{"id":28565,"date":"2023-12-07T05:14:26","date_gmt":"2023-12-07T05:14:26","guid":{"rendered":"https:\/\/masterskills.org\/blog\/bieu-do-hop-box-plot-la-gi-dac-trung-va-vi-du.html"},"modified":"2023-12-22T21:38:10","modified_gmt":"2023-12-22T14:38:10","slug":"bieu-do-hop-box-plot-la-gi-dac-trung-va-vi-du","status":"publish","type":"post","link":"https:\/\/masterskills.org\/blog\/bieu-do-hop-box-plot-la-gi-dac-trung-va-vi-du.html","title":{"rendered":"Bi\u1ec3u \u0111\u1ed3 h\u1ed9p (Box Plot) l\u00e0 g\u00ec? \u0110\u1eb7c tr\u01b0ng v\u00e0 v\u00ed d\u1ee5"},"content":{"rendered":"
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H\u00ecnh minh h\u1ecda<\/p>\n<\/div>\n<\/div>\n

Bi\u1ec3u \u0111\u1ed3 h\u1ed9p (Box Plot)<\/font><\/h2>\n

\u0110\u1ecbnh ngh\u0129a<\/b><\/p>\n

Bi\u1ec3u \u0111\u1ed3 h\u1ed9p<\/b> trong ti\u1ebfng Anh l\u00e0 Box Plot<\/b> hay Box and Whisker plot<\/b>.<\/p>\n

Bi\u1ec3u \u0111\u1ed3 h\u1ed9p<\/i> do John Tukey s\u00e1ng t\u1ea1o ra n\u0103m 1977.<\/p>\n

Bi\u1ec3u \u0111\u1ed3 h\u1ed9p (Box plot)<\/i> hay c\u00f2n g\u1ecdi l\u00e0 bi\u1ec3u \u0111\u1ed3 h\u1ed9p v\u00e0 r\u00e2u (Box and whisker plot)<\/i> l\u00e0 bi\u1ec3u \u0111\u1ed3 di\u1ec5n t\u1ea3 5 v\u1ecb tr\u00ed ph\u00e2n b\u1ed1 c\u1ee7a d\u1eef li\u1ec7u, \u0111\u00f3 l\u00e0: gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t (min), t\u1ee9 ph\u00e2n v\u1ecb th\u1ee9 nh\u1ea5t (Q1), trung v\u1ecb (median), t\u1ee9 ph\u00e2n v\u1ecb th\u1ee9 3 (Q3) v\u00e0 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t (max).<\/p>\n

\u0110\u1eb7c tr\u01b0ng c\u1ee7a bi\u1ec3u \u0111\u1ed3 h\u1ed9p<\/font><\/h3>\n

– Bi\u1ec3u \u0111\u1ed3 h\u1ed9p<\/b> gi\u00fap bi\u1ec3u di\u1ec5n c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng quan tr\u1ecdng c\u1ee7a d\u00e3y s\u1ed1 nh\u01b0 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t (min), gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t (max), t\u1ee9 ph\u00e2n v\u1ecb (quartile), kho\u1ea3ng bi\u1ebfn thi\u00ean t\u1ee9 ph\u00e2n v\u1ecb (Interquartile Range) m\u1ed9t c\u00e1ch tr\u1ef1c quan, d\u1ec5 hi\u1ec3u.<\/p>\n

– Tr\u00ean bi\u1ec3u \u0111\u1ed3 h\u1ed9p, ngo\u00e0i c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng s\u1ed1 trung b\u00ecnh, trung v\u1ecb, c\u00f2n th\u1ec3 hi\u1ec7n m\u1ed9t s\u1ed1 th\u00f4ng s\u1ed1 sau:<\/p>\n

(1) S\u1ed1 ph\u00e2n t\u1eed hay c\u00f2n g\u1ecdi l\u00e0 t\u1ee9 ph\u00e2n v\u1ecb (Quartiles): T\u1ee9 ph\u00e2n v\u1ecb l\u00e0 \u0111\u1ea1i l\u01b0\u1ee3ng m\u00f4 t\u1ea3 s\u1ef1 ph\u00e2n b\u1ed1 v\u00e0 s\u1ef1 ph\u00e2n t\u00e1n c\u1ee7a t\u1eadp d\u1eef li\u1ec7u. S\u1ed1 ph\u00e2n t\u1eed c\u00f3 3 gi\u00e1 tr\u1ecb, \u0111\u00f3 l\u00e0 s\u1ed1 ph\u00e2n t\u1eed th\u1ee9 nh\u1ea5t (Q1), th\u1ee9 nh\u00ec (Q2) v\u00e0 th\u1ee9 ba (Q3). Ba gi\u00e1 tr\u1ecb n\u00e0y chia m\u1ed9t t\u1eadp h\u1ee3p d\u1eef li\u1ec7u (\u0111\u00e3 s\u1eafp x\u1ebfp d\u1eef li\u1ec7u theo tr\u1eadt t\u1eeb b\u00e9 \u0111\u1ebfn l\u1edbn) th\u00e0nh 4 ph\u1ea7n c\u00f3 s\u1ed1 l\u01b0\u1ee3ng quan s\u00e1t \u0111\u1ec1u nhau.<\/p>\n

T\u1ee9 ph\u00e2n v\u1ecb \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh nh\u01b0 sau:<\/p>\n

+ S\u1eafp x\u1ebfp c\u00e1c s\u1ed1 theo th\u1ee9 t\u1ef1 t\u0103ng d\u1ea7n<\/p>\n

+ C\u1eaft d\u00e3y s\u1ed1 th\u00e0nh 4 ph\u1ea7n b\u1eb1ng nhau<\/p>\n

+ T\u1ee9 ph\u00e2n v\u1ecb l\u00e0 c\u00e1c gi\u00e1 tr\u1ecb t\u1ea1i v\u1ecb tr\u00ed c\u1eaft<\/p>\n

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(2) Kho\u1ea3ng bi\u1ebfn thi\u00ean s\u1ed1 ph\u00e2n t\u1eed (Interquartile Range – IQR) IQR \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh nh\u01b0 sau:<\/p>\n

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V\u00ed d\u1ee5<\/font><\/h3>\n

X\u00e9t m\u1ed9t v\u00ed d\u1ee5 v\u1ec1 vi\u1ec7c s\u1eed d\u1ee5ng bi\u1ec3u \u0111\u1ed3 h\u1ed9p:<\/p>\n

D\u01b0\u1edbi \u0111\u00e2y m\u00f4 t\u1ea3 s\u1eed d\u1ee5ng bi\u1ec3u \u0111\u1ed3 h\u1ed9p \u0111\u1ec3 ph\u00e2n t\u00edch, nh\u1eadn bi\u1ebft v\u1ea5n \u0111\u1ec1.<\/p>\n

V\u00ed d\u1ee5, v\u1edbi s\u1ed1 li\u1ec7u thu th\u1eadp \u0111\u01b0\u1ee3c v\u1ec1 t\u1ec9<\/span> l\u1ec7 l\u00e0m l\u1ea1i (Rework Ratio) trong qu\u00e1 tr\u00ecnh s\u1ea3n xu\u1ea5t, (c\u00f3 xmin<\/sub> = 0,0; Q1 = 14,9; x = 19,0; x = 15,8; Q3 = 20,6; xmax<\/sub> =23,2) ta c\u00f3 bi\u1ec3u \u0111\u1ed3 h\u1ed9p v\u1edbi h\u00ecnh d\u00e1ng bi\u1ec3u \u0111\u1ed3 nh\u01b0 sau:<\/p>\n

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Ngu\u1ed3n: 6 Sigma – N\u1ed9i dung c\u01a1 b\u1ea3n v\u00e0 h\u01b0\u1edbng d\u1eabn \u00e1p d\u1ee5ng, NXB H\u1ed3ng \u0110\u1ee9c<\/p>\n<\/div>\n<\/div>\n

Trung b\u00ecnh t\u1ec9<\/span> l\u1ec7 l\u00e0m l\u1ea1i l\u00e0 15,8%, trung v\u1ecb l\u00e0 19%.<\/p>\n

D\u1eef li\u1ec7u c\u00f3 xu h\u01b0\u1edbng nghi\u00eang nhi\u1ec1u v\u1ec1 ph\u00eda tr\u00ean gi\u00e1 tr\u1ecb trung b\u00ecnh.<\/p>\n

Kho\u1ea3ng s\u1ed1 ph\u00e2n t\u1eed = Q3 – Q1 = 20,6 – 14,9 = 5,7<\/p>\n

Kho\u1ea3ng c\u00e1ch gi\u1eefa gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 nh\u1ecf nh\u1ea5t l\u00e0 23,2 – 0 = 23,2.<\/p>\n

Nh\u00ecn chung, t\u1ec9<\/span> l\u1ec7 l\u00e0m l\u1ea1i cao v\u00e0 qu\u00e1 tr\u00ecnh c\u00f3 s\u1ef1 dao \u0111\u1ed9ng l\u1edbn, kh\u00f4ng \u1ed5n \u0111\u1ecbnh, ki\u1ec3m so\u00e1t ch\u1ea5t l\u01b0\u1ee3ng k\u00e9m. Tuy nhi\u00ean, bi\u1ec3u \u0111\u1ed3 h\u1ed9p gi\u00fap nh\u00ecn tr\u1ef1c quan h\u01a1n khi so s\u00e1nh 3 giai \u0111o\u1ea1n ho\u1eb7c khu v\u1ef1c kh\u00e1c nhau nh\u01b0 h\u00ecnh d\u01b0\u1edbi \u0111\u00e2y:<\/p>\n

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Ngu\u1ed3n: 6 Sigma – N\u1ed9i dung c\u01a1 b\u1ea3n v\u00e0 h\u01b0\u1edbng d\u1eabn \u00e1p d\u1ee5ng, NXB H\u1ed3ng \u0110\u1ee9c<\/p>\n<\/div>\n<\/div>\n

Nh\u1eadn x\u00e9t:<\/b><\/p>\n

V\u1edbi ba l\u1ea7n thu th\u1eadp d\u1eef li\u1ec7u v\u1ec1 t\u1ec9<\/span> l\u1ec7 l\u00e0m l\u1ea1i v\u00e0o th\u1eddi \u0111i\u1ec3m th\u00e1ng 11\/2011, th\u00e1ng 3\/2012 v\u00e0 th\u00e1ng 6\/2012, d\u1eef li\u1ec7u v\u00e0o th\u1eddi \u0111i\u1ec3m th\u00e1ng 11\/2011 cho th\u1ea5y qu\u00e1 tr\u00ecnh ki\u1ec3m so\u00e1t l\u1ed7i k\u00e9m v\u00ec xu h\u01b0\u1edbng t\u1eadp trung c\u1ee7a d\u1eef li\u1ec7u (trung v\u1ecb) \u1edf m\u1ee9c cao, \u0111\u1ed9 dao \u0111\u1ed9ng l\u1edbn.<\/p>\n

Ki\u1ec3m so\u00e1t ch\u1ea5t l\u01b0\u1ee3ng v\u00e0o th\u1eddi \u0111i\u1ec3m th\u00e1ng 3\/2012 l\u00e0 t\u1ed1t nh\u1ea5t v\u00ec d\u1eef li\u1ec7u v\u1ec1 t\u1ec9<\/span> l\u1ec7 l\u00e0m l\u1ea1i t\u1eadp trung \u1edf m\u1ee9c th\u1ea5p, dao \u0111\u1ed9ng \u1edf ph\u1ea1m vi h\u1eb9p.<\/p>\n

(T\u00e0i li\u1ec7u tham kh\u1ea3o: 6 Sigma – N\u1ed9i dung c\u01a1 b\u1ea3n v\u00e0 h\u01b0\u1edbng d\u1eabn \u00e1p d\u1ee5ng, NXB H\u1ed3ng \u0110\u1ee9c;\u00a0Box plot\u00a0review, Khan Academy)<\/i><\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

\n Bi\u1ec3u \u0111\u1ed3 h\u1ed9p (ti\u1ebfng Anh: Box Plot hay Box and Whisker plot) l\u00e0 bi\u1ec3u \u0111\u1ed3 di\u1ec5n t\u1ea3 5 v\u1ecb tr\u00ed ph\u00e2n b\u1ed1 c\u1ee7a d\u1eef li\u1ec7u, \u0111\u00f3 l\u00e0: gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t (min), t\u1ee9 ph\u00e2n v\u1ecb th\u1ee9 nh\u1ea5t (Q1), trung v\u1ecb (median), t\u1ee9 ph\u00e2n v\u1ecb th\u1ee9 3 (Q3) v\u00e0 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t (max).\n <\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[416],"tags":[],"_links":{"self":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/28565"}],"collection":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/comments?post=28565"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/28565\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=28565"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=28565"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=28565"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}