{"id":278,"date":"2023-08-03T05:34:09","date_gmt":"2023-08-03T05:34:09","guid":{"rendered":"https:\/\/statorials.org\/id\/distribusi-sampling-mean\/"},"modified":"2023-08-03T05:34:09","modified_gmt":"2023-08-03T05:34:09","slug":"distribusi-sampling-mean","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/distribusi-sampling-mean\/","title":{"rendered":"Distribusi pengambilan sampel mean"},"content":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi sampling mean dalam statistik. Anda juga akan menemukan rumus distribusi pengambilan sampel rata-rata dan latihan penyelesaian langkah demi langkah. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-muestral-de-la-media\"><\/span> Berapakah distribusi sampling meannya?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Distribusi rata-rata pengambilan sampel<\/strong> (atau <strong>distribusi rata-rata pengambilan sampel<\/strong> ) adalah distribusi yang dihasilkan dari penghitungan rata-rata pengambilan sampel dari setiap kemungkinan sampel dari suatu populasi. Artinya, himpunan mean <a href=\"https:\/\/statorials.org\/id\/rata-rata-sampel\/\">sampel<\/a> dari semua sampel yang mungkin dari suatu populasi membentuk distribusi sampling dari mean tersebut.<\/p>\n<p> Atau dengan kata lain, jika kita mempelajari semua sampel yang dapat diambil dari suatu populasi dan menghitung rata-rata masing-masing sampel, maka himpunan nilai yang dihitung tersebut membentuk distribusi sampling dari mean sampel.<\/p>\n<p> Dalam statistik, distribusi sampling dari mean digunakan untuk menghitung probabilitas mendekati nilai mean populasi ketika menganalisis sampel tunggal. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-muestral-de-la-media\"><\/span> Rumus distribusi sampling mean<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Diberikan populasi yang mengikuti <a href=\"https:\/\/statorials.org\/id\/distribusi-normal\/\">distribusi probabilitas normal<\/a> dengan mean<\/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-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> dan deviasi standar<\/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> dan ukuran sampel diekstraksi<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> , distribusi sampling mean juga akan ditentukan oleh distribusi normal yang memiliki ciri-ciri 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-44571aa7337b095ab9c9fa1f746e93a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\mu_{\\overline{x}}=\\mu \\qquad \\sigma_{\\overline{x}}=\\cfrac{\\sigma}{\\sqrt{n}}\\\\[4ex]\\displaystyle N_{\\overline{x}}\\left(\\mu, \\frac{\\sigma}{\\sqrt{n}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"159\" style=\"vertical-align: 0px;\"><\/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-8ed084decbdfb365889aae767cf63e81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_{\\overline{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"20\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah mean dari distribusi sampling dari mean dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9067e28d896c7e5278763081c6cc40d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_{\\overline{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"19\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah deviasi standarnya. Lebih-lebih lagi,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7d78e2a2f2fae99a53eb087263cbb478_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\sigma}{\\sqrt{n}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"26\" style=\"vertical-align: -16px;\"><\/p>\n<p> adalah kesalahan standar distribusi sampling.<\/p>\n<p> <strong>Catatan:<\/strong> Jika populasi tidak mengikuti distribusi normal tetapi ukuran sampelnya besar (n&gt;30), distribusi sampling mean juga dapat didekati dengan distribusi normal sebelumnya dengan teorema limit pusat.<\/p>\n<p> Oleh karena itu, karena distribusi sampling dari mean mengikuti distribusi normal, <strong>rumus untuk menghitung probabilitas apa pun yang terkait dengan mean sampel<\/strong> adalah:<\/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-ecd8bcb78b739c50d01b8bad563e5cb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\overline{x}-\\mu}{\\displaystyle\\frac{\\sigma}{\\sqrt{n}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"81\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Emas:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a39858a792fb4fe9a3173e004701f2a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah sarana sampel.<\/li>\n<li style=\"margin-bottom:5px\">\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> Ini adalah rata-rata populasi.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah simpangan baku populasi.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah ukuran sampel.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah variabel yang ditentukan oleh distribusi normal standar N(0,1). <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-la-distribucion-muestral-de-la-media\"><\/span> Contoh nyata distribusi sampling mean<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah melihat definisi distribusi sampling mean dan rumus terkaitnya, mari kita selesaikan sebuah contoh untuk memahami konsepnya dengan lebih baik.<\/p>\n<ul>\n<li> Berat badan mahasiswa mengikuti distribusi normal dengan rata-rata 68 kg dan simpangan baku 9 kg. Bertekad:\n<ol>\n<li> Berapa peluang rata-rata sampel acak yang terdiri dari 25 siswa memiliki berat badan kurang dari 66 kg?<\/li>\n<li> Jika diambil 300 sampel yang masing-masing berjumlah 25 siswa, berapakah rata-rata sampel yang nilainya kurang dari 66 kg?<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p> Pertama-tama, kita harus menghitung nilai statistik yang bersangkutan, untuk ini kita menerapkan rumus yang kita lihat di atas:<\/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-b132f95081cac0e4028d5e8148514671_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\overline{x}-\\mu}{\\displaystyle\\frac{\\sigma}{\\sqrt{n}}}=\\frac{66-68}{\\displaystyle\\frac{9}{\\sqrt{25}}}=-1,11\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"238\" style=\"vertical-align: -38px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, probabilitas yang kita cari adalah yang sesuai dengan nilai Z=-1,11 di ekor kiri distribusi normal standar, yang dapat dengan mudah diperoleh dari tabel probabilitas Z. Oleh karena itu kami menggunakan tabel Z untuk menentukan probabilitas bahwa masalah tersebut menanyakan kepada kami: <\/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-0db3a516f2be44a78c4f69958a9f0d51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[\\overline{x}\\leq 66]=P[Z\\leq -1,11] =0,1335\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"283\" style=\"vertical-align: -5px;\"><\/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\/tabel-distribusi-normal\/\">Tabel Z<\/a><\/div>\n<p> Sekarang kita mengetahui probabilitas bahwa rata-rata sampel acak kurang dari 66 kg, untuk mengetahui jumlah rata-rata sampel kurang dari 66 kg dengan mengambil 300 sampel yang sama, kita perlu mengalikan probabilitas yang dihitung dengan jumlah total sampel yang diambil:<\/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-7d2519cbeabf4b272e6f5a1463472768_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0,1335\\cdot 300 =40,05 \\approx 40\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"200\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, sekitar 40 sampel yang diekstraksi memiliki rata-rata kurang dari 66 kg.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi sampling mean dalam statistik. Anda juga akan menemukan rumus distribusi pengambilan sampel rata-rata dan latihan penyelesaian langkah demi langkah. Berapakah distribusi sampling meannya? Distribusi rata-rata pengambilan sampel (atau distribusi rata-rata pengambilan sampel ) adalah distribusi yang dihasilkan dari penghitungan rata-rata pengambilan sampel dari setiap kemungkinan sampel dari suatu populasi. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Distribusi pengambilan sampel mean<\/title>\n<meta name=\"description\" content=\"Di sini Anda akan menemukan apa itu distribusi sampling mean, rumusnya, dan contoh konkrit distribusi sampling mean.\" \/>\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\/distribusi-sampling-mean\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Distribusi pengambilan sampel mean\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan apa itu distribusi sampling mean, rumusnya, dan contoh konkrit distribusi sampling mean.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/distribusi-sampling-mean\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T05:34:09+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_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\/distribusi-sampling-mean\/\",\"url\":\"https:\/\/statorials.org\/id\/distribusi-sampling-mean\/\",\"name\":\"\u25b7 Distribusi pengambilan sampel mean\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-08-03T05:34:09+00:00\",\"dateModified\":\"2023-08-03T05:34:09+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Di sini Anda akan menemukan apa itu distribusi sampling mean, rumusnya, dan contoh konkrit distribusi sampling mean.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/distribusi-sampling-mean\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/distribusi-sampling-mean\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/distribusi-sampling-mean\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribusi pengambilan sampel mean\"}]},{\"@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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