{"id":41,"date":"2026-06-07T00:57:01","date_gmt":"2026-06-07T00:57:01","guid":{"rendered":"https:\/\/blog.phantram.online\/tan-suat-bang-tan-so\/"},"modified":"2026-06-11T02:17:19","modified_gmt":"2026-06-11T02:17:19","slug":"tan-suat-bang-tan-so","status":"publish","type":"post","link":"https:\/\/1phantram.com\/blog\/tan-suat-bang-tan-so\/","title":{"rendered":"T\u1ea7n Su\u1ea5t L\u00e0 G\u00ec? C\u00e1ch L\u1eadp B\u1ea3ng T\u1ea7n S\u1ed1 V\u00e0 Bi\u1ec3u \u0110\u1ed3 C\u1ed9t"},"content":{"rendered":"<p><strong>T\u1ea7n su\u1ea5t<\/strong> l\u00e0 t\u1ec9 l\u1ec7 (ho\u1eb7c ph\u1ea7n tr\u0103m) bi\u1ec3u th\u1ecb m\u1ee9c \u0111\u1ed9 xu\u1ea5t hi\u1ec7n c\u1ee7a m\u1ed9t gi\u00e1 tr\u1ecb trong t\u1eadp d\u1eef li\u1ec7u so v\u1edbi t\u1ed5ng s\u1ed1 quan s\u00e1t. C\u00f2n <strong>t\u1ea7n s\u1ed1<\/strong> l\u00e0 s\u1ed1 l\u1ea7n m\u1ed9t gi\u00e1 tr\u1ecb xu\u1ea5t hi\u1ec7n. C\u1eb7p kh\u00e1i ni\u1ec7m t\u1ea7n s\u1ed1 \u2014 t\u1ea7n su\u1ea5t l\u00e0 n\u1ec1n t\u1ea3ng \u0111\u1ec3 l\u1eadp <strong>b\u1ea3ng t\u1ea7n s\u1ed1<\/strong> v\u00e0 v\u1ebd <strong>bi\u1ec3u \u0111\u1ed3 c\u1ed9t<\/strong> \u2014 hai c\u00f4ng c\u1ee5 c\u1ed1t l\u00f5i trong <a href=\"https:\/\/1phantram.com\/blog\/thong-ke-co-ban\/\">th\u1ed1ng k\u00ea c\u01a1 b\u1ea3n<\/a>. Hi\u1ec3u r\u00f5 t\u1ea7n su\u1ea5t v\u00e0 t\u1ea7n s\u1ed1 gi\u00fap b\u1ea1n t\u00f3m t\u1eaft t\u1eadp d\u1eef li\u1ec7u l\u1edbn th\u00e0nh d\u1ea1ng d\u1ec5 \u0111\u1ecdc, ph\u00e2n t\u00edch v\u00e0 tr\u00ecnh b\u00e0y.<\/p>\n<h2>T\u1ea7n S\u1ed1 V\u00e0 T\u1ea7n Su\u1ea5t L\u00e0 G\u00ec? Ph\u00e2n Bi\u1ec7t R\u00f5 R\u00e0ng<\/h2>\n<h3>T\u1ea7n s\u1ed1 (Frequency) l\u00e0 g\u00ec?<\/h3>\n<p><strong>T\u1ea7n s\u1ed1<\/strong> l\u00e0 s\u1ed1 l\u1ea7n (s\u1ed1 l\u01b0\u1ee3t) m\u1ed9t gi\u00e1 tr\u1ecb c\u1ee5 th\u1ec3 xu\u1ea5t hi\u1ec7n trong t\u1eadp d\u1eef li\u1ec7u. T\u1ea7n s\u1ed1 l\u00e0 con s\u1ed1 tuy\u1ec7t \u0111\u1ed1i, th\u01b0\u1eddng k\u00fd hi\u1ec7u l\u00e0 <strong>f<\/strong> ho\u1eb7c <strong>n<\/strong>.<\/p>\n<p><strong>V\u00ed d\u1ee5:<\/strong> Trong danh s\u00e1ch \u0111i\u1ec3m: 5, 6, 7, 7, 8, 7, 9, 6, 7, 8<br \/>\nT\u1ea7n s\u1ed1 c\u1ee7a \u0111i\u1ec3m 7 = 4 (xu\u1ea5t hi\u1ec7n 4 l\u1ea7n)<\/p>\n<h3>T\u1ea7n su\u1ea5t (Relative Frequency) l\u00e0 g\u00ec?<\/h3>\n<p><strong>T\u1ea7n su\u1ea5t t\u01b0\u01a1ng \u0111\u1ed1i<\/strong> l\u00e0 t\u1ec9 l\u1ec7 c\u1ee7a t\u1ea7n s\u1ed1 so v\u1edbi t\u1ed5ng s\u1ed1 quan s\u00e1t, th\u01b0\u1eddng t\u00ednh theo ph\u1ea7n tr\u0103m. T\u1ea7n su\u1ea5t cho bi\u1ebft &#8220;gi\u00e1 tr\u1ecb n\u00e0y chi\u1ebfm bao nhi\u00eau % trong to\u00e0n b\u1ed9 d\u1eef li\u1ec7u?&#8221;<\/p>\n<p style=\"background:#f5f5f5;padding:12px;font-family:monospace;text-align:center;\">\n<strong>T\u1ea7n su\u1ea5t (%) = (T\u1ea7n s\u1ed1 \/ T\u1ed5ng s\u1ed1 quan s\u00e1t) \u00d7 100%<\/strong>\n<\/p>\n<p>V\u00ed d\u1ee5 ti\u1ebfp: \u0110i\u1ec3m 7 c\u00f3 t\u1ea7n s\u1ed1 4, t\u1ed5ng = 10<br \/>\nT\u1ea7n su\u1ea5t \u0111i\u1ec3m 7 = (4\/10) \u00d7 100% = <strong>40%<\/strong><\/p>\n<h3>T\u1ea7n su\u1ea5t t\u00edch l\u0169y (Cumulative Frequency) l\u00e0 g\u00ec?<\/h3>\n<p><strong>T\u1ea7n su\u1ea5t t\u00edch l\u0169y<\/strong> l\u00e0 t\u1ed5ng t\u1ea7n su\u1ea5t c\u1ee7a m\u1ed9t gi\u00e1 tr\u1ecb v\u00e0 t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb nh\u1ecf h\u01a1n n\u00f3. N\u00f3 cho bi\u1ebft &#8220;bao nhi\u00eau % d\u1eef li\u1ec7u c\u00f3 gi\u00e1 tr\u1ecb \u2264 X?&#8221;<\/p>\n<h2>H\u01b0\u1edbng D\u1eabn L\u1eadp B\u1ea3ng T\u1ea7n S\u1ed1 Step-by-Step<\/h2>\n<h3>V\u00ed d\u1ee5 1: \u0110i\u1ec3m ki\u1ec3m tra to\u00e1n c\u1ee7a 20 h\u1ecdc sinh<\/h3>\n<p><strong>D\u1eef li\u1ec7u g\u1ed1c (raw data):<\/strong><br \/>\n7, 5, 8, 9, 7, 6, 8, 7, 10, 5, 6, 7, 8, 9, 7, 6, 8, 5, 7, 9<\/p>\n<p><strong>B\u01b0\u1edbc 1: X\u00e1c \u0111\u1ecbnh t\u1ea5t c\u1ea3 gi\u00e1 tr\u1ecb c\u00f3 th\u1ec3 xu\u1ea5t hi\u1ec7n:<\/strong> 5, 6, 7, 8, 9, 10<\/p>\n<p><strong>B\u01b0\u1edbc 2: \u0110\u1ebfm t\u1ea7n s\u1ed1 m\u1ed7i gi\u00e1 tr\u1ecb:<\/strong><br \/>\n5 \u2192 \u0111\u1ebfm: 5, 5, 5 \u2192 t\u1ea7n s\u1ed1 = 3<br \/>\n6 \u2192 \u0111\u1ebfm: 6, 6, 6 \u2192 t\u1ea7n s\u1ed1 = 3<br \/>\n7 \u2192 \u0111\u1ebfm: 7, 7, 7, 7, 7, 7 \u2192 t\u1ea7n s\u1ed1 = 6<br \/>\n8 \u2192 \u0111\u1ebfm: 8, 8, 8, 8 \u2192 t\u1ea7n s\u1ed1 = 4<br \/>\n9 \u2192 \u0111\u1ebfm: 9, 9, 9 \u2192 t\u1ea7n s\u1ed1 = 3<br \/>\n10 \u2192 \u0111\u1ebfm: 10 \u2192 t\u1ea7n s\u1ed1 = 1<\/p>\n<p><strong>B\u01b0\u1edbc 3: L\u1eadp b\u1ea3ng t\u1ea7n s\u1ed1 \u0111\u1ea7y \u0111\u1ee7:<\/strong><\/p>\n<table border=\"1\" cellpadding=\"8\" cellspacing=\"0\" style=\"border-collapse:collapse;width:100%\">\n<thead>\n<tr style=\"background:#e8f4fd\">\n<th>\u0110i\u1ec3m (x\u1d62)<\/th>\n<th>T\u1ea7n s\u1ed1 (f\u1d62)<\/th>\n<th>T\u1ea7n su\u1ea5t (%)<\/th>\n<th>T\u1ea7n s\u1ed1 t\u00edch l\u0169y<\/th>\n<th>T\u1ea7n su\u1ea5t t\u00edch l\u0169y (%)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>5<\/td>\n<td>3<\/td>\n<td>15%<\/td>\n<td>3<\/td>\n<td>15%<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>3<\/td>\n<td>15%<\/td>\n<td>6<\/td>\n<td>30%<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>6<\/td>\n<td>30%<\/td>\n<td>12<\/td>\n<td>60%<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>4<\/td>\n<td>20%<\/td>\n<td>16<\/td>\n<td>80%<\/td>\n<\/tr>\n<tr>\n<td>9<\/td>\n<td>3<\/td>\n<td>15%<\/td>\n<td>19<\/td>\n<td>95%<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>1<\/td>\n<td>5%<\/td>\n<td>20<\/td>\n<td>100%<\/td>\n<\/tr>\n<tr style=\"background:#f9f9f9\">\n<td><strong>T\u1ed5ng<\/strong><\/td>\n<td><strong>20<\/strong><\/td>\n<td><strong>100%<\/strong><\/td>\n<td>&#8211;<\/td>\n<td>&#8211;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>\u0110\u1ecdc hi\u1ec3u b\u1ea3ng:<\/strong><\/p>\n<ul>\n<li>\u0110i\u1ec3m 7 l\u00e0 \u0111i\u1ec3m ph\u1ed5 bi\u1ebfn nh\u1ea5t (<a href=\"https:\/\/1phantram.com\/blog\/mode-yeu-vi-la-gi\/\">mode<\/a> = 7), chi\u1ebfm 30% h\u1ecdc sinh.<\/li>\n<li>60% h\u1ecdc sinh \u0111\u1ea1t \u0111i\u1ec3m \u2264 7 (t\u1ea7n su\u1ea5t t\u00edch l\u0169y c\u1ee7a \u0111i\u1ec3m 7).<\/li>\n<li>80% h\u1ecdc sinh \u0111\u1ea1t \u0111i\u1ec3m \u2264 8 \u2014 ch\u1ec9 20% \u0111\u1ea1t 9-10.<\/li>\n<\/ul>\n<h2>B\u1ea3ng T\u1ea7n S\u1ed1 Nh\u00f3m \u2014 Khi D\u1eef Li\u1ec7u Li\u00ean T\u1ee5c<\/h2>\n<p>Khi d\u1eef li\u1ec7u li\u00ean t\u1ee5c ho\u1eb7c c\u00f3 nhi\u1ec1u gi\u00e1 tr\u1ecb kh\u00e1c nhau, ta nh\u00f3m v\u00e0o c\u00e1c kho\u1ea3ng (class intervals). V\u00ed d\u1ee5: \u0111i\u1ec3m thi 0-100, chi\u1ec1u cao, c\u00e2n n\u1eb7ng.<\/p>\n<h3>V\u00ed d\u1ee5 2: Kh\u1ea3o s\u00e1t th\u1eddi gian h\u1ecdc b\u00e0i m\u1ed7i ng\u00e0y (ph\u00fat) c\u1ee7a 30 h\u1ecdc sinh<\/h3>\n<p>D\u1eef li\u1ec7u: 45, 60, 30, 90, 120, 75, 60, 45, 80, 100, 30, 55, 70, 90, 60, 45, 85, 110, 50, 70, 60, 40, 95, 75, 60, 55, 80, 100, 45, 65<\/p>\n<p><strong>Ch\u1ecdn kho\u1ea3ng nh\u00f3m: 30 ph\u00fat (0-30, 31-60, 61-90, 91-120)<\/strong><\/p>\n<table border=\"1\" cellpadding=\"8\" cellspacing=\"0\" style=\"border-collapse:collapse;width:100%\">\n<thead>\n<tr style=\"background:#e8f4fd\">\n<th>Kho\u1ea3ng th\u1eddi gian (ph\u00fat)<\/th>\n<th>T\u1ea7n s\u1ed1<\/th>\n<th>T\u1ea7n su\u1ea5t (%)<\/th>\n<th>T\u1ea7n su\u1ea5t t\u00edch l\u0169y (%)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>30 \u2013 60<\/td>\n<td>12<\/td>\n<td>40%<\/td>\n<td>40%<\/td>\n<\/tr>\n<tr>\n<td>61 \u2013 90<\/td>\n<td>11<\/td>\n<td>36.7%<\/td>\n<td>76.7%<\/td>\n<\/tr>\n<tr>\n<td>91 \u2013 120<\/td>\n<td>7<\/td>\n<td>23.3%<\/td>\n<td>100%<\/td>\n<\/tr>\n<tr style=\"background:#f9f9f9\">\n<td><strong>T\u1ed5ng<\/strong><\/td>\n<td><strong>30<\/strong><\/td>\n<td><strong>100%<\/strong><\/td>\n<td>&#8211;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Nh\u1eadn x\u00e9t:<\/strong> 40% h\u1ecdc sinh h\u1ecdc d\u01b0\u1edbi 1 gi\u1edd\/ng\u00e0y. 76.7% h\u1ecdc d\u01b0\u1edbi 90 ph\u00fat\/ng\u00e0y. Ch\u1ec9 23.3% h\u1ecdc tr\u00ean 90 ph\u00fat.<\/p>\n<h2>Bi\u1ec3u \u0110\u1ed3 C\u1ed9t (Histogram) T\u1eeb B\u1ea3ng T\u1ea7n S\u1ed1<\/h2>\n<p>B\u1ea3ng t\u1ea7n s\u1ed1 l\u00e0 n\u1ec1n t\u1ea3ng \u0111\u1ec3 v\u1ebd bi\u1ec3u \u0111\u1ed3 c\u1ed9t (bar chart cho d\u1eef li\u1ec7u r\u1eddi r\u1ea1c, histogram cho d\u1eef li\u1ec7u li\u00ean t\u1ee5c). C\u00e1c \u0111\u1eb7c \u0111i\u1ec3m c\u1ea7n ch\u00fa \u00fd:<\/p>\n<ul>\n<li><strong>Tr\u1ee5c ngang (X):<\/strong> C\u00e1c gi\u00e1 tr\u1ecb ho\u1eb7c kho\u1ea3ng gi\u00e1 tr\u1ecb<\/li>\n<li><strong>Tr\u1ee5c d\u1ecdc (Y):<\/strong> T\u1ea7n s\u1ed1 ho\u1eb7c t\u1ea7n su\u1ea5t (%)<\/li>\n<li><strong>Chi\u1ec1u cao c\u1ed9t:<\/strong> Th\u1ec3 hi\u1ec7n t\u1ea7n s\u1ed1 ho\u1eb7c t\u1ea7n su\u1ea5t c\u1ee7a m\u1ed7i gi\u00e1 tr\u1ecb<\/li>\n<li><strong>\u0110\u01b0\u1eddng t\u1ea7n su\u1ea5t t\u00edch l\u0169y (ogive):<\/strong> \u0110\u01b0\u1eddng cong n\u1ed1i c\u00e1c \u0111i\u1ec3m t\u1ea7n su\u1ea5t t\u00edch l\u0169y<\/li>\n<\/ul>\n<h3>\u0110\u1ecdc bi\u1ec3u \u0111\u1ed3 c\u1ed9t nh\u01b0 th\u1ebf n\u00e0o?<\/h3>\n<ul>\n<li>C\u1ed9t cao nh\u1ea5t = gi\u00e1 tr\u1ecb c\u00f3 t\u1ea7n s\u1ed1 l\u1edbn nh\u1ea5t = mode<\/li>\n<li>H\u00ecnh d\u1ea1ng ph\u00e2n ph\u1ed1i: chu\u1ea9n (h\u00ecnh chu\u00f4ng), l\u1ec7ch tr\u00e1i, l\u1ec7ch ph\u1ea3i, bimodal<\/li>\n<li>Kho\u1ea3ng tr\u1ed1ng gi\u1eefa c\u00e1c c\u1ed9t c\u00f3 th\u1ec3 l\u00e0 outlier ho\u1eb7c kho\u1ea3ng thi\u1ebfu d\u1eef li\u1ec7u<\/li>\n<\/ul>\n<h2>\u1ee8ng D\u1ee5ng T\u1ea7n Su\u1ea5t Trong Th\u1ef1c T\u1ebf<\/h2>\n<h3>Kh\u1ea3o s\u00e1t kh\u00e1ch h\u00e0ng<\/h3>\n<p>Sau khi thu th\u1eadp \u0111\u00e1nh gi\u00e1 s\u1ea3n ph\u1ea9m t\u1eeb 500 kh\u00e1ch h\u00e0ng (thang 1-5), l\u1eadp b\u1ea3ng t\u1ea7n s\u1ed1 cho th\u1ea5y ph\u1ea7n l\u1edbn (68%) \u0111\u00e1nh gi\u00e1 4-5 sao \u2014 th\u00f4ng tin tr\u1ef1c ti\u1ebfp v\u1ec1 m\u1ee9c \u0111\u1ed9 h\u00e0i l\u00f2ng, h\u1eefu \u00edch h\u01a1n nhi\u1ec1u so v\u1edbi ch\u1ec9 nh\u00ecn v\u00e0o \u0111i\u1ec3m trung b\u00ecnh.<\/p>\n<h3>Ph\u00e2n t\u00edch k\u1ebft qu\u1ea3 thi qu\u1ed1c gia<\/h3>\n<p>B\u1ed9 GD-\u0110T c\u00f4ng b\u1ed1 b\u1ea3ng ph\u00e2n ph\u1ed1i \u0111i\u1ec3m thi THPT \u2014 \u0111\u00e2y ch\u00ednh l\u00e0 b\u1ea3ng t\u1ea7n su\u1ea5t. T\u1eeb \u0111\u00e2y c\u00f3 th\u1ec3 th\u1ea5y: bao nhi\u00eau % h\u1ecdc sinh \u0111\u1ea1t 7+ \u0111i\u1ec3m, \u0111i\u1ec3m n\u00e0o ph\u1ed5 bi\u1ebfn nh\u1ea5t, ph\u1ed5 \u0111i\u1ec3m c\u1ee7a t\u1eebng m\u00f4n.<\/p>\n<h3>Ph\u00e2n t\u00edch h\u00e0nh vi ng\u01b0\u1eddi d\u00f9ng website<\/h3>\n<p>B\u1ea3ng t\u1ea7n s\u1ed1 th\u1eddi gian truy c\u1eadp: bao nhi\u00eau % ng\u01b0\u1eddi d\u00f9ng \u1edf l\u1ea1i d\u01b0\u1edbi 1 ph\u00fat (bounce rate), 1-3 ph\u00fat, tr\u00ean 3 ph\u00fat. Th\u00f4ng tin n\u00e0y quy\u1ebft \u0111\u1ecbnh chi\u1ebfn l\u01b0\u1ee3c c\u1ea3i thi\u1ec7n UX.<\/p>\n<h2>C\u00e1ch L\u1eadp B\u1ea3ng T\u1ea7n S\u1ed1 Trong Excel<\/h2>\n<ol>\n<li><strong>D\u1eef li\u1ec7u r\u1eddi r\u1ea1c:<\/strong> D\u00f9ng COUNTIF cho t\u1eebng gi\u00e1 tr\u1ecb: <code>=COUNTIF($A$1:$A$20, B1)<\/code><\/li>\n<li><strong>D\u1eef li\u1ec7u nh\u00f3m:<\/strong> D\u00f9ng FREQUENCY array formula: <code>{=FREQUENCY(data, bins)}<\/code> (nh\u1eadp Ctrl+Shift+Enter)<\/li>\n<li><strong>T\u1ea7n su\u1ea5t (%):<\/strong> Chia t\u1ea7n s\u1ed1 cho t\u1ed5ng: <code>=C2\/SUM($C$2:$C$7)*100<\/code><\/li>\n<li><strong>T\u1ea7n s\u1ed1 t\u00edch l\u0169y:<\/strong> C\u1ed9ng d\u1ed3n: <code>=D2+C3<\/code> (t\u1eeb h\u00e0ng 3 tr\u1edf xu\u1ed1ng)<\/li>\n<li><strong>Bi\u1ec3u \u0111\u1ed3:<\/strong> Ch\u1ecdn d\u1eef li\u1ec7u \u2192 Insert \u2192 Bar Chart ho\u1eb7c Histogram<\/li>\n<\/ol>\n<h2>T\u1ea7n Su\u1ea5t V\u00e0 T\u1ec9 L\u1ec7 Ph\u1ea7n Tr\u0103m \u2014 Li\u00ean H\u1ec7 M\u1eadt Thi\u1ebft<\/h2>\n<p>T\u1ea7n su\u1ea5t t\u01b0\u01a1ng \u0111\u1ed1i th\u1ef1c ch\u1ea5t ch\u00ednh l\u00e0 t\u1ec9 l\u1ec7 ph\u1ea7n tr\u0103m. M\u1ed7i khi b\u1ea1n n\u00f3i &#8220;40% h\u1ecdc sinh \u0111\u1ea1t \u0111i\u1ec3m 7&#8221;, b\u1ea1n \u0111ang d\u00f9ng t\u1ea7n su\u1ea5t theo d\u1ea1ng ph\u1ea7n tr\u0103m. \u0110\u00e2y l\u00e0 ng\u00f4n ng\u1eef th\u1ed1ng k\u00ea ph\u1ed5 bi\u1ebfn nh\u1ea5t trong b\u00e1o c\u00e1o v\u00e0 tr\u00ecnh b\u00e0y d\u1eef li\u1ec7u.<\/p>\n<p>\u0110\u1ec3 t\u00ednh nhanh t\u1ea7n su\u1ea5t (%) t\u1eeb t\u1ea7n s\u1ed1, h\u00e3y d\u00f9ng <a href=\"https:\/\/1phantram.com\/blog\/tinh-phan-tram\/\">c\u00f4ng c\u1ee5 t\u00ednh ph\u1ea7n tr\u0103m t\u1ea1i 1phantram.com<\/a> \u2014 nh\u1eadp t\u1ea7n s\u1ed1 v\u00e0 t\u1ed5ng s\u1ed1 quan s\u00e1t, ra ngay t\u1ea7n su\u1ea5t %.<\/p>\n<p>\u0110\u1ecdc th\u00eam v\u1ec1 c\u00e1ch \u1ee9ng d\u1ee5ng ph\u1ea7n tr\u0103m trong ph\u00e2n t\u00edch th\u1ed1ng k\u00ea t\u1ea1i b\u00e0i: <a href=\"https:\/\/1phantram.com\/blog\/ti-le-phan-tram-trong-thong-ke\/\">T\u1ec9 l\u1ec7 ph\u1ea7n tr\u0103m trong th\u1ed1ng k\u00ea<\/a>.<\/p>\n<h2>C\u00e2u H\u1ecfi Th\u01b0\u1eddng G\u1eb7p (FAQ)<\/h2>\n<h3>T\u1ea7n s\u1ed1 v\u00e0 t\u1ea7n su\u1ea5t kh\u00e1c nhau \u1edf \u0111i\u1ec3m n\u00e0o?<\/h3>\n<p>T\u1ea7n s\u1ed1 l\u00e0 con s\u1ed1 tuy\u1ec7t \u0111\u1ed1i (s\u1ed1 l\u1ea7n xu\u1ea5t hi\u1ec7n). T\u1ea7n su\u1ea5t l\u00e0 con s\u1ed1 t\u01b0\u01a1ng \u0111\u1ed1i (t\u1ec9 l\u1ec7 so v\u1edbi t\u1ed5ng). V\u00ed d\u1ee5: \u0111i\u1ec3m 7 c\u00f3 t\u1ea7n s\u1ed1 6 v\u00e0 t\u1ea7n su\u1ea5t 30% (trong t\u1ed5ng 20 h\u1ecdc sinh). Khi so s\u00e1nh gi\u1eefa c\u00e1c nh\u00f3m c\u00f3 k\u00edch th\u01b0\u1edbc kh\u00e1c nhau, ph\u1ea3i d\u00f9ng t\u1ea7n su\u1ea5t, kh\u00f4ng d\u00f9ng t\u1ea7n s\u1ed1.<\/p>\n<h3>B\u1ea3ng t\u1ea7n s\u1ed1 nh\u00f3m n\u00ean c\u00f3 bao nhi\u00eau kho\u1ea3ng?<\/h3>\n<p>Quy t\u1eafc Sturges: S\u1ed1 kho\u1ea3ng \u2248 1 + 3.322 \u00d7 log\u2081\u2080(n). V\u1edbi n = 30: \u2248 5-6 kho\u1ea3ng. V\u1edbi n = 100: \u2248 7-8 kho\u1ea3ng. Th\u1ef1c t\u1ebf, th\u01b0\u1eddng ch\u1ecdn 5-10 kho\u1ea3ng sao cho m\u1ed7i kho\u1ea3ng c\u00f3 \u00edt nh\u1ea5t 5 quan s\u00e1t.<\/p>\n<h3>T\u1ea7n su\u1ea5t t\u00edch l\u0169y d\u00f9ng \u0111\u1ec3 l\u00e0m g\u00ec?<\/h3>\n<p>T\u1ea7n su\u1ea5t t\u00edch l\u0169y cho bi\u1ebft &#8220;bao nhi\u00eau % d\u1eef li\u1ec7u c\u00f3 gi\u00e1 tr\u1ecb \u2264 X&#8221;. \u1ee8ng d\u1ee5ng: t\u00ecm ph\u00e2n v\u1ecb (percentile), median (\u0111i\u1ec3m c\u00f3 t\u1ea7n su\u1ea5t t\u00edch l\u0169y = 50%), Q1 (25%) v\u00e0 Q3 (75%). \u0110\u01b0\u1eddng ogive (\u0111\u01b0\u1eddng t\u1ea7n su\u1ea5t t\u00edch l\u0169y) gi\u00fap tr\u1ef1c quan h\u00f3a ph\u00e2n ph\u1ed1i t\u00edch l\u0169y.<\/p>\n<h3>Histogram v\u00e0 bi\u1ec3u \u0111\u1ed3 c\u1ed9t c\u00f3 kh\u00e1c nhau kh\u00f4ng?<\/h3>\n<p>C\u00f3. Bi\u1ec3u \u0111\u1ed3 c\u1ed9t (bar chart) d\u00f9ng cho d\u1eef li\u1ec7u r\u1eddi r\u1ea1c ho\u1eb7c \u0111\u1ecbnh t\u00ednh \u2014 c\u00e1c c\u1ed9t kh\u00f4ng ch\u1ea1m nhau. Histogram d\u00f9ng cho d\u1eef li\u1ec7u li\u00ean t\u1ee5c \u0111\u01b0\u1ee3c nh\u00f3m \u2014 c\u00e1c c\u1ed9t ch\u1ea1m nhau v\u00ec c\u00e1c kho\u1ea3ng li\u00ean ti\u1ebfp. \u0110\u00e2y l\u00e0 ph\u00e2n bi\u1ec7t k\u1ef9 thu\u1eadt quan tr\u1ecdng trong tr\u00ecnh b\u00e0y d\u1eef li\u1ec7u.<\/p>\n<h3>T\u1ea7n su\u1ea5t t\u00edch l\u0169y v\u00e0 ph\u00e2n v\u1ecb li\u00ean h\u1ec7 nh\u01b0 th\u1ebf n\u00e0o?<\/h3>\n<p>Tr\u1ef1c ti\u1ebfp. Ph\u00e2n v\u1ecb th\u1ee9 p (p-th percentile) l\u00e0 gi\u00e1 tr\u1ecb c\u00f3 t\u1ea7n su\u1ea5t t\u00edch l\u0169y = p%. Median = ph\u00e2n v\u1ecb 50%, Q1 = ph\u00e2n v\u1ecb 25%, Q3 = ph\u00e2n v\u1ecb 75%. B\u1ea3ng t\u1ea7n su\u1ea5t t\u00edch l\u0169y l\u00e0 c\u00f4ng c\u1ee5 \u0111\u1ecdc ph\u00e2n v\u1ecb tr\u1ef1c ti\u1ebfp m\u00e0 kh\u00f4ng c\u1ea7n s\u1eafp x\u1ebfp to\u00e0n b\u1ed9 d\u1eef li\u1ec7u.<\/p>\n<h2>K\u1ebft Lu\u1eadn<\/h2>\n<p>B\u1ea3ng t\u1ea7n s\u1ed1 v\u00e0 t\u1ea7n su\u1ea5t l\u00e0 b\u01b0\u1edbc \u0111\u1ea7u ti\u00ean v\u00e0 quan tr\u1ecdng nh\u1ea5t trong m\u1ecdi ph\u00e2n t\u00edch d\u1eef li\u1ec7u. T\u1eeb b\u1ea3ng t\u1ea7n s\u1ed1, b\u1ea1n c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh <a href=\"https:\/\/1phantram.com\/blog\/mode-yeu-vi-la-gi\/\">mode<\/a>, \u01b0\u1edbc t\u00ednh <a href=\"https:\/\/1phantram.com\/blog\/trung-vi-median-la-gi\/\">median<\/a>, v\u1ebd bi\u1ec3u \u0111\u1ed3, v\u00e0 nh\u1eadn di\u1ec7n ph\u00e2n ph\u1ed1i d\u1eef li\u1ec7u. \u0110\u00e2y l\u00e0 n\u1ec1n t\u1ea3ng \u0111\u1ec3 ti\u1ebfn l\u00ean c\u00e1c ph\u00e2n t\u00edch ph\u1ee9c t\u1ea1p h\u01a1n nh\u01b0 ki\u1ec3m \u0111\u1ecbnh gi\u1ea3 thuy\u1ebft v\u00e0 ph\u00e2n t\u00edch h\u1ed3i quy.<\/p>\n<p>Xem l\u1ea1i t\u1ed5ng quan \u0111\u1ea7y \u0111\u1ee7 v\u1ec1 t\u1ea5t c\u1ea3 c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng th\u1ed1ng k\u00ea t\u1ea1i <a href=\"https:\/\/1phantram.com\/blog\/thong-ke-co-ban\/\">h\u01b0\u1edbng d\u1eabn th\u1ed1ng k\u00ea c\u01a1 b\u1ea3n t\u1eeb A-Z<\/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 nhanh t\u1ea7n su\u1ea5t (%) t\u1eeb t\u1ea7n s\u1ed1 v\u00e0 t\u1ed5ng s\u1ed1 quan s\u00e1t, ph\u1ee5c v\u1ee5 l\u1eadp b\u1ea3ng t\u1ea7n s\u1ed1 ch\u00ednh x\u00e1c!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>T\u1ea7n su\u1ea5t l\u00e0 t\u1ec9 l\u1ec7 (ho\u1eb7c ph\u1ea7n tr\u0103m) bi\u1ec3u th\u1ecb m\u1ee9c \u0111\u1ed9 xu\u1ea5t hi\u1ec7n c\u1ee7a m\u1ed9t gi\u00e1 tr\u1ecb trong t\u1eadp d\u1eef li\u1ec7u so v\u1edbi t\u1ed5ng&#8230;<\/p>\n","protected":false},"author":1,"featured_media":1051,"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-41","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\/41","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=41"}],"version-history":[{"count":1,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/posts\/41\/revisions"}],"predecessor-version":[{"id":54,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/posts\/41\/revisions\/54"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/media\/1051"}],"wp:attachment":[{"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/media?parent=41"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/categories?post=41"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/tags?post=41"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}