{"id":2256,"date":"2026-04-25T02:38:17","date_gmt":"2026-04-25T02:38:17","guid":{"rendered":"https:\/\/77.buffdemo.com\/index.php\/2026\/04\/25\/toan-12-cac-so-dac-trung-do-muc-do-phan-tan\/"},"modified":"2026-04-25T02:38:17","modified_gmt":"2026-04-25T02:38:17","slug":"toan-12-cac-so-dac-trung-do-muc-do-phan-tan","status":"publish","type":"post","link":"https:\/\/77.buffdemo.com\/index.php\/2026\/04\/25\/toan-12-cac-so-dac-trung-do-muc-do-phan-tan\/","title":{"rendered":"To\u00e1n 12 Ch\u01b0\u01a1ng 3: C\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng \u0111o m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n cho m\u1eabu s\u1ed1 gh\u00e9p nh\u00f3m"},"content":{"rendered":"<div class=\"entry-content single-page\">\n<p>Chia s\u1ebb t\u00e0i li\u1ec7u To\u00e1n 12 Ch\u01b0\u01a1ng 3: C\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng \u0111o m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n cho m\u1eabu s\u1ed1 gh\u00e9p nh\u00f3m c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi.<\/p>\n<div class=\"code-block code-block-2\" style=\"margin: 8px auto; text-align: center; display: block; clear: both;\">\n<div> <\/div>\n<\/div>\n<h2 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-67e60069c8de7c716b8fbba5bb57fd37\" id=\"h-n\u1ed9i-dung-tai-li\u1ec7u-ch\u01b0\u01a1ng-cac-s\u1ed1-d\u1eb7c-tr\u01b0ng-do-m\u1ee9c-d\u1ed9-phan-tan-cho-m\u1eabu-s\u1ed1-ghep-nhom\"><span class=\"ez-toc-section\" id=\"Noi_dung_tai_lieu_Chuong_cac_so_dac_trung_do_muc_do_phan_tan_cho_mau_so_ghep_nhom\"><\/span>N\u1ed9i dung t\u00e0i li\u1ec7u Ch\u01b0\u01a1ng c\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng \u0111o m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n cho m\u1eabu s\u1ed1 gh\u00e9p nh\u00f3m<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>B\u1ed9 t\u00e0i li\u1ec7u n\u00e0y bao g\u1ed3m\u00a0b\u00e0i gi\u1ea3ng, l\u1eddi gi\u1ea3i v\u00e0 \u0111\u1ec1 ki\u1ec3m tra\u00a0v\u1ec1\u00a0C\u00e1c S\u1ed1 \u0110\u1eb7c Tr\u01b0ng \u0110o M\u1ee9c \u0110\u1ed9 Ph\u00e2n T\u00e1n c\u1ee7a M\u1eabu S\u1ed1 Li\u1ec7u Gh\u00e9p Nh\u00f3m\u00a0trong m\u00f4n To\u00e1n l\u1edbp 12.<\/p>\n<p><strong>\u0110i\u1ec3m nh\u1ea5n quan tr\u1ecdng:<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li><strong>T\u00ednh x\u1ea5p x\u1ec9:<\/strong>\u00a0C\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m (<img loading=\"lazy\" decoding=\"async\" alt=\"R, \\Delta Q, S^2, S\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"19\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-a1bb6bdafa2365a73bdf5a47b01ce61b_l3.png\" style=\"vertical-align: -4px;\" title=\"Rendered by QuickLaTeX.com\" width=\"98\"\/>) l\u00e0 gi\u00e1 tr\u1ecb x\u1ea5p x\u1ec9 cho c\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng t\u01b0\u01a1ng \u1ee9ng c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u g\u1ed1c.<\/li>\n<li><strong>\u0110o l\u01b0\u1eddng Ph\u00e2n t\u00e1n v\u00e0 R\u1ee7i ro:<\/strong>\u00a0Ph\u01b0\u01a1ng sai v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u0111o m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n c\u1ee7a d\u1eef li\u1ec7u xung quanh s\u1ed1 trung b\u00ecnh. Trong l\u0129nh v\u1ef1c \u0111\u1ea7u t\u01b0 (c\u1ed5 phi\u1ebfu, kinh doanh), \u0111\u1ed9 l\u1ec7ch chu\u1ea9n c\u00e0ng l\u1edbn th\u01b0\u1eddng t\u01b0\u01a1ng \u1ee9ng v\u1edbi \u0111\u1ed9 r\u1ee7i ro cao h\u01a1n.<\/li>\n<li><strong>\u1ea2nh h\u01b0\u1edfng c\u1ee7a Gi\u00e1 tr\u1ecb Ngo\u1ea1i l\u1ec7:<\/strong>\u00a0Kho\u1ea3ng bi\u1ebfn thi\u00ean (<img loading=\"lazy\" decoding=\"async\" alt=\"\\text{R}\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-2f5226c99419dce3f74026b9386d55df_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"13\"\/>) b\u1ecb \u1ea3nh h\u01b0\u1edfng m\u1ea1nh b\u1edfi c\u00e1c gi\u00e1 tr\u1ecb ngo\u1ea1i l\u1ec7, trong khi Kho\u1ea3ng t\u1ee9 ph\u00e2n v\u1ecb (<img loading=\"lazy\" decoding=\"async\" alt=\"\\Delta Q\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"17\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-60a9f211cdaa5c154ef5ef98529605a4_l3.png\" style=\"vertical-align: -4px;\" title=\"Rendered by QuickLaTeX.com\" width=\"29\"\/>) \u00edt b\u1ecb \u1ea3nh h\u01b0\u1edfng h\u01a1n.<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\" id=\"h-cac-ch\u1ee7-d\u1ec1-ch\u01b0\u01a1ng-3\"><span class=\"ez-toc-section\" id=\"Cac_chu_de_chuong_3\"><\/span><strong>C\u00e1c ch\u1ee7 \u0111\u1ec1 ch\u01b0\u01a1ng 3<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<figure class=\"wp-block-table\">\n<table>\n<thead>\n<tr>\n<th>Ch\u1ee7 \u0111\u1ec1<\/th>\n<th>M\u00f4 t\u1ea3 t\u00f3m t\u1eaft<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Kho\u1ea3ng Bi\u1ebfn Thi\u00ean v\u00e0 Kho\u1ea3ng T\u1ee9 Ph\u00e2n V\u1ecb<\/td>\n<td>Cung c\u1ea5p \u0111\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c t\u00ednh (<img loading=\"lazy\" decoding=\"async\" alt=\"R\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-866592f6d913376ce9261673a52125c5_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"14\"\/>, <img loading=\"lazy\" decoding=\"async\" alt=\"\\Delta Q\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"17\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-60a9f211cdaa5c154ef5ef98529605a4_l3.png\" style=\"vertical-align: -4px;\" title=\"Rendered by QuickLaTeX.com\" width=\"29\"\/>, <img loading=\"lazy\" decoding=\"async\" alt=\"Q_i\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"16\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-b79ab5472f4195b7c710319a6c89551b_l3.png\" style=\"vertical-align: -4px;\" title=\"Rendered by QuickLaTeX.com\" width=\"19\"\/>), v\u00ed d\u1ee5 minh h\u1ecda v\u00e0 \u00fd ngh\u0129a c\u1ee7a kho\u1ea3ng bi\u1ebfn thi\u00ean v\u00e0 kho\u1ea3ng t\u1ee9 ph\u00e2n v\u1ecb cho m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m. C\u00e1c t\u00e0i li\u1ec7u c\u0169ng \u0111\u1ec1 c\u1eadp \u0111\u1ebfn c\u00e1ch x\u00e1c \u0111\u1ecbnh v\u00e0 x\u1eed l\u00fd gi\u00e1 tr\u1ecb ngo\u1ea1i l\u1ec7.<\/td>\n<\/tr>\n<tr>\n<td>Ph\u01b0\u01a1ng Sai v\u00e0 \u0110\u1ed9 L\u1ec7ch Chu\u1ea9n<\/td>\n<td>Tr\u00ecnh b\u00e0y c\u00f4ng th\u1ee9c t\u00ednh ph\u01b0\u01a1ng sai (<img loading=\"lazy\" decoding=\"async\" alt=\"S^2\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"15\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-439d98854f56dce4112fc135c5965379_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"19\"\/>) v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n (<img loading=\"lazy\" decoding=\"async\" alt=\"S\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-2e1f6e68534ba082130a4e98e0a442bf_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"12\"\/>) cho m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m, th\u00f4ng qua gi\u00e1 tr\u1ecb \u0111\u1ea1i di\u1ec7n v\u00e0 t\u1ea7n s\u1ed1 c\u1ee7a nh\u00f3m. C\u00e1c v\u00ed d\u1ee5 minh h\u1ecda c\u00e1ch t\u00ednh to\u00e1n v\u00e0 s\u1eed d\u1ee5ng \u0111\u1ed9 l\u1ec7ch chu\u1ea9n \u0111\u1ec3 so s\u00e1nh m\u1ee9c \u0111\u1ed9 \u0111\u1ed3ng \u0111\u1ec1u ho\u1eb7c r\u1ee7i ro (\u0111\u1ea7u t\u01b0, c\u1ed5 phi\u1ebfu).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<p class=\"has-text-align-left\"><strong>Xem tr\u01b0\u1edbc t\u00e0i li\u1ec7u:<\/strong><\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" alt=\"C\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng \u0111o m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n cho m\u1eabu s\u1ed1 gh\u00e9p nh\u00f3m\" class=\"wp-image-8446\" height=\"387\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/image-16.png\" width=\"1175\"\/><\/figure>\n<h3 class=\"wp-block-heading\" id=\"h-cac-d\u1ea1ng-bai-t\u1eadp-ch\u01b0\u01a1ng-cac-s\u1ed1-d\u1eb7c-tr\u01b0ng-do-m\u1ee9c-d\u1ed9-phan-tan\"><span class=\"ez-toc-section\" id=\"Cac_dang_bai_tap_chuong_cac_so_dac_trung_do_muc_do_phan_tan\"><\/span>C\u00e1c d\u1ea1ng b\u00e0i t\u1eadp ch\u01b0\u01a1ng c\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng \u0111o m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1. D\u1ea1ng B\u00e0i T\u1eadp T\u00ednh To\u00e1n Tr\u1ef1c Ti\u1ebfp<\/strong><\/p>\n<p>\u0110\u00e2y l\u00e0 d\u1ea1ng c\u01a1 b\u1ea3n nh\u1ea5t, y\u00eau c\u1ea7u h\u1ecdc sinh t\u00ednh to\u00e1n c\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng \u0111o m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n d\u1ef1a tr\u00ean b\u1ea3ng t\u1ea7n s\u1ed1 gh\u00e9p nh\u00f3m \u0111\u00e3 cho.<\/p>\n<ul class=\"wp-block-list\">\n<li><strong>T\u00ednh Kho\u1ea3ng Bi\u1ebfn Thi\u00ean (<img loading=\"lazy\" decoding=\"async\" alt=\"R\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-866592f6d913376ce9261673a52125c5_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"14\"\/>):<\/strong>\n<ul class=\"wp-block-list\">\n<li>S\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c <img loading=\"lazy\" decoding=\"async\" alt=\"R = u_{k+1} - u_1\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"17\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-3822b83eb44998f5dc7c757bf48a5892_l3.png\" style=\"vertical-align: -5px;\" title=\"Rendered by QuickLaTeX.com\" width=\"111\"\/> (hi\u1ec7u s\u1ed1 gi\u1eefa \u0111\u1ea7u m\u00fat ph\u1ea3i c\u1ee7a nh\u00f3m cu\u1ed1i c\u00f9ng v\u00e0 \u0111\u1ea7u m\u00fat tr\u00e1i c\u1ee7a nh\u00f3m \u0111\u1ea7u ti\u00ean).<\/li>\n<li><em>V\u00ed d\u1ee5:<\/em>\u00a0T\u00ednh <img loading=\"lazy\" decoding=\"async\" alt=\"R\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-866592f6d913376ce9261673a52125c5_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"14\"\/> cho m\u1eabu s\u1ed1 li\u1ec7u v\u1ec1 th\u1eddi gian t\u1ef1 h\u1ecdc hay l\u01b0\u01a1ng th\u00e1ng.<\/li>\n<\/ul>\n<\/li>\n<li><strong>T\u00ednh Kho\u1ea3ng T\u1ee9 Ph\u00e2n V\u1ecb (<img loading=\"lazy\" decoding=\"async\" alt=\"\\Delta Q\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"17\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-60a9f211cdaa5c154ef5ef98529605a4_l3.png\" style=\"vertical-align: -4px;\" title=\"Rendered by QuickLaTeX.com\" width=\"29\"\/>):<\/strong>\n<ul class=\"wp-block-list\">\n<li>Y\u00eau c\u1ea7u t\u00ednh T\u1ee9 ph\u00e2n v\u1ecb th\u1ee9 nh\u1ea5t (<img loading=\"lazy\" decoding=\"async\" alt=\"Q_1\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"16\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-634c3e2b211a507bef7de0f7ebe5f928_l3.png\" style=\"vertical-align: -4px;\" title=\"Rendered by QuickLaTeX.com\" width=\"20\"\/>) v\u00e0 T\u1ee9 ph\u00e2n v\u1ecb th\u1ee9 ba (<img loading=\"lazy\" decoding=\"async\" alt=\"Q_3\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"16\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-983c785ca9a46d4ac58ff0bcddf3a2ea_l3.png\" style=\"vertical-align: -4px;\" title=\"Rendered by QuickLaTeX.com\" width=\"21\"\/>) tr\u01b0\u1edbc, sau \u0111\u00f3 t\u00ednh <img loading=\"lazy\" decoding=\"async\" alt=\"\\Delta Q = Q_3 - Q_1\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"17\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-e1874f044e3464c1159b2d4b6c504dd2_l3.png\" style=\"vertical-align: -4px;\" title=\"Rendered by QuickLaTeX.com\" width=\"116\"\/>.<\/li>\n<li><em>V\u00ed d\u1ee5:<\/em>\u00a0T\u00ednh <img loading=\"lazy\" decoding=\"async\" alt=\"\\Delta Q\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"17\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-60a9f211cdaa5c154ef5ef98529605a4_l3.png\" style=\"vertical-align: -4px;\" title=\"Rendered by QuickLaTeX.com\" width=\"29\"\/> cho m\u1eabu s\u1ed1 li\u1ec7u v\u1ec1 \u0111i\u1ec7n l\u01b0\u1ee3ng pin ho\u1eb7c c\u00e2n n\u1eb7ng h\u1ecdc sinh.<\/li>\n<\/ul>\n<\/li>\n<li><strong>T\u00ednh Ph\u01b0\u01a1ng Sai (<img loading=\"lazy\" decoding=\"async\" alt=\"S^2\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"15\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-439d98854f56dce4112fc135c5965379_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"19\"\/>) v\u00e0 \u0110\u1ed9 L\u1ec7ch Chu\u1ea9n (<img loading=\"lazy\" decoding=\"async\" alt=\"S\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-2e1f6e68534ba082130a4e98e0a442bf_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"12\"\/>):<\/strong>\n<ul class=\"wp-block-list\">\n<li>Y\u00eau c\u1ea7u t\u00ednh S\u1ed1 trung b\u00ecnh (<img loading=\"lazy\" decoding=\"async\" alt=\"\\bar{x}\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"11\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-ad8ea828b63ab444c59bb98b88cb6dee_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"10\"\/>) tr\u01b0\u1edbc, sau \u0111\u00f3 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c ph\u01b0\u01a1ng sai v\u00e0 l\u1ea5y c\u0103n b\u1eadc hai \u0111\u1ec3 t\u00ecm \u0111\u1ed9 l\u1ec7ch chu\u1ea9n.<\/li>\n<li><em>V\u00ed d\u1ee5:<\/em>\u00a0T\u00ednh <img loading=\"lazy\" decoding=\"async\" alt=\"S^2\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"15\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-439d98854f56dce4112fc135c5965379_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"19\"\/> v\u00e0 <img loading=\"lazy\" decoding=\"async\" alt=\"S\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-2e1f6e68534ba082130a4e98e0a442bf_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"12\"\/> cho c\u00e2n n\u1eb7ng m\u00edt, th\u1eddi gian truy c\u1eadp internet, ho\u1eb7c n\u0103ng su\u1ea5t l\u00faa.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>2. D\u1ea1ng B\u00e0i T\u1eadp So S\u00e1nh v\u00e0 \u1ee8ng D\u1ee5ng<\/strong><\/p>\n<p>D\u1ea1ng b\u00e0i n\u00e0y t\u1eadp trung v\u00e0o vi\u1ec7c hi\u1ec3u \u00fd ngh\u0129a c\u1ee7a c\u00e1c ch\u1ec9 s\u1ed1 ph\u00e2n t\u00e1n \u0111\u1ec3 \u0111\u01b0a ra nh\u1eadn \u0111\u1ecbnh th\u1ef1c t\u1ebf.<\/p>\n<ul class=\"wp-block-list\">\n<li><strong>So S\u00e1nh \u0110\u1ed9 Ph\u00e2n T\u00e1n\/\u0110\u1ed9 \u0110\u1ed3ng \u0110\u1ec1u:<\/strong>\n<ul class=\"wp-block-list\">\n<li>S\u1eed d\u1ee5ng <img loading=\"lazy\" decoding=\"async\" alt=\"R\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-866592f6d913376ce9261673a52125c5_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"14\"\/> ho\u1eb7c <img loading=\"lazy\" decoding=\"async\" alt=\"S\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-2e1f6e68534ba082130a4e98e0a442bf_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"12\"\/> \u0111\u1ec3 so s\u00e1nh xem m\u1eabu s\u1ed1 li\u1ec7u n\u00e0o \u00edt ph\u00e2n t\u00e1n (\u0111\u1ed3ng \u0111\u1ec1u) h\u01a1n.<\/li>\n<li><em>V\u00ed d\u1ee5:<\/em>\u00a0So s\u00e1nh \u0111i\u1ec3m trung b\u00ecnh c\u1ee7a hai l\u1edbp h\u1ecdc (11A v\u00e0 11B) \u0111\u1ec3 xem l\u1edbp n\u00e0o c\u00f3 k\u1ebft qu\u1ea3 \u0111\u1ed3ng \u0111\u1ec1u h\u01a1n.<\/li>\n<li><em>V\u00ed d\u1ee5:<\/em>\u00a0So s\u00e1nh \u0111\u1ed9 ph\u00e2n t\u00e1n c\u1ee7a n\u1eeda gi\u1eefa (d\u1ef1a tr\u00ean <img loading=\"lazy\" decoding=\"async\" alt=\"\\Delta Q\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"17\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-60a9f211cdaa5c154ef5ef98529605a4_l3.png\" style=\"vertical-align: -4px;\" title=\"Rendered by QuickLaTeX.com\" width=\"29\"\/>) c\u1ee7a hai m\u1eabu s\u1ed1 li\u1ec7u.<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u1ee8ng D\u1ee5ng v\u00e0o \u0110\u1ed9 R\u1ee7i Ro:<\/strong>\n<ul class=\"wp-block-list\">\n<li>S\u1eed d\u1ee5ng Ph\u01b0\u01a1ng sai (<img loading=\"lazy\" decoding=\"async\" alt=\"S^2\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"15\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-439d98854f56dce4112fc135c5965379_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"19\"\/>) ho\u1eb7c \u0110\u1ed9 l\u1ec7ch chu\u1ea9n (<img loading=\"lazy\" decoding=\"async\" alt=\"S\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"12\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-2e1f6e68534ba082130a4e98e0a442bf_l3.png\" style=\"vertical-align: 0px;\" title=\"Rendered by QuickLaTeX.com\" width=\"12\"\/>) \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 \u0111\u1ed9 r\u1ee7i ro trong \u0111\u1ea7u t\u01b0 t\u00e0i ch\u00ednh (c\u1ed5 phi\u1ebfu, kinh doanh). Ch\u1ec9 s\u1ed1 c\u00e0ng l\u1edbn th\u00ec r\u1ee7i ro c\u00e0ng cao.<\/li>\n<li><em>V\u00ed d\u1ee5:<\/em>\u00a0So s\u00e1nh \u0111\u1ed9 r\u1ee7i ro c\u1ee7a hai ph\u01b0\u01a1ng \u00e1n \u0111\u1ea7u t\u01b0 A v\u00e0 B.<\/li>\n<\/ul>\n<\/li>\n<li><strong>T\u00ednh Sai S\u1ed1 T\u01b0\u01a1ng \u0110\u1ed1i:<\/strong>\n<ul class=\"wp-block-list\">\n<li>T\u00ednh sai s\u1ed1 t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a \u0111\u1ed9 l\u1ec7ch chu\u1ea9n c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m so v\u1edbi m\u1eabu s\u1ed1 li\u1ec7u g\u1ed1c.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>3. D\u1ea1ng B\u00e0i T\u1eadp L\u00fd Thuy\u1ebft v\u00e0 Kh\u00e1i Ni\u1ec7m<\/strong><\/p>\n<p>\u0110\u00e2y l\u00e0 d\u1ea1ng c\u00e2u h\u1ecfi tr\u1eafc nghi\u1ec7m ho\u1eb7c \u0111\u00fang\/sai, t\u1eadp trung v\u00e0o c\u00e1c kh\u00e1i ni\u1ec7m, \u00fd ngh\u0129a v\u00e0 c\u00f4ng th\u1ee9<\/p>\n<ul class=\"wp-block-list\">\n<li><strong>C\u00f4ng Th\u1ee9c:<\/strong>\u00a0Nh\u1eadn di\u1ec7n c\u00f4ng th\u1ee9c \u0111\u00fang c\u1ee7a s\u1ed1 trung b\u00ecnh, ph\u01b0\u01a1ng sai, \u0111\u1ed9 l\u1ec7ch chu\u1ea9n, v\u00e0 kho\u1ea3ng bi\u1ebfn thi\u00ean cho m\u1eabu s\u1ed1 li\u1ec7u gh\u00e9p nh\u00f3m.<\/li>\n<li><strong>\u00dd Ngh\u0129a:<\/strong>\u00a0X\u00e1c \u0111\u1ecbnh vai tr\u00f2 c\u1ee7a c\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng (v\u00ed d\u1ee5: Ph\u01b0\u01a1ng sai, \u0111\u1ed9 l\u1ec7ch chu\u1ea9n d\u00f9ng \u0111\u1ec3 \u0111o m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n; kho\u1ea3ng t\u1ee9 ph\u00e2n v\u1ecb \u0111o m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n c\u1ee7a n\u1eeda gi\u1eefa d\u1eef li\u1ec7u).<\/li>\n<li><strong>Nh\u1eadn \u0110\u1ecbnh \u0110\u00fang\/Sai:<\/strong>\u00a0\u0110\u00e1nh gi\u00e1 c\u00e1c m\u1ec7nh \u0111\u1ec1 v\u1ec1 m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c ch\u1ec9 s\u1ed1 (v\u00ed d\u1ee5: Ph\u01b0\u01a1ng sai c\u00e0ng l\u1edbn th\u00ec m\u1eabu s\u1ed1 li\u1ec7u c\u00e0ng ph\u00e2n t\u00e1n) ho\u1eb7c c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t (v\u00ed d\u1ee5: \u0110\u1ed9 l\u1ec7ch chu\u1ea9n c\u00f3 c\u00f9ng \u0111\u01a1n v\u1ecb v\u1edbi \u0111\u01a1n v\u1ecb c\u1ee7a m\u1eabu s\u1ed1 li\u1ec7u).<\/li>\n<li><strong>Gi\u00e1 tr\u1ecb Ngo\u1ea1i l\u1ec7:<\/strong>\u00a0Nh\u1eadn bi\u1ebft v\u00e0 x\u1eed l\u00fd c\u00e1c gi\u00e1 tr\u1ecb ngo\u1ea1i l\u1ec7 (d\u1ef1a tr\u00ean c\u00f4ng th\u1ee9c <img loading=\"lazy\" decoding=\"async\" alt=\"Q_3 + 1,5\\Delta Q\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"17\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-0887a01a0f977ef1b642b836dedbb3d3_l3.png\" style=\"vertical-align: -4px;\" title=\"Rendered by QuickLaTeX.com\" width=\"98\"\/> v\u00e0 <img loading=\"lazy\" decoding=\"async\" alt=\"Q_1 - 1,5\\Delta Q\" class=\"ql-img-inline-formula quicklatex-auto-format\" height=\"17\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/quicklatex-com-493c5c16631f28bf36145e26d49a0614_l3.png\" style=\"vertical-align: -4px;\" title=\"Rendered by QuickLaTeX.com\" width=\"98\"\/>).<\/li>\n<\/ul>\n<h2 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-0e7531f0dccc7e64a8ff26a6091e2b5c\" id=\"h-t\u1ea3i-tai-li\u1ec7u-toan-12-ch\u01b0\u01a1ng-3-cac-s\u1ed1-d\u1eb7c-tr\u01b0ng-do-m\u1ee9c-d\u1ed9-phan-tan-cho-m\u1eabu-s\u1ed1-ghep-nhom\"><span class=\"ez-toc-section\" id=\"Tai_tai_lieu_Toan_12_Chuong_3_Cac_so_dac_trung_do_muc_do_phan_tan_cho_mau_so_ghep_nhom\"><\/span>T\u1ea3i t\u00e0i li\u1ec7u To\u00e1n 12 Ch\u01b0\u01a1ng 3: C\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng \u0111o m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n cho m\u1eabu s\u1ed1 gh\u00e9p nh\u00f3m<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>C\u00e1c b\u1ea1n c\u00f3 th\u1ec3 t\u1ea3i t\u00e0i li\u1ec7u \u00f4n t\u1eadp mi\u1ec5n ph\u00ed \u1edf \u0111\u00e2y nh\u00e9<\/p>\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-white-color has-luminous-vivid-orange-background-color has-text-color has-background has-link-color has-text-align-center wp-element-button\" href=\"https:\/\/drive.google.com\/drive\/folders\/1AAYBrN7lepL5488hLbRz9U6aU5_7Z8Gr?usp=sharing\" rel=\"noreferrer noopener nofollow\" target=\"_blank\"><strong>T\u1ea2I T\u00c0I LI\u1ec6U (\u0110\u1ec0 + \u0110\u00c1P \u00c1N)<\/strong><\/a><\/div>\n<\/div>\n<p>Tham kh\u1ea3o: <strong><a href=\"https:\/\/tailieuonthi.org\/toan-12-chuong-2-vector-va-he-truc-toa-do\/\" rel=\"noreferrer noopener\" target=\"_blank\">To\u00e1n 12 Vector v\u00e0 h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 kh\u00f4ng gian<\/a><\/strong><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Chia s\u1ebb t\u00e0i li\u1ec7u To\u00e1n 12 Ch\u01b0\u01a1ng 3: C\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng \u0111o m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n cho m\u1eabu s\u1ed1 gh\u00e9p nh\u00f3m c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi. N\u1ed9i dung t\u00e0i li\u1ec7u Ch\u01b0\u01a1ng c\u00e1c s\u1ed1 \u0111\u1eb7c tr\u01b0ng \u0111o m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n cho m\u1eabu s\u1ed1 gh\u00e9p nh\u00f3m B\u1ed9 t\u00e0i li\u1ec7u n\u00e0y [&#8230;]\n","protected":false},"author":1,"featured_media":2240,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22,23,26],"tags":[],"class_list":["post-2256","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tai-lieu-thpt","category-tai-lieu-toan","category-toan-12"],"_links":{"self":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/2256","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/comments?post=2256"}],"version-history":[{"count":0,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/2256\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/2240"}],"wp:attachment":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=2256"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=2256"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=2256"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}