{"id":92,"date":"2020-12-14T04:51:01","date_gmt":"2020-12-14T04:51:01","guid":{"rendered":"https:\/\/datasciencebasic.com\/?p=92"},"modified":"2021-03-14T08:33:25","modified_gmt":"2021-03-14T08:33:25","slug":"mot-so-khai-niem-xac-suat-thong-ke-co-ban-thuong-su-dung-trong-phan-tich-du-lieu-phan-1","status":"publish","type":"post","link":"https:\/\/datasciencebasic.com\/?p=92","title":{"rendered":"M\u1ed9t s\u1ed1 kh\u00e1i ni\u1ec7m x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea c\u01a1 b\u1ea3n th\u01b0\u1eddng s\u1eed d\u1ee5ng trong ph\u00e2n t\u00edch d\u1eef li\u1ec7u (Ph\u1ea7n 1)"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">X\u00e1c su\u1ea5t th\u1ed1ng k\u00ea \u0111\u00f3ng m\u1ed9t vai tr\u00f2 quan tr\u1ecdng trong c\u00e1c d\u1ef1 \u00e1n v\u1ec1 khoa h\u1ecdc d\u1eef li\u1ec7u. M\u1ecdi nh\u00e0 khoa h\u1ecdc d\u1eef li\u1ec7u \u0111\u1ec1u ph\u1ea3i \u00e1p d\u1ee5ng x\u00e1c su\u1ea5t th\u1ed1ng k\u00ea \u0111\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 b\u1ed9 d\u1eef li\u1ec7u v\u00e0 tr\u00edch xu\u1ea5t c\u00e1c th\u00f4ng tin chi ti\u1ebft. Do \u0111\u00f3, m\u1ed9t nh\u00e0 khoa h\u1ecdc d\u1eef li\u1ec7u nh\u1ea5t thi\u1ebft ph\u1ea3i hi\u1ec3u r\u00f5 v\u1ec1 c\u00e1c kh\u00e1i ni\u1ec7m th\u1ed1ng k\u00ea c\u01a1 b\u1ea3n.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Trong b\u00e0i vi\u1ebft n\u00e0y, t\u00f4i s\u1ebd cung c\u1ea5p cho b\u1ea1n th\u00f4ng tin chi ti\u1ebft v\u1ec1 c\u00e1c kh\u00e1i ni\u1ec7m th\u1ed1ng k\u00ea c\u01a1 b\u1ea3n th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong khoa h\u1ecdc d\u1eef li\u1ec7u v\u00e0 m\u1ed9t s\u1ed1 v\u00ed d\u1ee5 minh h\u1ecda<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. Ch\u1ecdn m\u1eabu (Sampling)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ch\u1ecdn m\u1eabu (sampling) l\u00e0 vi\u1ec7c l\u1ef1a ch\u1ecdn m\u1ed9t t\u1eadp h\u1ee3p con d\u1eef li\u1ec7u t\u1eeb to\u00e0n b\u1ed9 d\u1eef li\u1ec7u t\u1ed5ng th\u1ec3 (population). V\u00ed d\u1ee5 m\u1ed9t c\u00f4ng ty mu\u1ed1n hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 s\u1edf th\u00edch c\u1ee7a kh\u00e1ch h\u00e0ng. Vi\u1ec7c y\u00eau c\u1ea7u t\u1ea5t c\u1ea3 kh\u00e1ch h\u00e0ng tham gia v\u00e0o m\u1ed9t cu\u1ed9c kh\u1ea3o s\u00e1t \u0111\u00f4i khi kh\u00f4ng kh\u1ea3 thi do s\u1ed1 l\u01b0\u1ee3ng kh\u00e1ch h\u00e0ng l\u00e0 qu\u00e1 l\u1edbn. Khi \u0111\u00f3 ch\u00fang ta c\u1ea7n l\u1ef1a ch\u1ecdn m\u1ed9t nh\u00f3m \u0111\u1ed1i t\u01b0\u1ee3ng m\u1ee5c ti\u00eau t\u1eeb t\u1eadp h\u1ee3p to\u00e0n b\u1ed9 kh\u00e1ch h\u00e0ng c\u1ee7a c\u00f4ng ty \u0111\u1ec3 ti\u1ebfn h\u00e0nh kh\u1ea3o s\u00e1t, vi\u1ec7c l\u1ef1a ch\u1ecdn n\u00e0y ch\u00ednh l\u00e0 qu\u00e1 tr\u00ecnh ch\u1ecdn m\u1eabu (sampling). Trong khu\u00f4n kh\u1ed5 b\u00e0i vi\u1ebft n\u00e0y, t\u00f4i s\u1ebd ch\u1ec9 \u0111\u1ec1 c\u1ea5p \u0111\u1ebfn c\u00e1c ph\u01b0\u01a1ng ph\u00e1p ch\u1ecdn m\u1eabu theo x\u00e1c su\u1ea5t (probability sampling). Ch\u1ecdn m\u1eabu theo x\u00e1c su\u1ea5t d\u1ef1a tr\u00ean gi\u1ea3 \u0111\u1ecbnh l\u00e0 m\u1ecdi th\u00e0nh vi\u00ean c\u1ee7a qu\u1ea7n th\u1ec3 \u0111\u1ec1u c\u00f3 c\u01a1 h\u1ed9i \u0111\u01b0\u1ee3c ch\u1ecdn. \u0110\u00e2y l\u00e0 ph\u01b0\u01a1ng ph\u00e1p th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong nghi\u00ean c\u1ee9u \u0111\u1ecbnh l\u01b0\u1ee3ng \u0111\u1ec3 t\u1ea1o ra k\u1ebft qu\u1ea3 nghi\u00ean c\u1ee9u mang t\u00ednh \u0111\u1ea1i di\u1ec7n cho to\u00e0n b\u1ed9 t\u1ed5ng th\u1ec3. C\u00f3 b\u1ed1n ph\u01b0\u01a1ng ph\u00e1p ch\u1ecdn m\u1eabu theo x\u00e1c xu\u1ea5t ch\u00ednh:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>Ph\u01b0\u01a1ng ph\u00e1p ch\u1ecdn m\u1eabu ng\u1eabu nhi\u00ean \u0111\u01a1n gi\u1ea3n (Simple random sampling)<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ph\u01b0\u01a1ng ph\u00e1p ch\u1ecdn m\u1eabu ng\u1eabu nhi\u00ean \u0111\u01a1n gi\u1ea3n l\u00e0 ph\u01b0\u01a1ng ph\u00e1p m\u00e0 trong \u0111\u00f3 ch\u00fang ta ch\u1ec9 ch\u1ecdn m\u1eabu m\u1ed9t c\u00e1ch ng\u1eabu nhi\u00ean t\u1eeb d\u1eef li\u1ec7u t\u1ed5ng th\u1ec3.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">V\u00ed d\u1ee5 trong tr\u01b0\u1eddng h\u1ee3p kh\u1ea3o s\u00e1t kh\u00e1ch h\u00e0ng c\u1ee7a c\u00f4ng ty n\u00f3i tr\u00ean, b\u1ea1n mu\u1ed1n ch\u1ecdn ra ng\u1eabu nhi\u00ean 100 kh\u00e1ch h\u00e0ng t\u1eeb t\u1ed5ng s\u1ed1 1000 kh\u00e1ch h\u00e0ng c\u1ee7a c\u00f4ng ty. B\u1ea1n g\u00e1n cho m\u1ed7i kh\u00e1ch h\u00e0ng trong c\u01a1 s\u1edf d\u1eef li\u1ec7u m\u1ed9t m\u00e3 s\u1ed1 \u0111\u1ea1i di\u1ec7n (ID) t\u1eeb 1 \u0111\u1ebfn 1000, sau \u0111\u00f3 s\u1eed d\u1ee5ng tr\u00ecnh t\u1ea1o s\u1ed1 ng\u1eabu nhi\u00ean \u0111\u1ec3 t\u1ea1o ra 100 s\u1ed1 r\u1ed3i ch\u1ecdn c\u00e1c kh\u00e1ch h\u00e0ng c\u00f3 m\u00e3 s\u1ed1 ID n\u00e0y.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Nh\u01b0\u1ee3c \u0111i\u1ec3m c\u1ee7a ph\u01b0\u01a1ng ph\u00e1p n\u00e0y l\u00e0 ch\u00fang ta c\u00f3 th\u1ec3 v\u00f4 t\u00ecnh b\u1ecf qua nh\u1eefng d\u1eef li\u1ec7u quan tr\u1ecdng c\u00f3 trong b\u1ed9 d\u1eef li\u1ec7u g\u1ed1c, do \u0111\u00f3 m\u1eabu ch\u00fang ta ch\u1ecdn c\u00f3 th\u1ec3 kh\u00f4ng \u0111\u1ea1i di\u1ec7n \u0111\u01b0\u1ee3c cho t\u1ed5ng th\u1ec3.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>Ph\u01b0\u01a1ng ph\u00e1p ch\u1ecdn m\u1eabu<\/em><\/strong> <strong><em>c\u00f3 h\u1ec7 th\u1ed1ng (Systematic sampling)<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ch\u1ecdn m\u1eabu h\u1ec7 th\u1ed1ng t\u01b0\u01a1ng t\u1ef1 nh\u01b0 ch\u1ecdn m\u1eabu ng\u1eabu nhi\u00ean \u0111\u01a1n gi\u1ea3n, nh\u01b0ng c\u00f2n th\u01b0\u1eddng d\u1ec5 ti\u1ebfn h\u00e0nh h\u01a1n m\u1ed9t ch\u00fat. M\u1ecdi th\u00e0nh vi\u00ean c\u1ee7a qu\u1ea7n th\u1ec3 \u0111\u1ec1u \u0111\u01b0\u1ee3c g\u1eafn v\u1edbi m\u1ed9t con s\u1ed1, nh\u01b0ng thay v\u00ec ch\u1ecdn c\u00e1c s\u1ed1 ng\u1eabu nhi\u00ean, c\u00e1c c\u00e1 th\u1ec3 \u0111\u01b0\u1ee3c ch\u1ecdn theo m\u1ed9t quy lu\u1eadt nh\u1ea5t \u0111\u1ecbnh.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">V\u00ed d\u1ee5 t\u1ea5t c\u1ea3 1000 kh\u00e1ch h\u00e0ng c\u1ee7a c\u00f4ng ty \u0111\u01b0\u1ee3c li\u1ec7t k\u00ea theo s\u1ed1 th\u1ee9 t\u1ef1 t\u1eeb 1 \u0111\u1ebfn 1000. Trong 10 s\u1ed1 \u0111\u1ea7u ti\u00ean, b\u1ea1n ch\u1ecdn ng\u1eabu nhi\u00ean m\u1ed9t \u0111i\u1ec3m b\u1eaft \u0111\u1ea7u: s\u1ed1 8. T\u1eeb s\u1ed1 8 tr\u1edf \u0111i, c\u1ee9 c\u00e1ch 10 s\u1ed1 b\u1ea1n ch\u1ecdn m\u1ed9t s\u1ed1 (8, 18, 28, 38, v.v.), cu\u1ed1i c\u00f9ng b\u1ea1n s\u1ebd c\u00f3 \u0111\u01b0\u1ee3c m\u1ed9t m\u1eabu g\u1ed3m 100 kh\u00e1ch h\u00e0ng.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Khi s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p n\u00e0y, \u0111i\u1ec1u quan tr\u1ecdng l\u00e0 b\u1ea1n ph\u1ea3i ch\u1eafc ch\u1eafn kh\u00f4ng c\u00f3 quy lu\u1eadt \u1ea9n n\u00e0o trong vi\u1ec7c s\u1eafp x\u1ebfp c\u00e1c m\u1eabu c\u1ee7a t\u1ed5ng th\u1ec3 d\u1eabn \u0111\u1ebfn l\u00e0m thi\u00ean l\u1ec7ch vi\u1ec7c l\u1ef1a ch\u1ecdn. V\u00ed d\u1ee5: n\u1ebfu c\u01a1 s\u1edf d\u1eef li\u1ec7u kh\u00e1ch h\u00e0ng \u0111\u01b0\u1ee3c li\u1ec7t k\u00ea theo c\u00e1c nh\u00f3m, v\u00e0 trong m\u1ed7i nh\u00f3m kh\u00e1ch h\u00e0ng l\u1ea1i \u0111\u01b0\u1ee3c s\u1eafp x\u1ebfp theo th\u1ee9 t\u1ef1 t\u1eeb m\u1edbi \u0111\u1ebfn c\u0169, th\u00ec r\u1ea5t c\u00f3 th\u1ec3 v\u1edbi c\u00e1ch ch\u1ecdn m\u1eabu nh\u01b0 tr\u00ean b\u1ea1n s\u1ebd ch\u1ecdn h\u1ea7u h\u1ebft kh\u00e1ch h\u00e0ng c\u0169 m\u00e0 b\u1ecf qua c\u00e1c kh\u00e1ch h\u00e0ng m\u1edbi.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>Ph\u01b0\u01a1ng ph\u00e1p ch\u1ecdn m\u1eabu ph\u00e2n t\u1ea7ng (Stratified sampling)<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ch\u1ecdn m\u1eabu ph\u00e2n t\u1ea7ng d\u1ef1a v\u00e0o vi\u1ec7c ph\u00e2n chia to\u00e0n b\u1ed9 qu\u1ea7n th\u1ec3 th\u00e0nh c\u00e1c t\u1eadp h\u1ee3p con c\u00f3 c\u00e1c \u0111\u1eb7c t\u00ednh kh\u00e1c bi\u1ec7t nhau. \u0110i\u1ec1u \u0111\u00f3 cho ph\u00e9p b\u1ea1n r\u00fat ra k\u1ebft lu\u1eadn ch\u00ednh x\u00e1c h\u01a1n b\u1eb1ng c\u00e1ch \u0111\u1ea3m b\u1ea3o r\u1eb1ng m\u1ecdi t\u1eadp h\u1ee3p con \u0111\u1ec1u \u0111\u01b0\u1ee3c th\u1ec3 hi\u1ec7n \u0111\u00fang trong m\u1eabu.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0110\u1ec3 s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p ch\u1ecdn m\u1eabu n\u00e0y, b\u1ea1n chia to\u00e0n b\u1ed9 qu\u1ea7n th\u1ec3 th\u00e0nh c\u00e1c t\u1eadp h\u1ee3p con (\u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u201cstrata &#8211; t\u1ea7ng l\u1edbp\u201d) d\u1ef1a tr\u00ean c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m nh\u1ea5t \u0111\u1ecbnh (v\u00ed d\u1ee5: gi\u1edbi t\u00ednh, \u0111\u1ed9 tu\u1ed5i, thu nh\u1eadp, v.v\u2026).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D\u1ef1a tr\u00ean t\u1ef7 l\u1ec7 c\u1ee7a m\u1ed7i t\u1eadp h\u1ee3p tr\u00ean to\u00e0n b\u1ed9 qu\u1ea7n th\u1ec3, b\u1ea1n t\u00ednh to\u00e1n c\u1ea7n ph\u1ea3i l\u1eaby m\u1eabu bao nhi\u00eau ng\u01b0\u1eddi t\u1eeb m\u1ed7i t\u1eadp h\u1ee3p con. Sau \u0111\u00f3, b\u1ea1n s\u1eed d\u1ee5ng c\u00e1ch ch\u1ecdn m\u1eabu ng\u1eabu nhi\u00ean ho\u1eb7c c\u00f3 h\u1ec7 th\u1ed1ng \u0111\u1ec3 ch\u1ecdn m\u1ed9t m\u1eabu t\u1eeb m\u1ed7i t\u1eadp h\u1ee3p con n\u00e0y.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">V\u00ed d\u1ee5, c\u00f4ng ty c\u00f3 600 kh\u00e1ch h\u00e0ng n\u1eef v\u00e0 400 kh\u00e1ch h\u00e0ng nam. B\u1ea1n mu\u1ed1n \u0111\u1ea3m b\u1ea3o r\u1eb1ng m\u1eabu c\u0169ng ph\u1ea3n \u00e1nh \u0111\u00fang t\u1ec9 l\u1ec7 gi\u1edbi t\u00ednh c\u1ee7a kh\u00e1ch h\u00e0ng, v\u00ec v\u1eady b\u1ea1n s\u1eafp x\u1ebfp to\u00e0n b\u1ed9 d\u1eef li\u1ec7u kh\u00e1ch h\u00e0ng th\u00e0nh hai t\u1eadp h\u1ee3p con d\u1ef1a tr\u00ean gi\u1edbi t\u00ednh. Sau \u0111\u00f3, tr\u00ean t\u1eadp h\u1ee3p kh\u00e1ch h\u00e0ng n\u1eef, b\u1ea1n ch\u1ecdn ng\u1eabu nhi\u00ean 60 m\u1eabu, v\u00e0 ch\u1ecdn ng\u1eabu nhi\u00ean 40 m\u1eabu tr\u00ean t\u1eadp h\u1ee3p kh\u00e1ch h\u00e0ng nam. K\u1ebft qu\u1ea3 l\u00e0 b\u1ea1n c\u00f3 m\u1ed9t m\u1eabu 100 kh\u00e1ch h\u00e0ng v\u1edbi \u0111\u00fang t\u1ec9 l\u1ec7 gi\u1edbi t\u00ednh c\u1ee7a to\u00e0n b\u1ed9 kh\u00e1ch h\u00e0ng c\u1ee7a c\u00f4ng ty.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>Ph\u01b0\u01a1ng ph\u00e1p ch\u1ecdn m\u1eabu theo c\u1ee5m (Cluster sampling)<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ch\u1ecdn m\u1eabu theo c\u1ee5m c\u0169ng li\u00ean quan \u0111\u1ebfn vi\u1ec7c ph\u00e2n chia to\u00e0n b\u1ed9 qu\u1ea7n th\u1ec3 th\u00e0nh c\u00e1c t\u1eadp h\u1ee3p con (\u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u201ccluster \u2013 c\u1ee5m\u201d), nh\u01b0ng m\u1ed7i t\u1eadp h\u1ee3p con ph\u1ea3i c\u00f3 c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m t\u01b0\u01a1ng t\u1ef1 v\u1edbi to\u00e0n b\u1ed9 qu\u1ea7n th\u1ec3. Thay v\u00ec ch\u1ecdn m\u1ed9t s\u1ed1 c\u00e1 th\u1ec3 t\u1eeb t\u1ea5t c\u1ea3 c\u00e1c c\u1ee5m, b\u1ea1n s\u1ebd ch\u1ec9 ch\u1ecdn ng\u1eabu nhi\u00ean m\u1ed9t s\u1ed1 c\u1ee5m nh\u1ea5t \u0111\u1ecbnh.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">N\u1ebfu th\u1ef1c t\u1ebf cho ph\u00e9p, b\u1ea1n c\u00f3 th\u1ec3 ch\u1ecdn h\u1ebft t\u1ea5t c\u1ea3 c\u00e1c c\u00e1 th\u1ec3 t\u1eeb m\u1ed7i c\u1ee5m d\u1eef li\u1ec7u. N\u1ebfu c\u00e1c c\u1ee5m qu\u00e1 l\u1edbn, b\u1ea1n c\u0169ng c\u00f3 th\u1ec3 ch\u1ecdn ch\u1ec9 m\u1ed9t s\u1ed5 c\u00e1 th\u1ec3 t\u1eeb m\u1ed7i c\u1ee5m b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng m\u1ed9t trong c\u00e1c k\u1ef9 thu\u1eadt ch\u1ecdn m\u1eabu \u1edf tr\u00ean.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ph\u01b0\u01a1ng ph\u00e1p n\u00e0y h\u1eefu \u00edch \u0111\u1ec3 x\u1eed l\u00fd c\u00e1c qu\u1ea7n th\u1ec3 l\u1edbn v\u00e0 ph\u00e2n t\u00e1n, nh\u01b0ng c\u00f3 nhi\u1ec1u r\u1ee7i ro sai s\u00f3t h\u01a1n trong m\u1eabu, v\u00ec c\u00f3 th\u1ec3 c\u00f3 s\u1ef1 kh\u00e1c bi\u1ec7t \u0111\u00e1ng k\u1ec3 gi\u1eefa c\u00e1c c\u1ee5m. R\u1ea5t kh\u00f3 \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o r\u1eb1ng c\u00e1c c\u1ee5m \u0111\u01b0\u1ee3c ch\u1ecdn th\u1ef1c s\u1ef1 \u0111\u1ea1i di\u1ec7n cho to\u00e0n b\u1ed9 qu\u1ea7n th\u1ec3.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">V\u00ed d\u1ee5 c\u00f4ng ty n\u00f3i tr\u00ean c\u00f3 chi nh\u00e1nh t\u1ea1i 10 th\u00e0nh ph\u1ed1 tr\u00ean to\u00e0n qu\u1ed1c (t\u1ea5t c\u1ea3 \u0111\u1ec1u c\u00f3 s\u1ed1 l\u01b0\u1ee3ng kh\u00e1ch h\u00e0ng v\u00e0 c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a kh\u00e1ch h\u00e0ng g\u1ea7n nh\u01b0 t\u01b0\u01a1ng t\u1ef1). B\u1ea1n kh\u00f4ng c\u00f3 kh\u1ea3 n\u0103ng \u0111i \u0111\u1ebfn m\u1ecdi v\u0103n ph\u00f2ng \u0111\u1ec3 ti\u1ebfn h\u00e0nh kh\u1ea3o s\u00e1t, v\u00ec v\u1eady, b\u1ea1n s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p l\u1ea5y m\u1eabu ng\u1eabu nhi\u00ean \u0111\u1ec3 ch\u1ecdn ra 3 v\u0103n ph\u00f2ng &#8211; \u0111\u00e2y l\u00e0 c\u00e1c c\u1ee5m c\u1ee7a b\u1ea1n &#8211; r\u1ed3i t\u1eeb \u0111\u00f3 b\u1ea1n ch\u1ecdn ra ti\u1ebfp c\u00e1c c\u00e1 th\u1ec3 t\u1eeb m\u1ed7i c\u1ee5m n\u00e0y theo m\u1ed9t trong ba c\u00e1ch n\u00eau tr\u00ean.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. Th\u1ed1ng k\u00ea m\u00f4 t\u1ea3 (descriptive statistics)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Th\u1ed1ng k\u00ea m\u00f4 t\u1ea3 cung c\u1ea5p ph\u00e2n t\u00edch c\u1ea5p cao v\u1ec1 c\u00e1c t\u00ednh n\u0103ng kh\u00e1c nhau c\u00f3 trong t\u1eadp d\u1eef li\u1ec7u. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 k\u1ef9 thu\u1eadt th\u1ed1ng k\u00ea m\u00f4 t\u1ea3 th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>Bi\u1ec3u \u0111\u1ed3 Histogram<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bi\u1ec3u \u0111\u1ed3 Histogram r\u1ea5t h\u1eefu \u00edch \u0111\u1ec3 hi\u1ec3u s\u1ef1 ph\u00e2n b\u1ed1 c\u1ee7a c\u00e1c thu\u1ed9c t\u00ednh trong t\u1eadp d\u1eef li\u1ec7u. Vi\u1ec7c hi\u1ec3u s\u1ef1 ph\u00e2n b\u1ed1 c\u1ee7a c\u00e1c thu\u1ed9c t\u00ednh trong t\u1eadp d\u1eef li\u1ec7u r\u1ea5t quan tr\u1ecdng, v\u00ec n\u00f3 s\u1ebd quy\u1ebft \u0111\u1ecbnh vi\u1ec7c c\u1ea7n l\u1ef1a ch\u1ecdn thu\u1eadt to\u00e1n n\u00e0o \u0111\u1ec3 ph\u00e2n t\u00edch d\u1ef1 \u0111o\u00e1n. V\u00ed d\u1ee5, khi ch\u00fang ta s\u1eed d\u1ee5ng thu\u1eadt to\u00e1n h\u1ed3i quy tuy\u1ebfn t\u00ednh (linear regression), m\u1ed9t trong nh\u1eefng gi\u1ea3 \u0111\u1ecbnh (assumption) l\u00e0 c\u00e1c thu\u1ed9c t\u00ednh \u0111\u1ec1u c\u00f3 ph\u00e2n ph\u1ed1i chu\u1ea9n (normal distribution). D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t v\u00ed d\u1ee5 v\u1ec1 bi\u1ec3u \u0111\u1ed5 Histogram c\u1ee7a m\u1ed9t ph\u00e2n ph\u1ed1i chu\u1ea9n:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"363\" height=\"317\" src=\"https:\/\/i0.wp.com\/datasciencebasic.com\/wp-content\/uploads\/2021\/03\/normal-distribution.png?resize=363%2C317&#038;ssl=1\" alt=\"\" class=\"wp-image-93\" srcset=\"https:\/\/i0.wp.com\/datasciencebasic.com\/wp-content\/uploads\/2021\/03\/normal-distribution.png?w=363&amp;ssl=1 363w, https:\/\/i0.wp.com\/datasciencebasic.com\/wp-content\/uploads\/2021\/03\/normal-distribution.png?resize=300%2C262&amp;ssl=1 300w\" sizes=\"auto, (max-width: 363px) 100vw, 363px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Ngu\u1ed3n: <a href=\"https:\/\/libguides.library.kent.edu\/SPSS\/FrequenciesContinuous\">https:\/\/libguides.library.kent.edu\/SPSS\/FrequenciesContinuous<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>Xu h\u01b0\u1edbng t\u1eadp trung (central tendency)<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C\u00e1c th\u01b0\u1edbc \u0111o kh\u00e1c nhau c\u1ee7a xu h\u01b0\u1edbng t\u1eadp trung l\u00e0 gi\u00e1 tr\u1ecb trung b\u00ecnh (mean), trung v\u1ecb (median) v\u00e0 y\u1ebfu v\u1ecb (mode), nh\u1eefng gi\u00e1 tr\u1ecb n\u00e0y \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111i\u1ec3m trung t\u00e2m trong ph\u00e2n ph\u1ed1i. Nh\u00ecn chung, gi\u00e1 tr\u1ecb trung b\u00ecnh l\u00e0 m\u1ed9t th\u01b0\u1edbc \u0111o t\u1ed1t \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111i\u1ec3m trung t\u00e2m. Trong tr\u01b0\u1eddng h\u1ee3p d\u1eef li\u1ec7u b\u1ecb l\u1ec7ch (skew), trung v\u1ecb c\u00f3 th\u1ec3 l\u00e0 th\u01b0\u1edbc \u0111o t\u1ed1t h\u01a1n v\u00e0 trong tr\u01b0\u1eddng h\u1ee3p d\u1eef li\u1ec7u c\u00f3 d\u1ea1ng th\u1ee9 t\u1ef1 (ordinal), s\u1eed d\u1ee5ng trung v\u1ecb ho\u1eb7c y\u1ebfu v\u1ecb s\u1ebd t\u1ed1t h\u01a1n l\u00e0 gi\u00e1 tr\u1ecb trung b\u00ecnh.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"510\" src=\"https:\/\/i0.wp.com\/datasciencebasic.com\/wp-content\/uploads\/2021\/03\/skewness.png?resize=722%2C510&#038;ssl=1\" alt=\"\" class=\"wp-image-94\" srcset=\"https:\/\/i0.wp.com\/datasciencebasic.com\/wp-content\/uploads\/2021\/03\/skewness.png?w=722&amp;ssl=1 722w, https:\/\/i0.wp.com\/datasciencebasic.com\/wp-content\/uploads\/2021\/03\/skewness.png?resize=300%2C212&amp;ssl=1 300w, https:\/\/i0.wp.com\/datasciencebasic.com\/wp-content\/uploads\/2021\/03\/skewness.png?resize=720%2C509&amp;ssl=1 720w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Ngu\u1ed3n: <a href=\"https:\/\/guides.douglascollege.ca\/stats\/centraltendency\">https:\/\/guides.douglascollege.ca\/stats\/centraltendency<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>\u0110\u1ed9 nghi\u00eang (skewness) v\u00e0 \u0111\u1ed9 nh\u1ecdn (kurtosis)<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0110\u1ed9 nghi\u00eang (skewness) \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh xem ph\u00e2n ph\u1ed1i l\u00e0 \u0111\u1ed1i x\u1ee9ng (t\u1ee9c l\u00e0 ph\u00e2n ph\u1ed1i chu\u1ea9n) hay kh\u00f4ng \u0111\u1ed1i x\u1ee9ng (ph\u00e2n ph\u1ed1i l\u1ec7ch). Khi gi\u00e1 tr\u1ecb c\u1ee7a \u0111\u1ed9 l\u1ec7ch b\u1eb1ng 0 th\u00ec \u0111i\u1ec1u \u0111\u00f3 c\u00f3 ngh\u0129a l\u00e0 ph\u00e2n ph\u1ed1i l\u00e0 chu\u1ea9n. Gi\u00e1 tr\u1ecb \u00e2m c\u00f3 ngh\u0129a l\u00e0 d\u1eef li\u1ec7u b\u1ecb l\u1ec7ch \u00e2m ngh\u0129a l\u00e0 c\u00f3 m\u1ed9t \u0111u\u00f4i d\u00e0i \u1edf b\u00ean tr\u00e1i c\u1ee7a ph\u00e2n ph\u1ed1i v\u00e0 l\u1ec7ch d\u01b0\u01a1ng c\u00f3 ngh\u0129a l\u00e0 c\u00f3 m\u1ed9t \u0111u\u00f4i d\u00e0i \u1edf b\u00ean ph\u1ea3i c\u1ee7a ph\u00e2n ph\u1ed1i.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">R\u1ea5t nhi\u1ec1u d\u1eef li\u1ec7u t\u00e0i ch\u00ednh s\u1ebd b\u1ecb l\u1ec7ch v\u1ec1 ph\u00eda b\u00ean ph\u1ea3i (\u0111\u1ed9 l\u1ec7ch d\u01b0\u01a1ng), v\u00ed d\u1ee5 t\u00e0i s\u1ea3n c\u1ee7a c\u00e1c c\u00e1 nh\u00e2n, gi\u00e1 nh\u00e0 \u1edf, d\u1eef li\u1ec7u chi ti\u00eau v.v&#8230; Trong t\u1ea5t c\u1ea3 nh\u1eefng tr\u01b0\u1eddng h\u1ee3p n\u00e0y, gi\u00e1 tr\u1ecb trung b\u00ecnh v\u00e0 trung v\u1ecb s\u1ebd cao h\u01a1n nhi\u1ec1u so v\u1edbi y\u1ebfu v\u1ecb, v\u00ec m\u1eb7c d\u00f9 ph\u1ea7n l\u1edbn c\u00e1c gi\u00e1 tr\u1ecb s\u1ebd n\u1eb1m xung quanh y\u1ebfu v\u1ecb, s\u1ebd c\u00f3 m\u1ed9t s\u1ed1 \u00edt c\u00e1c quan s\u00e1t c\u00f3 gi\u00e1 tr\u1ecb r\u1ea5t cao (v\u00ed d\u1ee5 m\u1ed9t v\u00e0i ng\u01b0\u1eddi gi\u00e0u nh\u1ea5t s\u1ebd c\u00f3 t\u00e0i s\u1ea3n v\u01b0\u1ee3t xa s\u1ed1 \u0111\u00f4ng). Trong khi x\u00e2y d\u1ef1ng m\u00f4 h\u00ecnh d\u1ef1 \u0111o\u00e1n, ch\u00fang ta kh\u00f4ng th\u1ec3 b\u1ecf qua nh\u1eefng gi\u00e1 tr\u1ecb \u0111\u00f3, nh\u01b0ng \u0111\u1ed3ng th\u1eddi c\u0169ng kh\u00f4ng th\u1ec3 \u0111\u01b0a ngay c\u00e1c gi\u00e1 tr\u1ecb n\u00e0y v\u00e0o m\u00f4 h\u00ecnh, v\u00ec nhi\u1ec1u m\u00f4 h\u00ecnh d\u1ef1 \u0111o\u00e1n s\u1ebd kh\u00f4ng s\u1eed d\u1ee5ng \u0111\u01b0\u1ee3c v\u1edbi c\u00e1c d\u1eef li\u1ec7u c\u00f3 ph\u00e2n ph\u1ed1i l\u1ec7ch. Trong c\u00e1c tr\u01b0\u1eddng h\u1ee3p n\u00e0y, b\u1ea1n s\u1ebd c\u1ea7n ph\u1ea3i s\u1eed d\u1ee5ng c\u00e1c k\u1ef9 thu\u1eadt chuy\u1ec3n \u0111\u1ed5i d\u1eef li\u1ec7u ph\u00f9 h\u1ee3p.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0110\u1ed9 nh\u1ecdn (kurtosis) c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u01b0\u1edbc t\u00ednh s\u1ed1 l\u01b0\u1ee3ng c\u00e1c gi\u00e1 tr\u1ecb ngo\u1ea1i l\u1ec7 trong d\u1eef li\u1ec7u. Gi\u00e1 tr\u1ecb kurtosis b\u1eb1ng 0 c\u00f3 ngh\u0129a l\u00e0 ph\u00e2n ph\u1ed1i l\u00e0 ph\u00e2n ph\u1ed1i chu\u1ea9n v\u1edbi kh\u00f4ng nhi\u1ec1u gi\u00e1 tr\u1ecb ngo\u1ea1i l\u1ec7. Gi\u00e1 tr\u1ecb kurtosis cao cho th\u1ea5y r\u1eb1ng c\u00f3 th\u1ec3 c\u00f3 nhi\u1ec1u gi\u00e1 tr\u1ecb ngo\u1ea1i l\u1ec7 trong d\u1eef li\u1ec7u v\u00e0 kurtosis th\u1ea5p c\u00f3 ngh\u0129a l\u00e0 \u00edt ngo\u1ea1i l\u1ec7 h\u01a1n trong d\u1eef li\u1ec7u.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"568\" height=\"144\" src=\"https:\/\/i0.wp.com\/datasciencebasic.com\/wp-content\/uploads\/2021\/03\/kurtosis.png?resize=568%2C144&#038;ssl=1\" alt=\"\" class=\"wp-image-95\" srcset=\"https:\/\/i0.wp.com\/datasciencebasic.com\/wp-content\/uploads\/2021\/03\/kurtosis.png?w=568&amp;ssl=1 568w, https:\/\/i0.wp.com\/datasciencebasic.com\/wp-content\/uploads\/2021\/03\/kurtosis.png?resize=300%2C76&amp;ssl=1 300w\" sizes=\"auto, (max-width: 568px) 100vw, 568px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">Ngu\u1ed3n: <a href=\"https:\/\/community.sw.siemens.com\/s\/article\/kurtosis\">https:\/\/community.sw.siemens.com\/s\/article\/kurtosis<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C\u1ea3 \u0111\u1ed9 nghi\u00eang (skewness) v\u00e0 \u0111\u1ed9 nh\u1ecdn (kurtosis) \u0111\u1ec1u h\u1eefu \u00edch \u0111\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 s\u1ef1 ph\u00e2n b\u1ed1 c\u1ee7a d\u1eef li\u1ec7u, t\u1eeb \u0111\u00f3 \u0111\u01b0a ra ph\u01b0\u01a1ng \u00e1n x\u1eed l\u00fd n\u1ebfu ph\u00e1t hi\u1ec7n th\u1ea5y t\u1eadp d\u1eef li\u1ec7u kh\u00f4ng c\u00f3 ph\u00e2n ph\u1ed1i g\u1ea7n nh\u01b0 ph\u00e2n ph\u1ed1i chu\u1ea9n. Ch\u1eb3ng h\u1ea1n n\u1ebfu nh\u01b0 n\u1ebfu d\u1eef li\u1ec7u b\u1ecb l\u1ec7ch nhi\u1ec1u v\u00e0\/ ho\u1eb7c c\u00f3 m\u1ed9t s\u1ed1 l\u01b0\u1ee3ng l\u1edbn c\u00e1c gi\u00e1 tr\u1ecb ngo\u1ea1i l\u1ec7 th\u00ec c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng ph\u00e9p bi\u1ebfn \u0111\u1ed5i ph\u00f9 h\u1ee3p nh\u01b0 l\u1ea5y logarit \u0111\u1ec3 x\u1eed l\u00fd d\u1eef li\u1ec7u tr\u01b0\u1edbc khi ti\u1ebfn h\u00e0nh ph\u00e2n t\u00edch.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>\u0110\u1ed9 bi\u1ebfn \u0111\u1ed9ng c\u1ee7a d\u1eef li\u1ec7u<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0110\u1ed9 bi\u1ebfn \u0111\u1ed9ng c\u1ee7a d\u1eef li\u1ec7u trong th\u1ed1ng k\u00ea (variability) \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u0111o l\u01b0\u1eddng s\u1ef1 ph\u00e2n b\u1ed1 c\u1ee7a d\u1eef li\u1ec7u xung quanh gi\u00e1 tr\u1ecb trung b\u00ecnh. C\u00e1c ph\u01b0\u01a1ng ph\u00e1p kh\u00e1c nhau c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u0111o \u0111\u1ed9 bi\u1ebfn \u0111\u1ed9ng c\u1ee7a d\u1eef li\u1ec7u l\u00e0 gi\u00e1 tr\u1ecb ph\u00e2n v\u1ecb (percentile), \u0111\u1ed9 l\u1ec7ch chu\u1ea9n (standard deviation) v\u00e0 ph\u01b0\u01a1ng sai (variance).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ch\u1eb3ng h\u1ea1n m\u1ed9t c\u00f4ng ty th\u01b0\u01a1ng m\u1ea1i \u0111i\u1ec7n t\u1eed \u0111ang th\u1ef1c hi\u1ec7n m\u1ed9t s\u1ed1 thay \u0111\u1ed5i v\u1ec1 thi\u1ebft k\u1ebf \u0111\u1ec3 c\u1ea3i thi\u1ec7n th\u1eddi gian m\u1ed7i kh\u00e1ch h\u00e0ng c\u1ea7n s\u1eed d\u1ee5ng \u0111\u1ec3 th\u1ef1c hi\u1ec7n m\u1ed9t giao d\u1ecbch. Tr\u01b0\u1edbc khi thay \u0111\u1ed5i thi\u1ebft k\u1ebf, th\u1eddi gian ho\u00e0n th\u00e0nh m\u1ed9t giao d\u1ecbch trung b\u00ecnh l\u00e0 10 ph\u00fat v\u1edbi \u0111\u1ed9 l\u1ec7ch chu\u1ea9n 2 ph\u00fat. Sau khi thay \u0111\u1ed5i thi\u1ebft k\u1ebf, th\u1eddi gian c\u1ea7n thi\u1ebft \u0111\u1ec3 ho\u00e0n th\u00e0nh giao d\u1ecbch trung b\u00ecnh l\u00e0 9 ph\u00fat v\u1edbi \u0111\u1ed9 l\u1ec7ch chu\u1ea9n 3 ph\u00fat. T\u1eeb \u0111\u00e2y c\u00f3 th\u1ec3 \u0111\u00e1nh gi\u00e1 s\u1ef1 thay \u0111\u1ed1i thi\u1ebft k\u1ebf \u0111\u00e3 c\u00f3 t\u00e1c d\u1ee5ng l\u00e0m gi\u1ea3m th\u1eddi gian ho\u00e0n th\u00e0nh giao d\u1ecbch, nh\u01b0ng m\u1ee9c \u0111\u1ed9 t\u00e1c d\u1ee5ng c\u1ee5 th\u1ec3 l\u00ean m\u1ed7i kh\u00e1ch h\u00e0ng l\u00e0 kh\u00e1c nhau.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ngo\u00e0i ra, vi\u1ec7c t\u00ednh to\u00e1n \u0111\u1ed9 bi\u1ebfn \u0111\u1ed9ng c\u1ee7a d\u1eef li\u1ec7u c\u0169ng s\u1ebd l\u00e0 c\u01a1 s\u1edf \u0111\u1ec3 c\u00e1c thu\u1eadt to\u00e1n d\u1ef1a tr\u00ean kho\u1ea3ng c\u00e1ch nh\u01b0 K-Means ho\u1eb7c KNN.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>X\u00e1c su\u1ea5t th\u1ed1ng k\u00ea \u0111\u00f3ng m\u1ed9t vai tr\u00f2 quan tr\u1ecdng trong c\u00e1c d\u1ef1 \u00e1n v\u1ec1 khoa h\u1ecdc d\u1eef li\u1ec7u. M\u1ecdi [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[3],"tags":[],"class_list":["post-92","post","type-post","status-publish","format-standard","hentry","category-kien-thuc"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=\/wp\/v2\/posts\/92","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=92"}],"version-history":[{"count":3,"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=\/wp\/v2\/posts\/92\/revisions"}],"predecessor-version":[{"id":102,"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=\/wp\/v2\/posts\/92\/revisions\/102"}],"wp:attachment":[{"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=92"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=92"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/datasciencebasic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=92"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}