{"id":38,"date":"2026-06-07T00:51:29","date_gmt":"2026-06-07T00:51:29","guid":{"rendered":"https:\/\/blog.phantram.online\/trung-vi-median-la-gi\/"},"modified":"2026-06-11T02:19:24","modified_gmt":"2026-06-11T02:19:24","slug":"trung-vi-median-la-gi","status":"publish","type":"post","link":"https:\/\/1phantram.com\/blog\/trung-vi-median-la-gi\/","title":{"rendered":"Trung V\u1ecb (Median) L\u00e0 G\u00ec? C\u00e1ch T\u00ednh V\u00e0 Khi N\u00e0o D\u00f9ng Thay Trung B\u00ecnh"},"content":{"rendered":"

Trung v\u1ecb (Median)<\/strong> l\u00e0 gi\u00e1 tr\u1ecb n\u1eb1m ch\u00ednh gi\u1eefa c\u1ee7a m\u1ed9t d\u00e3y s\u1ed1 \u0111\u00e3 \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp theo th\u1ee9 t\u1ef1 t\u0103ng d\u1ea7n ho\u1eb7c gi\u1ea3m d\u1ea7n. Trong th\u1ed1ng k\u00ea c\u01a1 b\u1ea3n<\/a>, trung v\u1ecb l\u00e0 m\u1ed9t trong ba \u0111\u1ea1i l\u01b0\u1ee3ng \u0111o xu h\u01b0\u1edbng trung t\u00e2m quan tr\u1ecdng nh\u1ea5t, c\u00f9ng v\u1edbi trung b\u00ecnh c\u1ed9ng (mean)<\/a> v\u00e0 mode. \u0110i\u1ec3m \u0111\u1eb7c bi\u1ec7t c\u1ee7a trung v\u1ecb: n\u00f3 kh\u00f4ng b\u1ecb \u1ea3nh h\u01b0\u1edfng b\u1edfi c\u00e1c gi\u00e1 tr\u1ecb c\u1ef1c \u0111oan, l\u00e0m cho n\u00f3 tr\u1edf th\u00e0nh th\u01b0\u1edbc \u0111o \u0111\u00e1ng tin c\u1eady h\u01a1n trong nhi\u1ec1u t\u00ecnh hu\u1ed1ng th\u1ef1c t\u1ebf.<\/p>\n

Trung V\u1ecb (Median) L\u00e0 G\u00ec? \u0110\u1ecbnh Ngh\u0129a \u0110\u1ea7y \u0110\u1ee7<\/h2>\n

Trung v\u1ecb l\u00e0 gi\u00e1 tr\u1ecb chia d\u00e3y s\u1ed1 (\u0111\u00e3 s\u1eafp x\u1ebfp) th\u00e0nh hai ph\u1ea7n b\u1eb1ng nhau: 50% gi\u00e1 tr\u1ecb nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng median, v\u00e0 50% gi\u00e1 tr\u1ecb l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng median. Median c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ph\u00e2n v\u1ecb 50%<\/strong> hay ph\u00e2n v\u1ecb th\u1ee9 hai (Q2)<\/strong>.<\/p>\n

K\u00fd hi\u1ec7u: Median \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 Me<\/strong> ho\u1eb7c Md<\/strong> ho\u1eb7c \u0111\u01a1n gi\u1ea3n l\u00e0 M\u0303<\/strong>.<\/p>\n

Kh\u00f4ng gi\u1ed1ng nh\u01b0 trung b\u00ecnh c\u1ed9ng, median kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o gi\u00e1 tr\u1ecb c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c ph\u1ea7n t\u1eed \u2014 n\u00f3 ch\u1ec9 ph\u1ee5 thu\u1ed9c v\u00e0o v\u1ecb tr\u00ed gi\u1eefa trong d\u00e3y s\u1ed1 \u0111\u00e3 s\u1eafp x\u1ebfp.<\/p>\n

C\u00e1ch T\u00ednh Trung V\u1ecb Cho D\u00e3y S\u1ed1 L\u1ebb<\/h2>\n

Khi t\u1eadp d\u1eef li\u1ec7u c\u00f3 s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed l\u1ebb (n l\u00e0 s\u1ed1 l\u1ebb)<\/strong>, trung v\u1ecb l\u00e0 gi\u00e1 tr\u1ecb n\u1eb1m \u0111\u00fang \u1edf v\u1ecb tr\u00ed gi\u1eefa:<\/p>\n

\nV\u1ecb tr\u00ed median = (n + 1) \/ 2<\/strong>\n<\/p>\n

V\u00ed d\u1ee5:<\/strong> D\u00e3y s\u1ed1 7 ph\u1ea7n t\u1eed: 3, 7, 8, 12, 15, 19, 24 (\u0111\u00e3 s\u1eafp x\u1ebfp)
\nn = 7 (l\u1ebb) \u2192 V\u1ecb tr\u00ed = (7+1)\/2 = 4
\nMedian = ph\u1ea7n t\u1eed th\u1ee9 4 = 12<\/strong><\/p>\n

Ki\u1ec3m tra: c\u00f3 3 gi\u00e1 tr\u1ecb nh\u1ecf h\u01a1n 12 (3, 7, 8) v\u00e0 3 gi\u00e1 tr\u1ecb l\u1edbn h\u01a1n 12 (15, 19, 24). \u2713<\/p>\n

C\u00e1ch T\u00ednh Trung V\u1ecb Cho D\u00e3y S\u1ed1 Ch\u1eb5n<\/h2>\n

Khi t\u1eadp d\u1eef li\u1ec7u c\u00f3 s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed ch\u1eb5n (n l\u00e0 s\u1ed1 ch\u1eb5n)<\/strong>, kh\u00f4ng c\u00f3 ph\u1ea7n t\u1eed n\u00e0o \u1edf \u0111\u00fang gi\u1eefa. Trung v\u1ecb l\u00e0 trung b\u00ecnh c\u1ed9ng c\u1ee7a hai ph\u1ea7n t\u1eed \u1edf gi\u1eefa:<\/p>\n

\nMedian = (gi\u00e1 tr\u1ecb th\u1ee9 n\/2 + gi\u00e1 tr\u1ecb th\u1ee9 n\/2 + 1) \/ 2<\/strong>\n<\/p>\n

V\u00ed d\u1ee5:<\/strong> D\u00e3y s\u1ed1 6 ph\u1ea7n t\u1eed: 4, 9, 11, 14, 18, 23 (\u0111\u00e3 s\u1eafp x\u1ebfp)
\nn = 6 (ch\u1eb5n) \u2192 Hai ph\u1ea7n t\u1eed gi\u1eefa: th\u1ee9 3 v\u00e0 th\u1ee9 4 = 11 v\u00e0 14
\nMedian = (11 + 14) \/ 2 = 25 \/ 2 = 12.5<\/strong><\/p>\n

L\u01b0u \u00fd: 12.5 kh\u00f4ng xu\u1ea5t hi\u1ec7n trong t\u1eadp d\u1eef li\u1ec7u g\u1ed1c \u2014 \u0111\u00e2y l\u00e0 gi\u00e1 tr\u1ecb trung gian \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n.<\/p>\n

H\u01b0\u1edbng D\u1eabn T\u00ednh Trung V\u1ecb Step-by-Step<\/h2>\n
    \n
  1. B\u01b0\u1edbc 1:<\/strong> Thu th\u1eadp to\u00e0n b\u1ed9 d\u1eef li\u1ec7u.<\/li>\n
  2. B\u01b0\u1edbc 2:<\/strong> S\u1eafp x\u1ebfp d\u1eef li\u1ec7u theo th\u1ee9 t\u1ef1 t\u0103ng d\u1ea7n (t\u1eeb nh\u1ecf \u0111\u1ebfn l\u1edbn).<\/li>\n
  3. B\u01b0\u1edbc 3:<\/strong> \u0110\u1ebfm s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed (n).<\/li>\n
  4. B\u01b0\u1edbc 4a:<\/strong> N\u1ebfu n l\u1ebb \u2192 Median = gi\u00e1 tr\u1ecb t\u1ea1i v\u1ecb tr\u00ed (n+1)\/2.<\/li>\n
  5. B\u01b0\u1edbc 4b:<\/strong> N\u1ebfu n ch\u1eb5n \u2192 Median = trung b\u00ecnh c\u1ee7a gi\u00e1 tr\u1ecb th\u1ee9 n\/2 v\u00e0 (n\/2 + 1).<\/li>\n<\/ol>\n

    V\u00ed D\u1ee5 Th\u1ef1c T\u1ebf: Thu Nh\u1eadp V\u00e0 B\u1ea5t \u0110\u1ed9ng S\u1ea3n<\/h2>\n

    T\u1ea1i sao b\u00e1o c\u00e1o thu nh\u1eadp d\u00f9ng median thay v\u00ec mean?<\/h3>\n

    \u0110\u00e2y l\u00e0 v\u00ed d\u1ee5 kinh \u0111i\u1ec3n trong th\u1ed1ng k\u00ea. Gi\u1ea3 s\u1eed thu nh\u1eadp h\u00e0ng th\u00e1ng c\u1ee7a 9 ng\u01b0\u1eddi trong m\u1ed9t nh\u00f3m b\u1ea1n (tri\u1ec7u \u0111\u1ed3ng):<\/p>\n

    D\u1eef li\u1ec7u g\u1ed1c:<\/strong> 8, 10, 12, 11, 9, 13, 10, 15, 150<\/p>\n

    Sau khi s\u1eafp x\u1ebfp:<\/strong> 8, 9, 10, 10, 11, 12, 13, 15, 150<\/p>\n\n\n\n\n\n\n
    \u0110\u1ea1i l\u01b0\u1ee3ng<\/th>\nK\u1ebft qu\u1ea3<\/th>\nNh\u1eadn x\u00e9t<\/th>\n<\/tr>\n<\/thead>\n
    Mean (trung b\u00ecnh)<\/td>\n(8+9+10+10+11+12+13+15+150)\/9 = 26.4 tri\u1ec7u<\/strong><\/td>\nB\u1ecb k\u00e9o l\u00ean b\u1edfi gi\u00e1 tr\u1ecb 150 tri\u1ec7u<\/td>\n<\/tr>\n
    Median (trung v\u1ecb)<\/td>\nV\u1ecb tr\u00ed 5 = 11 tri\u1ec7u<\/strong><\/td>\nPh\u1ea3n \u00e1nh \u0111\u00fang thu nh\u1eadp \u0111i\u1ec3n h\u00ecnh<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Mean 26.4 tri\u1ec7u cho th\u1ea5y “thu nh\u1eadp trung b\u00ecnh” g\u00e2y hi\u1ec3u l\u1ea7m v\u00ec ph\u1ea7n l\u1edbn m\u1ecdi ng\u01b0\u1eddi ch\u1ec9 ki\u1ebfm 8-15 tri\u1ec7u. Median 11 tri\u1ec7u m\u1edbi ph\u1ea3n \u00e1nh thu nh\u1eadp c\u1ee7a ng\u01b0\u1eddi “\u1edf gi\u1eefa” th\u1ef1c s\u1ef1.<\/p>\n

    \u0110\u00e2y ch\u00ednh x\u00e1c l\u00e0 l\u00fd do T\u1ed5ng c\u1ee5c Th\u1ed1ng k\u00ea v\u00e0 c\u00e1c t\u1ed5 ch\u1ee9c qu\u1ed1c t\u1ebf (IMF, World Bank) th\u01b0\u1eddng c\u00f4ng b\u1ed1 median household income<\/em> thay v\u00ec mean khi so s\u00e1nh m\u1ee9c s\u1ed1ng.<\/p>\n

    Gi\u00e1 b\u1ea5t \u0111\u1ed9ng s\u1ea3n \u2014 t\u1ea1i sao lu\u00f4n d\u00f9ng median?<\/h3>\n

    Gi\u00e1 nh\u00e0 t\u1ea1i TP.HCM qu\u00fd 1\/2024 (t\u1ef7 \u0111\u1ed3ng): 2.5, 3.0, 3.2, 3.5, 4.0, 4.2, 4.8, 5.0, 50, 80<\/p>\n

    Mean = (2.5+3.0+3.2+3.5+4.0+4.2+4.8+5.0+50+80)\/10 = 160.2\/10 = 16.02 t\u1ef7<\/strong> (b\u1ecb k\u00e9o l\u00ean b\u1edfi 2 c\u0103n bi\u1ec7t th\u1ef1 cao c\u1ea5p)<\/p>\n

    Median = (4.0 + 4.2)\/2 = 4.1 t\u1ef7<\/strong> (ph\u1ea3n \u00e1nh gi\u00e1 nh\u00e0 th\u1ef1c t\u1ebf c\u1ee7a ph\u1ea7n l\u1edbn giao d\u1ecbch)<\/p>\n

    Khi m\u1ed9t m\u00f4i gi\u1edbi n\u00f3i “gi\u00e1 trung b\u00ecnh” \u2014 h\u00e3y h\u1ecfi xem h\u1ecd \u0111ang n\u00f3i v\u1ec1 mean hay median!<\/p>\n

    So S\u00e1nh Median V\u00e0 Mean: Khi N\u00e0o D\u00f9ng C\u00e1i N\u00e0o?<\/h2>\n\n\n\n\n\n\n\n\n\n\n
    Ti\u00eau ch\u00ed so s\u00e1nh<\/th>\nMedian (Trung v\u1ecb)<\/th>\nMean (Trung b\u00ecnh c\u1ed9ng)<\/th>\n<\/tr>\n<\/thead>\n
    Ch\u1ecbu \u1ea3nh h\u01b0\u1edfng outlier<\/td>\n\u274c Kh\u00f4ng (kh\u00e1ng outlier)<\/td>\n\u2705 C\u00f3 (r\u1ea5t nh\u1ea1y c\u1ea3m)<\/td>\n<\/tr>\n
    Ph\u00e2n ph\u1ed1i l\u1ec7ch<\/td>\n\u2705 Ph\u00f9 h\u1ee3p<\/td>\n\u274c Kh\u00f4ng ph\u00f9 h\u1ee3p<\/td>\n<\/tr>\n
    Ph\u00e2n ph\u1ed1i chu\u1ea9n\/\u0111\u1ed1i x\u1ee9ng<\/td>\n\u2705 D\u00f9ng \u0111\u01b0\u1ee3c<\/td>\n\u2705 T\u1ed1t h\u01a1n (d\u00f9ng to\u00e0n d\u1eef li\u1ec7u)<\/td>\n<\/tr>\n
    D\u1ec5 t\u00ednh<\/td>\nC\u1ea7n s\u1eafp x\u1ebfp tr\u01b0\u1edbc<\/td>\nC\u1ed9ng v\u00e0 chia<\/td>\n<\/tr>\n
    D\u00f9ng trong ph\u00e9p t\u00ednh ti\u1ebfp theo<\/td>\nH\u1ea1n ch\u1ebf<\/td>\n\u2705 D\u1ec5 d\u00f9ng h\u01a1n (mean c\u1ee7a mean)<\/td>\n<\/tr>\n
    \u1ee8ng d\u1ee5ng \u0111i\u1ec3n h\u00ecnh<\/td>\nThu nh\u1eadp, nh\u00e0 \u0111\u1ea5t, th\u1eddi gian ch\u1edd<\/td>\n\u0110i\u1ec3m thi, nhi\u1ec7t \u0111\u1ed9, chi\u1ec1u cao<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Median Trong C\u00e1c L\u0129nh V\u1ef1c Th\u1ef1c T\u1ebf<\/h2>\n

    Trong y t\u1ebf: Th\u1eddi gian s\u1ed1ng s\u00f3t<\/h3>\n

    Trong nghi\u00ean c\u1ee9u ung th\u01b0, “median survival time” (th\u1eddi gian s\u1ed1ng trung v\u1ecb) l\u00e0 th\u01b0\u1edbc \u0111o ti\u00eau chu\u1ea9n. N\u00f3 cho bi\u1ebft: 50% b\u1ec7nh nh\u00e2n s\u1ed1ng l\u00e2u h\u01a1n X th\u00e1ng, 50% ng\u1eafn h\u01a1n. Mean kh\u00f4ng ph\u00f9 h\u1ee3p v\u00ec m\u1ed9t s\u1ed1 b\u1ec7nh nh\u00e2n c\u00f3 th\u1ec3 s\u1ed1ng c\u1ef1c k\u1ef3 l\u00e2u, k\u00e9o l\u1ec7ch k\u1ebft qu\u1ea3.<\/p>\n

    Trong kinh t\u1ebf: GDP b\u00ecnh qu\u00e2n \u0111\u1ea7u ng\u01b0\u1eddi<\/h3>\n

    Nhi\u1ec1u n\u01b0\u1edbc c\u00f3 GDP\/ng\u01b0\u1eddi (mean) cao nh\u01b0ng b\u1ea5t b\u00ecnh \u0111\u1eb3ng l\u1edbn. Median income th\u1ea5p h\u01a1n nhi\u1ec1u cho th\u1ea5y c\u1ee7a c\u1ea3i t\u1eadp trung v\u00e0o thi\u1ec3u s\u1ed1. H\u1ec7 s\u1ed1 Gini v\u00e0 median income l\u00e0 hai ch\u1ec9 s\u1ed1 b\u1ed5 sung nhau \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 th\u1ef1c tr\u1ea1ng kinh t\u1ebf.<\/p>\n

    Trong IT: Th\u1eddi gian ph\u1ea3n h\u1ed3i server<\/h3>\n

    K\u1ef9 s\u01b0 backend th\u01b0\u1eddng d\u00f9ng P50 (median), P95, P99 \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 hi\u1ec7u su\u1ea5t. P50 = 200ms ngh\u0129a l\u00e0 50% request ho\u00e0n th\u00e0nh d\u01b0\u1edbi 200ms \u2014 th\u00f4ng tin th\u1ef1c t\u1ebf h\u01a1n mean v\u00ec m\u1ed9t v\u00e0i request ch\u1eadm b\u1ea5t th\u01b0\u1eddng kh\u00f4ng k\u00e9o l\u1ec7ch P50.<\/p>\n

    T\u00ednh Median Trong Excel V\u00e0 Google Sheets<\/h2>\n

    H\u00e0m t\u00ednh trung v\u1ecb trong Excel\/Google Sheets:<\/p>\n