> <sub>jika<\/sub> <em>X<\/em> <sub>1<\/sub> <sub>,<\/sub> maka berdistribusi normal ditentukan dengan rumus 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-7c518ada589db37029302048824df42a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Y=\\sum_{i=1}^n X_i \\sim N\\left(n\\cdot \\mu,\\sigma \\cdot \\sqrt{n}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"234\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicio-resuelto-del-teorema-central-del-limite\"><\/span> Latihan terpecahkan dari teorema limit pusat<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agar Anda dapat sepenuhnya mengasimilasi konsep tersebut, berikut adalah latihan teorema limit pusat yang telah diselesaikan.<\/p>\n<ul>\n<li> Sebuah perusahaan menjual suku cadang yang digunakan untuk menggantikan komponen mainan tertentu. Sebuah koin mempunyai berat rata-rata 300 gram dan simpangan baku 50 gram. Jika seorang pelanggan memesan 100 buah dalam jumlah banyak, berapa peluang berat rata-rata potongan dalam satu batch lebih besar dari 305 g? Dan berapa peluang terambilnya 100 buah beratnya lebih dari 31 kg?<\/li>\n<\/ul>\n<p> Karena ukuran batchnya besar (n=100), kita dapat menerapkan teorema limit pusat untuk menyelesaikan masalah tersebut.<\/p>\n<p> Jadi, dengan menggunakan rumus teorema limit pusat, distribusi mean sampel dapat diperkirakan berdistribusi normal dengan parameter 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-9bc00b8814e098df988d7c695c66506a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle N\\left(\\mu,\\frac{\\sigma}{\\sqrt{n}}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"90\" style=\"vertical-align: -17px;\"><\/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-c62f30e3319566c578be2b03a2d983a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_{\\overline{X}}=\\mu=300\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"109\" style=\"vertical-align: -6px;\"><\/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-3d9f3d2d9a4272dca9d9e34626ff8290_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_{\\overline{X}}=\\cfrac{\\sigma}{\\sqrt{n}}=\\cfrac{50}{\\sqrt{100}}=5\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"173\" 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-a2ccad42b29091909256610fdd711e39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle N\\left(300,5\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sekarang kita melakukan proses pengetikan sehingga kita dapat menemukan probabilitas yang diminta oleh latihan tersebut. Untuk melakukan ini, kita perlu mengurangi mean dari distribusi lalu membaginya dengan deviasi standar:<\/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-aabd7d1605e6518f17d8fc6199becc44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P\\left(\\overline{X}>305\\right)=P\\left(Z>\\frac{305-300}{5}\\right)=P\\left(Z>1\\right)&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;43&#8243; width=&#8221;381&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<p> Jadi, untuk mencari peluang bahwa berat rata-rata potongan dalam lot lebih besar dari 305 g, kita harus melihat nilai Z&gt;1 pada <a href=\"https:\/\/statorials.org\/id\/tabel-distribusi-normal\/\">tabel distribusi normal<\/a> :<\/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-05ad215d26ded143bc689eb37c00f30e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P\\left(\\overline{X}>305\\right)=P\\left(Z>1\\right)=0,1587&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;22&#8243; width=&#8221;276&#8243; style=&#8221;vertical-align: -7px;&#8221;><\/p>\n<\/p>\n<p> Di sisi lain, berkat teorema limit pusat kita dapat mengetahui bahwa kumpulan 100 koin dapat mendekati distribusi normal, karena semua koin mengikuti distribusi yang sama. Oleh karena itu, untuk menentukan probabilitas suatu kumpulan 100 koin memiliki berat lebih dari 31 kg, kita harus menerapkan rumus lain dari teorema limit pusat:<\/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-7c518ada589db37029302048824df42a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Y=\\sum_{i=1}^n X_i \\sim N\\left(n\\cdot \\mu,\\sigma \\cdot \\sqrt{n}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"234\" style=\"vertical-align: -21px;\"><\/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-22186501d443fa0104f80ab2210937ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Y\\sim N\\left(100\\cdot 300,50\\cdot \\sqrt{100}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"221\" style=\"vertical-align: -11px;\"><\/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-f2c36d2fd557394ea1f4f80d887d1625_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Y\\sim N\\left(30000,500\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>Jadi kita ulangi proses pengetikan, lalu cari probabilitas kedua yang ditanyakan soal kepada kita:<\/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-4e3dfdc2ecc330ef981fba7476b5e13e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P\\left(Y>31000\\right)=P\\left(Z>\\frac{31000-30000}{500}\\right)=P\\left(Z>2\\right)&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;43&#8243; width=&#8221;430&#8243; style=&#8221;vertical-align: -17px;&#8221;><\/p>\n<\/p>\n<p> Terakhir, kita dapat menentukan probabilitas suatu batch yang terdiri dari 100 buah akan memiliki berat lebih dari 31 kg menggunakan tabel distribusi normal: <\/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-01523dbe603d64f1a7ca3187d96b062c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P\\left(Y>31000\\right)=P\\left(Z>2\\right)=0,0228&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;19&#8243; width=&#8221;289&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/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\/hukum-bilangan-besar\/\">Hukum bilangan besar<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Artikel ini menjelaskan apa itu teorema limit pusat (CLT) dan kegunaannya dalam statistik. Anda juga akan menemukan rumus teorema limit pusat dan contoh penerapannya yang diselesaikan langkah demi langkah. Apa teorema limit pusat? Dalam statistik, teorema batas pusat , juga disebut teorema batas pusat , menyatakan bahwa distribusi rata-rata sampel mendekati distribusi normal seiring bertambahnya [&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 limit pusat<\/title>\n<meta name=\"description\" content=\"Di sini Anda akan menemukan apa itu teorema limit pusat (atau teorema limit pusat), kegunaannya, rumusnya, dan latihan penyelesaiannya.\" \/>\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-batas-pusat-2\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Teorema limit pusat\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan apa itu teorema limit pusat (atau teorema limit pusat), kegunaannya, rumusnya, dan latihan penyelesaiannya.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/teorema-batas-pusat-2\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-01T08:06:03+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/theoreme-central-limite.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=\"3 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/teorema-batas-pusat-2\/\",\"url\":\"https:\/\/statorials.org\/id\/teorema-batas-pusat-2\/\",\"name\":\"\u25b7 Teorema limit pusat\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-08-01T08:06:03+00:00\",\"dateModified\":\"2023-08-01T08:06:03+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Di sini Anda akan menemukan apa itu teorema limit pusat (atau teorema limit pusat), kegunaannya, rumusnya, dan latihan penyelesaiannya.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/teorema-batas-pusat-2\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/teorema-batas-pusat-2\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/teorema-batas-pusat-2\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Teorema limit pusat\"}]},{\"@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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