{"id":37,"date":"2026-06-07T00:49:39","date_gmt":"2026-06-07T00:49:39","guid":{"rendered":"https:\/\/blog.phantram.online\/trung-binh-cong-la-gi\/"},"modified":"2026-06-11T02:20:15","modified_gmt":"2026-06-11T02:20:15","slug":"trung-binh-cong-la-gi","status":"publish","type":"post","link":"https:\/\/1phantram.com\/blog\/trung-binh-cong-la-gi\/","title":{"rendered":"Trung B\u00ecnh C\u1ed9ng L\u00e0 G\u00ec? C\u00f4ng Th\u1ee9c, V\u00ed D\u1ee5 V\u00e0 C\u00e1ch T\u00ednh Nhanh"},"content":{"rendered":"<p><strong>Trung b\u00ecnh c\u1ed9ng<\/strong> (hay c\u00f2n g\u1ecdi l\u00e0 mean) l\u00e0 ph\u00e9p t\u00ednh to\u00e1n h\u1ecdc c\u01a1 b\u1ea3n nh\u1ea5t trong th\u1ed1ng k\u00ea, \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng h\u00e0ng ng\u00e0y t\u1eeb t\u00ednh \u0111i\u1ec3m h\u1ecdc sinh, t\u00ednh l\u01b0\u01a1ng trung b\u00ecnh, \u0111\u1ebfn ph\u00e2n t\u00edch d\u1eef li\u1ec7u doanh nghi\u1ec7p. Trung b\u00ecnh c\u1ed9ng c\u1ee7a m\u1ed9t t\u1eadp s\u1ed1 li\u1ec7u l\u00e0 t\u1ed5ng t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb chia cho s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed trong t\u1eadp \u0111\u00f3. \u0110\u00e2y l\u00e0 th\u01b0\u1edbc \u0111o xu h\u01b0\u1edbng trung t\u00e2m (measure of central tendency) quan tr\u1ecdng nh\u1ea5t v\u00e0 ph\u1ed5 bi\u1ebfn nh\u1ea5t trong <a href=\"https:\/\/1phantram.com\/blog\/thong-ke-co-ban\/\">th\u1ed1ng k\u00ea c\u01a1 b\u1ea3n<\/a>.<\/p>\n<h2>Trung B\u00ecnh C\u1ed9ng L\u00e0 G\u00ec? \u0110\u1ecbnh Ngh\u0129a Ch\u00ednh X\u00e1c<\/h2>\n<p>Trung b\u00ecnh c\u1ed9ng (Arithmetic Mean) l\u00e0 gi\u00e1 tr\u1ecb \u0111\u1ea1i di\u1ec7n cho t\u1eadp d\u1eef li\u1ec7u, \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00e1ch c\u1ed9ng t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb l\u1ea1i v\u00e0 chia cho s\u1ed1 l\u01b0\u1ee3ng gi\u00e1 tr\u1ecb \u0111\u00f3. Trong to\u00e1n h\u1ecdc v\u00e0 th\u1ed1ng k\u00ea, trung b\u00ecnh c\u1ed9ng c\u1ee7a m\u1eabu \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 <strong>x\u0304<\/strong> (x-bar), c\u00f2n trung b\u00ecnh c\u1ee7a t\u1ed5ng th\u1ec3 \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 <strong>\u03bc<\/strong> (mu).<\/p>\n<p>V\u00ed d\u1ee5 \u0111\u01a1n gi\u1ea3n: B\u1ea1n mua 3 quy\u1ec3n s\u00e1ch v\u1edbi gi\u00e1 50.000\u0111, 80.000\u0111 v\u00e0 110.000\u0111. Gi\u00e1 trung b\u00ecnh = (50.000 + 80.000 + 110.000) \/ 3 = 80.000\u0111. \u0110\u00e2y ch\u00ednh l\u00e0 trung b\u00ecnh c\u1ed9ng.<\/p>\n<h2>C\u00f4ng Th\u1ee9c T\u00ednh Trung B\u00ecnh C\u1ed9ng<\/h2>\n<h3>C\u00f4ng th\u1ee9c t\u1ed5ng qu\u00e1t l\u00e0 g\u00ec?<\/h3>\n<p>C\u00f4ng th\u1ee9c t\u00ednh trung b\u00ecnh c\u1ed9ng cho t\u1eadp d\u1eef li\u1ec7u g\u1ed3m n ph\u1ea7n t\u1eed:<\/p>\n<p style=\"background:#f5f5f5;padding:12px;font-family:monospace;font-size:16px;text-align:center;\">\n<strong>x\u0304 = (x\u2081 + x\u2082 + x\u2083 + &#8230; + x\u2099) \/ n = \u03a3x\u1d62 \/ n<\/strong>\n<\/p>\n<p>Trong \u0111\u00f3:<\/p>\n<ul>\n<li><strong>x\u0304<\/strong>: trung b\u00ecnh c\u1ed9ng c\u1ee7a m\u1eabu<\/li>\n<li><strong>x\u2081, x\u2082, &#8230;, x\u2099<\/strong>: c\u00e1c gi\u00e1 tr\u1ecb trong t\u1eadp d\u1eef li\u1ec7u<\/li>\n<li><strong>n<\/strong>: s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed<\/li>\n<li><strong>\u03a3<\/strong>: k\u00fd hi\u1ec7u t\u1ed5ng (sigma)<\/li>\n<\/ul>\n<h3>C\u00f4ng th\u1ee9c trung b\u00ecnh c\u1ed9ng c\u00f3 tr\u1ecdng s\u1ed1 l\u00e0 g\u00ec?<\/h3>\n<p>Khi c\u00e1c gi\u00e1 tr\u1ecb kh\u00f4ng c\u00f3 vai tr\u00f2 ngang nhau (v\u00ed d\u1ee5: m\u00f4n c\u00f3 s\u1ed1 t\u00edn ch\u1ec9 kh\u00e1c nhau), ta d\u00f9ng <strong>trung b\u00ecnh c\u00f3 tr\u1ecdng s\u1ed1<\/strong>:<\/p>\n<p style=\"background:#f5f5f5;padding:12px;font-family:monospace;font-size:16px;text-align:center;\">\n<strong>x\u0304w = (w\u2081x\u2081 + w\u2082x\u2082 + &#8230; + w\u2099x\u2099) \/ (w\u2081 + w\u2082 + &#8230; + w\u2099)<\/strong>\n<\/p>\n<p>Trong \u0111\u00f3 <strong>w\u1d62<\/strong> l\u00e0 tr\u1ecdng s\u1ed1 c\u1ee7a gi\u00e1 tr\u1ecb th\u1ee9 i.<\/p>\n<h2>V\u00ed D\u1ee5 T\u00ednh Trung B\u00ecnh C\u1ed9ng Th\u1ef1c T\u1ebf<\/h2>\n<h3>V\u00ed d\u1ee5 1: T\u00ednh \u0111i\u1ec3m trung b\u00ecnh h\u1ecdc k\u1ef3 c\u1ee7a h\u1ecdc sinh<\/h3>\n<p>B\u1ea3ng \u0111i\u1ec3m h\u1ecdc k\u1ef3 1 c\u1ee7a Nam:<\/p>\n<table border=\"1\" cellpadding=\"8\" cellspacing=\"0\" style=\"border-collapse:collapse;width:100%\">\n<thead>\n<tr style=\"background:#e8f4fd\">\n<th>M\u00f4n h\u1ecdc<\/th>\n<th>\u0110i\u1ec3m<\/th>\n<th>S\u1ed1 ti\u1ebft\/tu\u1ea7n<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>To\u00e1n<\/td>\n<td>8.5<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>V\u0103n<\/td>\n<td>7.0<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>Anh<\/td>\n<td>9.0<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td>L\u00fd<\/td>\n<td>8.0<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>H\u00f3a<\/td>\n<td>7.5<\/td>\n<td>2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Trung b\u00ecnh \u0111\u01a1n gi\u1ea3n (kh\u00f4ng tr\u1ecdng s\u1ed1):<\/strong><br \/>\nx\u0304 = (8.5 + 7.0 + 9.0 + 8.0 + 7.5) \/ 5 = 40 \/ 5 = <strong>8.0 \u0111i\u1ec3m<\/strong><\/p>\n<p><strong>Trung b\u00ecnh c\u00f3 tr\u1ecdng s\u1ed1 (theo s\u1ed1 ti\u1ebft):<\/strong><br \/>\nx\u0304w = (8.5\u00d74 + 7.0\u00d74 + 9.0\u00d73 + 8.0\u00d72 + 7.5\u00d72) \/ (4+4+3+2+2)<br \/>\n= (34 + 28 + 27 + 16 + 15) \/ 15 = 120 \/ 15 = <strong>8.0 \u0111i\u1ec3m<\/strong><\/p>\n<p>Trong h\u1ec7 th\u1ed1ng gi\u00e1o d\u1ee5c Vi\u1ec7t Nam, \u0111i\u1ec3m trung b\u00ecnh h\u1ecdc k\u1ef3 th\u01b0\u1eddng d\u00f9ng tr\u1ecdng s\u1ed1 theo s\u1ed1 ti\u1ebft c\u1ee7a t\u1eebng m\u00f4n.<\/p>\n<h3>V\u00ed d\u1ee5 2: T\u00ednh l\u01b0\u01a1ng trung b\u00ecnh nh\u00e2n vi\u00ean<\/h3>\n<p>Ph\u00f2ng k\u1ebf to\u00e1n c\u00f3 6 nh\u00e2n vi\u00ean v\u1edbi m\u1ee9c l\u01b0\u01a1ng (tri\u1ec7u \u0111\u1ed3ng): 12, 15, 13, 18, 14, 16<\/p>\n<p>Mean = (12 + 15 + 13 + 18 + 14 + 16) \/ 6 = 88 \/ 6 \u2248 <strong>14.67 tri\u1ec7u \u0111\u1ed3ng<\/strong><\/p>\n<p>\u0110\u00e2y l\u00e0 m\u1ee9c l\u01b0\u01a1ng \u0111\u1ea1i di\u1ec7n cho c\u1ea3 nh\u00f3m, h\u1eefu \u00edch khi so s\u00e1nh v\u1edbi ph\u00f2ng ban kh\u00e1c.<\/p>\n<h3>V\u00ed d\u1ee5 3: Nhi\u1ec7t \u0111\u1ed9 trung b\u00ecnh th\u00e1ng<\/h3>\n<p>Nhi\u1ec7t \u0111\u1ed9 cao nh\u1ea5t t\u1ea1i H\u00e0 N\u1ed9i trong 7 ng\u00e0y \u0111\u1ea7u th\u00e1ng 6 (\u00b0C): 33, 35, 34, 36, 32, 35, 34<\/p>\n<p>Mean = (33+35+34+36+32+35+34) \/ 7 = 239 \/ 7 \u2248 <strong>34.1\u00b0C<\/strong><\/p>\n<p>C\u00e1c tr\u1ea1m kh\u00ed t\u01b0\u1ee3ng d\u00f9ng trung b\u00ecnh c\u1ed9ng \u0111\u1ec3 t\u00ednh nhi\u1ec7t \u0111\u1ed9 trung b\u00ecnh th\u00e1ng, n\u0103m v\u00e0 theo d\u00f5i bi\u1ebfn \u0111\u1ed5i kh\u00ed h\u1eadu.<\/p>\n<h2>Khi N\u00e0o N\u00ean D\u00f9ng Trung B\u00ecnh C\u1ed9ng?<\/h2>\n<p>Trung b\u00ecnh c\u1ed9ng ph\u00f9 h\u1ee3p nh\u1ea5t khi d\u1eef li\u1ec7u c\u1ee7a b\u1ea1n th\u1ecfa m\u00e3n c\u00e1c \u0111i\u1ec1u ki\u1ec7n sau:<\/p>\n<ul>\n<li>\u2705 D\u1eef li\u1ec7u ph\u00e2n ph\u1ed1i \u0111\u1ed1i x\u1ee9ng ho\u1eb7c g\u1ea7n \u0111\u1ed1i x\u1ee9ng (ph\u00e2n ph\u1ed1i chu\u1ea9n)<\/li>\n<li>\u2705 Kh\u00f4ng c\u00f3 gi\u00e1 tr\u1ecb ngo\u1ea1i l\u1ec7 (outlier) c\u1ef1c \u0111oan<\/li>\n<li>\u2705 D\u1eef li\u1ec7u \u0111\u1ecbnh l\u01b0\u1ee3ng (kh\u00f4ng d\u00f9ng cho d\u1eef li\u1ec7u \u0111\u1ecbnh t\u00ednh)<\/li>\n<li>\u2705 Mu\u1ed1n t\u1ed5ng h\u1ee3p th\u00f4ng tin t\u1eeb to\u00e0n b\u1ed9 t\u1eadp d\u1eef li\u1ec7u<\/li>\n<\/ul>\n<h2>Khi N\u00e0o Kh\u00f4ng N\u00ean D\u00f9ng Trung B\u00ecnh C\u1ed9ng?<\/h2>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 nh\u1eefng tr\u01b0\u1eddng h\u1ee3p trung b\u00ecnh c\u1ed9ng cho k\u1ebft qu\u1ea3 g\u00e2y hi\u1ec3u l\u1ea7m:<\/p>\n<h3>Tr\u01b0\u1eddng h\u1ee3p c\u00f3 outlier<\/h3>\n<p>Gi\u1ea3 s\u1eed thu nh\u1eadp 5 ng\u01b0\u1eddi (tri\u1ec7u \u0111\u1ed3ng): 10, 12, 11, 13, 500<br \/>\nMean = (10+12+11+13+500)\/5 = 546\/5 = <strong>109.2 tri\u1ec7u<\/strong> \u2014 ho\u00e0n to\u00e0n kh\u00f4ng \u0111\u1ea1i di\u1ec7n!<\/p>\n<p>Trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y, <a href=\"https:\/\/1phantram.com\/blog\/trung-vi-median-la-gi\/\"><strong>trung v\u1ecb (median)<\/strong><\/a> = 12 tri\u1ec7u ph\u1ea3n \u00e1nh th\u1ef1c t\u1ebf ch\u00ednh x\u00e1c h\u01a1n nhi\u1ec1u.<\/p>\n<h3>Tr\u01b0\u1eddng h\u1ee3p d\u1eef li\u1ec7u ph\u00e2n ph\u1ed1i l\u1ec7ch m\u1ea1nh<\/h3>\n<p>Gi\u00e1 nh\u00e0 t\u1ea1i TP.HCM c\u00f3 ph\u00e2n ph\u1ed1i l\u1ec7ch ph\u1ea3i (skewed right): \u0111a s\u1ed1 nh\u00e0 c\u00f3 gi\u00e1 3-5 t\u1ef7, nh\u01b0ng m\u1ed9t s\u1ed1 bi\u1ec7t th\u1ef1 50-100 t\u1ef7 k\u00e9o mean l\u00ean r\u1ea5t cao. Median s\u1ebd l\u00e0 th\u01b0\u1edbc \u0111o t\u1ed1t h\u01a1n.<\/p>\n<h3>Tr\u01b0\u1eddng h\u1ee3p d\u1eef li\u1ec7u \u0111\u1ecbnh t\u00ednh<\/h3>\n<p>B\u1ea1n kh\u00f4ng th\u1ec3 t\u00ednh trung b\u00ecnh c\u1ed9ng c\u1ee7a m\u00e0u s\u1eafc ho\u1eb7c ng\u00e0nh ngh\u1ec1. V\u1edbi d\u1eef li\u1ec7u \u0111\u1ecbnh t\u00ednh, d\u00f9ng <a href=\"https:\/\/1phantram.com\/blog\/mode-yeu-vi-la-gi\/\"><strong>mode (y\u1ebfu v\u1ecb)<\/strong><\/a> thay th\u1ebf.<\/p>\n<h2>So S\u00e1nh Trung B\u00ecnh C\u1ed9ng V\u1edbi C\u00e1c \u0110\u1ea1i L\u01b0\u1ee3ng Kh\u00e1c<\/h2>\n<table border=\"1\" cellpadding=\"8\" cellspacing=\"0\" style=\"border-collapse:collapse;width:100%\">\n<thead>\n<tr style=\"background:#e8f4fd\">\n<th>Ti\u00eau ch\u00ed<\/th>\n<th>Trung b\u00ecnh (Mean)<\/th>\n<th>Trung v\u1ecb (Median)<\/th>\n<th>Y\u1ebfu v\u1ecb (Mode)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>C\u00e1ch t\u00ednh<\/td>\n<td>T\u1ed5ng \/ n<\/td>\n<td>Gi\u00e1 tr\u1ecb gi\u1eefa<\/td>\n<td>Gi\u00e1 tr\u1ecb l\u1eb7p nhi\u1ec1u nh\u1ea5t<\/td>\n<\/tr>\n<tr>\n<td>\u1ea2nh h\u01b0\u1edfng b\u1edfi outlier<\/td>\n<td>R\u1ea5t cao<\/td>\n<td>Th\u1ea5p<\/td>\n<td>Kh\u00f4ng b\u1ecb \u1ea3nh h\u01b0\u1edfng<\/td>\n<\/tr>\n<tr>\n<td>D\u00f9ng cho d\u1eef li\u1ec7u \u0111\u1ecbnh t\u00ednh<\/td>\n<td>Kh\u00f4ng<\/td>\n<td>Kh\u00f4ng<\/td>\n<td>C\u00f3<\/td>\n<\/tr>\n<tr>\n<td>D\u00f9ng to\u00e0n b\u1ed9 d\u1eef li\u1ec7u<\/td>\n<td>C\u00f3<\/td>\n<td>Kh\u00f4ng<\/td>\n<td>Kh\u00f4ng<\/td>\n<\/tr>\n<tr>\n<td>Ph\u00f9 h\u1ee3p khi<\/td>\n<td>Ph\u00e2n ph\u1ed1i \u0111\u1ec1u, kh\u00f4ng c\u00f3 outlier<\/td>\n<td>C\u00f3 outlier, ph\u00e2n ph\u1ed1i l\u1ec7ch<\/td>\n<td>D\u1eef li\u1ec7u ph\u00e2n lo\u1ea1i<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>T\u00ednh Trung B\u00ecnh C\u1ed9ng Trong Excel V\u00e0 Google Sheets<\/h2>\n<p>Trong Excel v\u00e0 Google Sheets, b\u1ea1n d\u00f9ng h\u00e0m <strong>AVERAGE<\/strong>:<\/p>\n<ul>\n<li><code>=AVERAGE(A1:A10)<\/code> \u2014 t\u00ednh trung b\u00ecnh t\u1eeb \u00f4 A1 \u0111\u1ebfn A10<\/li>\n<li><code>=AVERAGE(5, 8, 12, 7)<\/code> \u2014 t\u00ednh trung b\u00ecnh tr\u1ef1c ti\u1ebfp<\/li>\n<li><code>=AVERAGEIF(B1:B10,\"&gt;0\")<\/code> \u2014 trung b\u00ecnh c\u00f3 \u0111i\u1ec1u ki\u1ec7n<\/li>\n<li><code>=AVERAGEIFS(...)<\/code> \u2014 trung b\u00ecnh v\u1edbi nhi\u1ec1u \u0111i\u1ec1u ki\u1ec7n<\/li>\n<\/ul>\n<p>V\u1edbi trung b\u00ecnh c\u00f3 tr\u1ecdng s\u1ed1, d\u00f9ng h\u00e0m SUMPRODUCT:<br \/>\n<code>=SUMPRODUCT(A1:A5, B1:B5)\/SUM(B1:B5)<\/code><br \/>\n(A1:A5 l\u00e0 gi\u00e1 tr\u1ecb, B1:B5 l\u00e0 tr\u1ecdng s\u1ed1)<\/p>\n<h2>Trung B\u00ecnh C\u1ed9ng V\u00e0 T\u1ec9 L\u1ec7 Ph\u1ea7n Tr\u0103m<\/h2>\n<p>Trung b\u00ecnh c\u1ed9ng th\u01b0\u1eddng \u0111\u01b0\u1ee3c k\u1ebft h\u1ee3p v\u1edbi ph\u00e9p t\u00ednh ph\u1ea7n tr\u0103m trong ph\u00e2n t\u00edch d\u1eef li\u1ec7u. V\u00ed d\u1ee5:<\/p>\n<ul>\n<li>\u0110i\u1ec3m trung b\u00ecnh t\u0103ng t\u1eeb 7.0 l\u00ean 7.5 \u2192 t\u0103ng <strong>7.14%<\/strong><\/li>\n<li>L\u01b0\u01a1ng trung b\u00ecnh ng\u00e0nh IT = 25 tri\u1ec7u, cao h\u01a1n b\u00ecnh qu\u00e2n qu\u1ed1c gia 15 tri\u1ec7u \u2192 cao h\u01a1n <strong>66.7%<\/strong><\/li>\n<\/ul>\n<p>\u0110\u1ec3 t\u00ednh nhanh c\u00e1c t\u1ec9 l\u1ec7 ph\u1ea7n tr\u0103m n\u00e0y, h\u00e3y <a href=\"https:\/\/1phantram.com\/blog\/tinh-phan-tram\/\">s\u1eed d\u1ee5ng c\u00f4ng c\u1ee5 t\u00ednh ph\u1ea7n tr\u0103m<\/a> t\u1ea1i 1phantram.com \u2014 ti\u1ec7n l\u1ee3i v\u00e0 ch\u00ednh x\u00e1c.<\/p>\n<h2>Nh\u1eefng L\u01b0u \u00dd Quan Tr\u1ecdng Khi T\u00ednh Trung B\u00ecnh C\u1ed9ng<\/h2>\n<ol>\n<li><strong>Ki\u1ec3m tra outlier tr\u01b0\u1edbc:<\/strong> D\u00f9ng bi\u1ec3u \u0111\u1ed3 box plot ho\u1eb7c nh\u00ecn v\u00e0o min\/max \u0111\u1ec3 ph\u00e1t hi\u1ec7n gi\u00e1 tr\u1ecb b\u1ea5t th\u01b0\u1eddng.<\/li>\n<li><strong>Xem x\u00e9t ph\u00e2n ph\u1ed1i d\u1eef li\u1ec7u:<\/strong> N\u1ebfu d\u1eef li\u1ec7u l\u1ec7ch nhi\u1ec1u, mean s\u1ebd b\u1ecb k\u00e9o v\u1ec1 ph\u00eda \u0111u\u00f4i.<\/li>\n<li><strong>Ghi r\u00f5 c\u1ee1 m\u1eabu:<\/strong> Trung b\u00ecnh c\u1ee7a 5 ng\u01b0\u1eddi v\u00e0 500 ng\u01b0\u1eddi c\u00f3 \u0111\u1ed9 tin c\u1eady r\u1ea5t kh\u00e1c nhau.<\/li>\n<li><strong>Kh\u00f4ng nh\u1ea7m trung b\u00ecnh c\u1ed9ng v\u1edbi trung b\u00ecnh nh\u00e2n:<\/strong> Trung b\u00ecnh nh\u00e2n (geometric mean) d\u00f9ng cho t\u1ed1c \u0111\u1ed9 t\u0103ng tr\u01b0\u1edfng, kh\u00f4ng ph\u1ea3i t\u1ed5ng gi\u00e1 tr\u1ecb.<\/li>\n<\/ol>\n<h2>C\u00e2u H\u1ecfi Th\u01b0\u1eddng G\u1eb7p (FAQ)<\/h2>\n<h3>Trung b\u00ecnh c\u1ed9ng v\u00e0 trung b\u00ecnh s\u1ed1 h\u1ecdc c\u00f3 kh\u00e1c nhau kh\u00f4ng?<\/h3>\n<p>Kh\u00f4ng. Trung b\u00ecnh c\u1ed9ng v\u00e0 trung b\u00ecnh s\u1ed1 h\u1ecdc (arithmetic mean) l\u00e0 c\u00f9ng m\u1ed9t kh\u00e1i ni\u1ec7m \u2014 t\u1ed5ng c\u00e1c gi\u00e1 tr\u1ecb chia cho s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed. Kh\u00e1i ni\u1ec7m &#8220;trung b\u00ecnh&#8221; trong \u0111\u1eddi s\u1ed1ng h\u00e0ng ng\u00e0y h\u1ea7u h\u1ebft \u0111\u1ec1 c\u1eadp \u0111\u1ebfn trung b\u00ecnh c\u1ed9ng.<\/p>\n<h3>Khi n\u00e0o d\u00f9ng trung b\u00ecnh c\u1ed9ng thay v\u00ec trung v\u1ecb?<\/h3>\n<p>D\u00f9ng trung b\u00ecnh c\u1ed9ng khi d\u1eef li\u1ec7u ph\u00e2n ph\u1ed1i \u0111\u1ec1u v\u00e0 kh\u00f4ng c\u00f3 outlier. D\u00f9ng <a href=\"https:\/\/1phantram.com\/blog\/trung-vi-median-la-gi\/\">trung v\u1ecb<\/a> khi d\u1eef li\u1ec7u c\u00f3 gi\u00e1 tr\u1ecb c\u1ef1c \u0111oan ho\u1eb7c ph\u00e2n ph\u1ed1i l\u1ec7ch \u2014 v\u00ed d\u1ee5 nh\u01b0 thu nh\u1eadp, gi\u00e1 nh\u00e0, th\u1eddi gian x\u1eed l\u00fd.<\/p>\n<h3>Trung b\u00ecnh c\u1ed9ng \u00e2m c\u00f3 \u00fd ngh\u0129a g\u00ec kh\u00f4ng?<\/h3>\n<p>C\u00f3. Trung b\u00ecnh c\u1ed9ng \u00e2m ho\u00e0n to\u00e0n h\u1ee3p l\u1ec7 v\u00e0 c\u00f3 \u00fd ngh\u0129a. V\u00ed d\u1ee5: nhi\u1ec7t \u0111\u1ed9 trung b\u00ecnh th\u00e1ng 1 \u1edf Siberia l\u00e0 \u00e2m, ho\u1eb7c l\u1ee3i nhu\u1eadn trung b\u00ecnh th\u00e1ng c\u1ee7a m\u1ed9t c\u00f4ng ty thua l\u1ed7 l\u00e0 \u00e2m. Gi\u00e1 tr\u1ecb \u00e2m cho bi\u1ebft &#8220;xu h\u01b0\u1edbng trung t\u00e2m&#8221; c\u1ee7a t\u1eadp s\u1ed1 li\u1ec7u n\u1eb1m d\u01b0\u1edbi 0.<\/p>\n<h3>C\u00f3 th\u1ec3 t\u00ednh trung b\u00ecnh c\u1ed9ng c\u1ee7a ph\u1ea7n tr\u0103m kh\u00f4ng?<\/h3>\n<p>\u0110\u01b0\u1ee3c, nh\u01b0ng ph\u1ea3i c\u1ea9n th\u1eadn. N\u1ebfu ph\u1ea7n tr\u0103m \u0111\u1ea1i di\u1ec7n cho c\u00e1c nh\u00f3m c\u00f3 k\u00edch th\u01b0\u1edbc kh\u00e1c nhau, b\u1ea1n c\u1ea7n d\u00f9ng trung b\u00ecnh c\u00f3 tr\u1ecdng s\u1ed1 thay v\u00ec trung b\u00ecnh \u0111\u01a1n gi\u1ea3n. V\u00ed d\u1ee5: t\u1ec9 l\u1ec7 chuy\u1ec3n \u0111\u1ed5i 30% c\u1ee7a chi\u1ebfn d\u1ecbch l\u1edbn v\u00e0 70% c\u1ee7a chi\u1ebfn d\u1ecbch nh\u1ecf kh\u00f4ng th\u1ec3 c\u1ed9ng l\u1ea1i chia 2 m\u00e0 ph\u1ea3i t\u00ednh theo s\u1ed1 l\u01b0\u1ee3ng ng\u01b0\u1eddi d\u00f9ng th\u1ef1c t\u1ebf.<\/p>\n<h3>Trung b\u00ecnh c\u1ed9ng c\u00f3 ph\u1ea3i l\u00e0 gi\u00e1 tr\u1ecb &#8220;th\u1ef1c&#8221; trong t\u1eadp d\u1eef li\u1ec7u kh\u00f4ng?<\/h3>\n<p>Kh\u00f4ng nh\u1ea5t thi\u1ebft. Trung b\u00ecnh c\u1ed9ng l\u00e0 m\u1ed9t gi\u00e1 tr\u1ecb \u0111\u1ea1i di\u1ec7n (representative value), c\u00f3 th\u1ec3 kh\u00f4ng t\u1ed3n t\u1ea1i th\u1ef1c s\u1ef1 trong t\u1eadp d\u1eef li\u1ec7u. V\u00ed d\u1ee5: \u0111i\u1ec3m trung b\u00ecnh 7.3 c\u00f3 th\u1ec3 kh\u00f4ng c\u00f3 h\u1ecdc sinh n\u00e0o \u0111\u00fang \u0111i\u1ec3m \u0111\u00f3. \u0110\u00e2y l\u00e0 \u0111i\u1ec3m kh\u00e1c bi\u1ec7t v\u1edbi mode \u2014 mode lu\u00f4n l\u00e0 gi\u00e1 tr\u1ecb th\u1ef1c c\u00f3 trong d\u1eef li\u1ec7u.<\/p>\n<h2>K\u1ebft Lu\u1eadn<\/h2>\n<p>Trung b\u00ecnh c\u1ed9ng l\u00e0 c\u00f4ng c\u1ee5 th\u1ed1ng k\u00ea \u0111\u01a1n gi\u1ea3n nh\u01b0ng m\u1ea1nh m\u1ebd, l\u00e0 \u0111i\u1ec3m xu\u1ea5t ph\u00e1t l\u00fd t\u01b0\u1edfng \u0111\u1ec3 hi\u1ec3u d\u1eef li\u1ec7u. N\u1eafm v\u1eefng c\u00f4ng th\u1ee9c, bi\u1ebft khi n\u00e0o n\u00ean v\u00e0 kh\u00f4ng n\u00ean d\u00f9ng mean, c\u00f9ng c\u00e1ch so s\u00e1nh v\u1edbi median v\u00e0 mode s\u1ebd gi\u00fap b\u1ea1n ph\u00e2n t\u00edch s\u1ed1 li\u1ec7u ch\u00ednh x\u00e1c v\u00e0 tr\u00e1nh c\u00e1c k\u1ebft lu\u1eadn sai l\u1ea7m.<\/p>\n<p>\u0110\u1ec3 t\u00ecm hi\u1ec3u th\u00eam v\u1ec1 c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng th\u1ed1ng k\u00ea li\u00ean quan, xem th\u00eam <a href=\"https:\/\/1phantram.com\/blog\/thong-ke-co-ban\/\">h\u01b0\u1edbng d\u1eabn th\u1ed1ng k\u00ea c\u01a1 b\u1ea3n to\u00e0n di\u1ec7n<\/a> ho\u1eb7c \u0111\u1ecdc v\u1ec1 <a href=\"https:\/\/1phantram.com\/blog\/trung-vi-median-la-gi\/\">trung v\u1ecb (median)<\/a> v\u00e0 <a href=\"https:\/\/1phantram.com\/blog\/mode-yeu-vi-la-gi\/\">mode (y\u1ebfu v\u1ecb)<\/a>.<\/p>\n<p style=\"background:#f0f7ff;padding:15px;border-left:4px solid #0066cc;\"><strong>\ud83d\udd22 D\u00f9ng ngay c\u00f4ng c\u1ee5 t\u00ednh % t\u1ea1i <a href=\"https:\/\/1phantram.com\">1phantram.com<\/a><\/strong> \u2014 T\u00ednh ph\u1ea7n tr\u0103m t\u0103ng\/gi\u1ea3m, ph\u1ea7n tr\u0103m so s\u00e1nh gi\u00e1 tr\u1ecb trung b\u00ecnh nhanh ch\u00f3ng v\u00e0 ch\u00ednh x\u00e1c!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Trung b\u00ecnh c\u1ed9ng (hay c\u00f2n g\u1ecdi l\u00e0 mean) l\u00e0 ph\u00e9p t\u00ednh to\u00e1n h\u1ecdc c\u01a1 b\u1ea3n nh\u1ea5t trong th\u1ed1ng k\u00ea, \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng h\u00e0ng ng\u00e0y t\u1eeb&#8230;<\/p>\n","protected":false},"author":1,"featured_media":1055,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"rank_math_title":"","rank_math_description":"","rank_math_focus_keyword":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-37","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-huong-dan"],"_links":{"self":[{"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/posts\/37","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/comments?post=37"}],"version-history":[{"count":1,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/posts\/37\/revisions"}],"predecessor-version":[{"id":46,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/posts\/37\/revisions\/46"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/media\/1055"}],"wp:attachment":[{"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/media?parent=37"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/categories?post=37"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/tags?post=37"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}