{"id":2154,"date":"2023-07-23T11:32:41","date_gmt":"2023-07-23T11:32:41","guid":{"rendered":"https:\/\/statorials.org\/id\/varians-dari-distribusi-probabilitas\/"},"modified":"2023-07-23T11:32:41","modified_gmt":"2023-07-23T11:32:41","slug":"varians-dari-distribusi-probabilitas","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/varians-dari-distribusi-probabilitas\/","title":{"rendered":"Cara menghitung varians dari distribusi probabilitas"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Distribusi probabilitas memberi tahu kita probabilitas suatu variabel acak mengambil nilai tertentu.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Misalnya, distribusi probabilitas berikut memberi tahu kita probabilitas bahwa tim sepak bola tertentu akan mencetak sejumlah gol dalam pertandingan tertentu:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14093 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyennedist1.png\" alt=\"\" width=\"261\" height=\"185\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">Untuk mencari <b>varians<\/b> suatu distribusi probabilitas, kita dapat menggunakan rumus berikut:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">\u03c3 <sup>2<\/sup> = \u03a3( <sub>xi<\/sub> -\u03bc) <sup>2<\/sup> * P( <sub>xi<\/sub> )<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">Emas:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>x <sub>i<\/sub> :<\/strong> Nilai <sup>ke-i<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03bc:<\/strong> Rata-rata distribusi<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>P(x <sub>i<\/sub> ) :<\/strong> Probabilitas nilai <sup>ke-i<\/sup><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Misalnya, pertimbangkan distribusi probabilitas kami untuk tim sepak bola:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14093 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyennedist1.png\" alt=\"\" width=\"261\" height=\"185\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">Jumlah rata-rata gol tim sepak bola akan dihitung sebagai berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bc = 0*0,18 + 1*0,34 + 2*0,35 + 3*0,11 + 4*0,02 = <strong>1,45<\/strong> gol.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Kami kemudian dapat menghitung variansnya sebagai berikut:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14122 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sddist1.png\" alt=\"Contoh Standar Deviasi Distribusi Probabilitas\" width=\"482\" height=\"195\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">Varians hanyalah jumlah dari nilai-nilai di kolom ketiga. Jadi, kami akan menghitungnya sebagai berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sup>\u03c32<\/sup> = 0,3785 + 0,0689 + 0,1059 + 0,2643 + 0,1301 = <strong>0,9475<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Contoh berikut menunjukkan cara menghitung varians distribusi probabilitas dalam beberapa skenario lainnya.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Contoh 1: Variasi kerusakan kendaraan<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Distribusi probabilitas berikut memberi tahu kita probabilitas bahwa suatu kendaraan akan mengalami sejumlah kegagalan baterai selama periode 10 tahun:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14097 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyennedist2.png\" alt=\"Contoh Mencari Rata-Rata Distribusi Probabilitas\" width=\"265\" height=\"160\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">Untuk mencari varians dari distribusi probabilitas ini, pertama-tama kita perlu menghitung jumlah rata-rata kegagalan yang diharapkan:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bc = 0*0,24 + 1*0,57 + 2*0,16 + 3*0,03 = <b>0,98<\/b> kegagalan.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Kami kemudian dapat menghitung variansnya sebagai berikut:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14123\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sddist2.png\" alt=\"Contoh penghitungan simpangan baku dan varians suatu distribusi probabilitas\" width=\"447\" height=\"152\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">Variansnya adalah jumlah nilai pada kolom ketiga. Jadi, kami akan menghitungnya sebagai berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sup>\u03c32<\/sup> = 0,2305 + 0,0002 + 0,1665 + 0,1224 = <strong>0,5196<\/strong><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Contoh 2: Variasi penjualan<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Distribusi probabilitas berikut memberi tahu kita probabilitas bahwa penjual tertentu akan menghasilkan sejumlah penjualan tertentu pada bulan mendatang:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14099 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyennedist4.png\" alt=\"\" width=\"257\" height=\"150\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">Untuk mencari varians dari distribusi probabilitas ini, pertama-tama kita perlu menghitung jumlah rata-rata penjualan yang diharapkan:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bc = 10*0,24 + 20*0,31 + 30*0,39 + 40*0,06 = <b>22,7<\/b> kotor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Kami kemudian dapat menghitung variansnya sebagai berikut:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14124 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sddist3.png\" alt=\"\" width=\"461\" height=\"154\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">Variansnya adalah jumlah nilai pada kolom ketiga. Jadi, kami akan menghitungnya sebagai berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sup>\u03c32<\/sup> = 38,7096 + 2,2599 + 20,7831 + 17,9574 = <strong>79,71<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Perhatikan bahwa kita juga dapat menggunakan kalkulator distribusi probabilitas untuk menghitung varians distribusi ini secara otomatis:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-19947 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/stdprob1.png\" alt=\"\" width=\"305\" height=\"517\" srcset=\"\" sizes=\"\"><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-19948 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/stdprob2.png\" alt=\"\" width=\"309\" height=\"186\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">Selisihnya adalah <strong>79,71<\/strong> . Ini sesuai dengan nilai yang kami hitung secara manual.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Distribusi probabilitas memberi tahu kita probabilitas suatu variabel acak mengambil nilai tertentu. Misalnya, distribusi probabilitas berikut memberi tahu kita probabilitas bahwa tim sepak bola tertentu akan mencetak sejumlah gol dalam pertandingan tertentu: Untuk mencari varians suatu distribusi probabilitas, kita dapat menggunakan rumus berikut: \u03c3 2 = \u03a3( xi -\u03bc) 2 * P( xi ) Emas: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Cara menghitung varians distribusi probabilitas - Statorial<\/title>\n<meta name=\"description\" content=\"Tutorial ini menjelaskan cara menghitung varians dari distribusi probabilitas, dengan sebuah contoh.\" \/>\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\/varians-dari-distribusi-probabilitas\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Cara menghitung varians distribusi probabilitas - Statorial\" \/>\n<meta property=\"og:description\" content=\"Tutorial ini menjelaskan cara menghitung varians dari distribusi probabilitas, dengan sebuah contoh.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/varians-dari-distribusi-probabilitas\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-23T11:32:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyennedist1.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=\"1 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/varians-dari-distribusi-probabilitas\/\",\"url\":\"https:\/\/statorials.org\/id\/varians-dari-distribusi-probabilitas\/\",\"name\":\"Cara menghitung varians distribusi probabilitas - Statorial\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-07-23T11:32:41+00:00\",\"dateModified\":\"2023-07-23T11:32:41+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Tutorial ini menjelaskan cara menghitung varians dari distribusi probabilitas, dengan sebuah contoh.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/varians-dari-distribusi-probabilitas\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/varians-dari-distribusi-probabilitas\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/varians-dari-distribusi-probabilitas\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Cara menghitung varians dari distribusi probabilitas\"}]},{\"@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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