{"id":1243,"date":"2023-07-27T04:01:05","date_gmt":"2023-07-27T04:01:05","guid":{"rendered":"https:\/\/statorials.org\/ar\/%d8%a7%d9%84%d8%aa%d8%a8%d8%a7%d9%8a%d9%86-%d9%81%d9%8a-%d8%b5\/"},"modified":"2023-07-27T04:01:05","modified_gmt":"2023-07-27T04:01:05","slug":"%d8%a7%d9%84%d8%aa%d8%a8%d8%a7%d9%8a%d9%86-%d9%81%d9%8a-%d8%b5","status":"publish","type":"post","link":"https:\/\/statorials.org\/ar\/%d8%a7%d9%84%d8%aa%d8%a8%d8%a7%d9%8a%d9%86-%d9%81%d9%8a-%d8%b5\/","title":{"rendered":"\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u0639\u064a\u0646\u0629 \u0648\u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0633\u0643\u0627\u0646\u064a \u0641\u064a r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p style=\";text-align:right;direction:rtl\"><span style=\"color: #000000;\"><strong>\u0627\u0644\u062a\u0628\u0627\u064a\u0646<\/strong> \u0647\u0648 \u0648\u0633\u064a\u0644\u0629 \u0644\u0642\u064a\u0627\u0633 \u0645\u062f\u0649 \u062a\u0648\u0632\u064a\u0639 \u0642\u064a\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u062d\u0648\u0644 \u0627\u0644\u0645\u062a\u0648\u0633\u0637.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0635\u064a\u063a\u0629 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u062a\u0628\u0627\u064a\u0646 <a href=\"https:\/\/statorials.org\/ar\/\u0627\u0644\u0633\u0643\u0627\u0646-\u0645\u0642\u0627\u0628\u0644-\u0627\u0644\u0639\u064a\u0646\u0629\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0644\u0644\u0633\u0643\u0627\u0646<\/a> \u0647\u064a:<\/span><\/p>\n<p style=\"text-align: center;;text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u03c3 <sup>2<\/sup><\/strong> = \u03a3 (x <sub>i<\/sub> \u2013 \u03bc) <sup>2<\/sup> \/ N<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u062d\u064a\u062b \u03bc \u0647\u0648 \u0645\u062a\u0648\u0633\u0637 \u0639\u062f\u062f \u0627\u0644\u0633\u0643\u0627\u0646\u060c \u0648x <sub>i<\/sub> \u0647\u0648 \u0627\u0644\u0639\u0646\u0635\u0631 <sup>\u0627\u0644\u0623\u0648\u0644<\/sup> \u0645\u0646 \u0627\u0644\u0633\u0643\u0627\u0646\u060c \u0648N \u0647\u0648 \u062d\u062c\u0645 \u0627\u0644\u0633\u0643\u0627\u0646\u060c \u0648\u03a3 \u0645\u062c\u0631\u062f \u0631\u0645\u0632 \u062e\u064a\u0627\u0644\u064a \u064a\u0639\u0646\u064a &#8220;\u0627\u0644\u0645\u062c\u0645\u0648\u0639&#8221;.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0635\u064a\u063a\u0629 \u0625\u064a\u062c\u0627\u062f \u062a\u0628\u0627\u064a\u0646 <a href=\"https:\/\/statorials.org\/ar\/\u0645\u062a\u0648\u0633\u0637-\u0627\u0644\u0639\u064a\u0646\u0629-\u0645\u0642\u0627\u0631\u0646\u0629-\u0628\u0645\u062a\u0648\u0633\u0637-\u0627\u0644\u0633\u0643\u0627\u0646\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0627\u0644\u0639\u064a\u0646\u0629<\/a> \u0647\u064a:<\/span><\/p>\n<p style=\"text-align: center;;text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0642 <sup>2<\/sup><\/strong> = \u03a3 (\u0633 <sub>\u0637<\/sub> &#8211; <span style=\"text-decoration: overline;\">\u0633<\/span> ) <sup>2<\/sup> \/ (\u0646-1)<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u062d\u064a\u062b <span style=\"text-decoration: overline;\">x<\/span> \u0647\u0648 \u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u0639\u064a\u0646\u0629\u060c \u0648x <sub>i<\/sub> \u0647\u0648 \u0639\u0646\u0635\u0631 <sup>\u0627\u0644\u0639\u064a\u0646\u0629<\/sup> i \u0648n \u0647\u0648 \u062d\u062c\u0645 \u0627\u0644\u0639\u064a\u0646\u0629.<\/span><\/p>\n<h3 style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0645\u062b\u0627\u0644: \u062d\u0633\u0627\u0628 \u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0639\u064a\u0646\u0629 \u0648\u0627\u0644\u0633\u0643\u0627\u0646 \u0641\u064a R<\/strong><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u0646 \u0644\u062f\u064a\u0646\u0627 \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0641\u064a R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define dataset<\/span>\ndata &lt;- c(2, 4, 4, 7, 8, 12, 14, 15, 19, 22)\n<\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0645\u0643\u0646\u0646\u0627 \u062d\u0633\u0627\u0628 <strong>\u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0639\u064a\u0646\u0629<\/strong> \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 <strong>var()<\/strong> \u0641\u064a R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate sample variance<\/span>\nvar(data)\n\n[1] 46.01111\n<\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0648\u064a\u0645\u0643\u0646\u0646\u0627 \u062d\u0633\u0627\u0628 <strong>\u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0633\u0643\u0627\u0646\u064a<\/strong> \u0628\u0628\u0633\u0627\u0637\u0629 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0636\u0631\u0628 \u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0639\u064a\u0646\u0629 \u0628\u0640 (n-1)\/n \u0643\u0645\u0627 \u064a\u0644\u064a:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#determine length of data\n<span style=\"color: #000000;\">n &lt;- <span style=\"color: #3366ff;\">length<\/span> (data)<\/span>\n\n#calculate population variance<\/span>\nvar(data) * (n-1)\/n\n\n[1] 41.41\n<\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0644\u0627\u062d\u0638 \u0623\u0646 \u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0645\u062c\u062a\u0645\u0639 \u0633\u064a\u0643\u0648\u0646 \u062f\u0627\u0626\u0645\u064b\u0627 \u0623\u0642\u0644 \u0645\u0646 \u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0639\u064a\u0646\u0629.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0645\u0646 \u0627\u0644\u0646\u0627\u062d\u064a\u0629 \u0627\u0644\u0639\u0645\u0644\u064a\u0629\u060c \u0646\u0642\u0648\u0645 \u0639\u0627\u062f\u0629\u064b \u0628\u062d\u0633\u0627\u0628 \u062a\u0628\u0627\u064a\u0646\u0627\u062a \u0627\u0644\u0639\u064a\u0646\u0629 \u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0645\u0646 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u0644\u0623\u0646\u0647 \u0645\u0646 \u063a\u064a\u0631 \u0627\u0644\u0645\u0639\u062a\u0627\u062f \u062c\u0645\u0639 \u0628\u064a\u0627\u0646\u0627\u062a \u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0633\u0643\u0627\u0646\u064a\u0629 \u0628\u0623\u0643\u0645\u0644\u0647\u0627.<\/span><\/p>\n<h3 style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0645\u062b\u0627\u0644: \u062d\u0633\u0627\u0628 \u062a\u0628\u0627\u064a\u0646 \u0639\u064a\u0646\u0629 \u0645\u0646 \u0639\u062f\u0629 \u0623\u0639\u0645\u062f\u0629<\/strong><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u0646 \u0644\u062f\u064a\u0646\u0627 \u0625\u0637\u0627\u0631 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a \u0641\u064a R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create data frame\n<span style=\"color: #000000;\">data &lt;- data.frame(a=c(1, 3, 4, 4, 6, 7, 8, 12),\n                   b=c(2, 4, 4, 5, 5, 6, 7, 16),\n                   c=c(6, 6, 7, 8, 8, 9, 9, 12))\n\n<span style=\"color: #008080;\">#view data frame<\/span>\ndata\n\n   ABC\n1 1 2 6\n2 3 4 6\n3 4 4 7\n4 4 5 8\n5 6 5 8\n6 7 6 9\n7 8 7 9\n8 12 16 12<\/span><\/span><\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 <a href=\"https:\/\/statorials.org\/ar\/\u062f\u0644\u064a\u0644-\u0644\u062a\u0637\u0628\u064a\u0642-lapply-sapply-\u0648tapply-\u0641\u064a-r\/\" target=\"_blank\" rel=\"noopener noreferrer\">sapply()<\/a> \u0644\u062d\u0633\u0627\u0628 \u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0639\u064a\u0646\u0629 \u0644\u0643\u0644 \u0639\u0645\u0648\u062f \u0641\u064a \u0625\u0637\u0627\u0631 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find sample variance of each column\n<span style=\"color: #000000;\">sapply(data, var)\n\n        ABC\n11.696429 18.125000 3.839286<\/span>\n<\/span><\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0648\u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0643\u0648\u062f \u0627\u0644\u062a\u0627\u0644\u064a \u0644\u062d\u0633\u0627\u0628 \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641 \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a \u0644\u0643\u0644 \u0639\u0645\u0648\u062f\u060c \u0648\u0647\u0648 \u0628\u0628\u0633\u0627\u0637\u0629 \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a \u0644\u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0639\u064a\u0646\u0629:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find sample standard deviation of each column\n<span style=\"color: #000000;\">sapply(data, sd)\n\n       ABC\n3.420004 4.257347 1.959410<\/span><\/span><\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><em>\u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0645\u0632\u064a\u062f \u0645\u0646 \u062f\u0631\u0648\u0633 R \u0647\u0646\u0627 .<\/em><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0647\u0648 \u0648\u0633\u064a\u0644\u0629 \u0644\u0642\u064a\u0627\u0633 \u0645\u062f\u0649 \u062a\u0648\u0632\u064a\u0639 \u0642\u064a\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u062d\u0648\u0644 \u0627\u0644\u0645\u062a\u0648\u0633\u0637. \u0635\u064a\u063a\u0629 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0644\u0644\u0633\u0643\u0627\u0646 \u0647\u064a: \u03c3 2 = \u03a3 (x i \u2013 \u03bc) 2 \/ N \u062d\u064a\u062b \u03bc \u0647\u0648 \u0645\u062a\u0648\u0633\u0637 \u0639\u062f\u062f \u0627\u0644\u0633\u0643\u0627\u0646\u060c \u0648x i \u0647\u0648 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0623\u0648\u0644 \u0645\u0646 \u0627\u0644\u0633\u0643\u0627\u0646\u060c \u0648N \u0647\u0648 \u062d\u062c\u0645 \u0627\u0644\u0633\u0643\u0627\u0646\u060c \u0648\u03a3 \u0645\u062c\u0631\u062f \u0631\u0645\u0632 \u062e\u064a\u0627\u0644\u064a \u064a\u0639\u0646\u064a &#8220;\u0627\u0644\u0645\u062c\u0645\u0648\u0639&#8221;. \u0635\u064a\u063a\u0629 \u0625\u064a\u062c\u0627\u062f \u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0639\u064a\u0646\u0629 \u0647\u064a: \u0642 [&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>\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0639\u064a\u0646\u0629 \u0648\u0627\u0644\u0633\u0643\u0627\u0646 \u0641\u064a R<\/title>\n<meta name=\"description\" content=\"\u064a\u0634\u0631\u062d \u0647\u0630\u0627 \u0627\u0644\u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u064a \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0639\u064a\u0646\u0629 \u0648\u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0633\u0643\u0627\u0646 \u0641\u064a R\u060c \u0645\u0639 \u0639\u062f\u0629 \u0623\u0645\u062b\u0644\u0629.\" \/>\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\/ar\/\u0627\u0644\u062a\u0628\u0627\u064a\u0646-\u0641\u064a-\u0635\/\" \/>\n<meta property=\"og:locale\" content=\"az_AZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" 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