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Gauss (1777 ~ 1855) l\u00e0 nh\u00e0 to\u00e1n h\u1ecdc v\u00e0 nh\u00e0 khoa h\u1ecdc t\u00e0i n\u0103ng ng\u01b0\u1eddi \u0110\u1ee9c, ng\u01b0\u1eddi \u0111\u00e3 c\u00f3 nhi\u1ec1u \u0111\u00f3ng g\u00f3p l\u1edbn cho c\u00e1c l\u0129nh v\u1ef1c khoa h\u1ecdc, nh\u01b0 l\u00fd thuy\u1ebft s\u1ed1, gi\u1ea3i t\u00edch, h\u00ecnh h\u1ecdc vi ph\u00e2n, khoa tr\u1eafc \u0111\u1ecba, t\u1eeb h\u1ecdc, thi\u00ean v\u0103n h\u1ecdc v\u00e0 quang h\u1ecdc. \u00d4ng \u0111\u00e3 ph\u00e1t hi\u1ec7n ra ph\u00e2n b\u1ed1 ch\u00ednh quy t\u1eeb nh\u1eefng sai l\u1ec7ch \u0111\u01b0\u1ee3c h\u00ecnh th\u00e0nh trong qu\u00e1 tr\u00ecnh \u0111o v\u1ecb tr\u00ed c\u1ee7a c\u00e1c thi\u00ean th\u1ec3. T\u1eeb trong ph\u00e2n b\u1ed1 ch\u00ednh quy n\u00e0y, c\u00e1c m\u1eabu th\u1eed \u0111\u01b0\u1ee3c ch\u1ecdn ra v\u00e0 v\u1ebd th\u00e0nh bi\u1ec3u \u0111\u1ed3 theo t\u1ea7n s\u1ed1 ph\u00e2n b\u1ed1. Bi\u1ec3u \u0111\u1ed3 n\u00e0y ng\u00e0y nay \u0111\u01b0\u1ee3c bi\u1ebft t\u1edbi v\u1edbi t\u00ean g\u1ecdi Histogram.<\/p>\n
Bi\u1ec3u \u0111\u1ed3 histogram l\u00e0 ph\u01b0\u01a1ng ph\u00e1p th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 sai l\u1ec7ch trong c\u00e1c c\u00f4ng \u0111o\u1ea1n t\u1ea1i c\u00f4ng x\u01b0\u1edfng. N\u00f3 \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng b\u1eb1ng c\u00e1ch chia gi\u00e1 tr\u1ecb \u0111o \u0111\u01b0\u1ee3c th\u00e0nh nhi\u1ec1u kho\u1ea3ng, t\u1eadp trung s\u1ed1 d\u1eef li\u1ec7u n\u1eb1m trong c\u00e1c kho\u1ea3ng \u0111\u00f3 r\u1ed3i bi\u1ec3u th\u1ecb th\u00e0nh bi\u1ec3u \u0111\u1ed3 d\u1ea1ng c\u1ed9t. Bi\u1ec3u \u0111\u1ed3 sau khi \u0111\u01b0\u1ee3c ho\u00e0n th\u00e0nh s\u1ebd cho ch\u00fang ta bi\u1ebft tr\u1ea1ng th\u00e1i c\u1ee7a c\u00f4ng \u0111o\u1ea1n s\u1ea3n xu\u1ea5t.<\/p>\n
L\u00e0m n\u1ed5i b\u1eadt v\u1ea5n \u0111\u1ec1 b\u1eb1ng c\u00e1ch \u0111\u00e1nh gi\u00e1 s\u1ef1 sai l\u1ec7ch so v\u1edbi gi\u00e1 tr\u1ecb trung b\u00ecnh<\/p>\n
Gi\u1ea3 s\u1eed n\u1ebfu th\u1eddi gian l\u00e0m vi\u1ec7c trung b\u00ecnh thay \u0111\u1ed5i t\u1eeb 30 ph\u00fat th\u00e0nh 60 ph\u00fat th\u00ec ch\u00fang ta s\u1ebd bi\u1ebft ngay r\u1eb1ng \u1edf \u0111\u00e2u \u0111\u00f3 \u0111\u00e3 c\u00f3 v\u1ea5n \u0111\u1ec1 \u0111\u00e3 x\u1ea3y ra. Tuy nhi\u00ean, c\u0169ng c\u00f3 nh\u1eefng tr\u01b0\u1eddng h\u1ee3p th\u1eddi gian l\u00e0m vi\u1ec7c trung b\u00ecnh c\u1ee7a m\u1ed7i nh\u00e2n vi\u00ean trong 2 v\u0103n ph\u00f2ng \u0111\u1ec1u l\u00e0 32,1 ph\u00fat nh\u01b0ng do s\u1ef1 sai l\u1ec7ch kh\u00e1c nhau n\u00ean v\u1eabn c\u00f3 th\u1ec3 c\u00f3 v\u1ea5n \u0111\u1ec1 trong \u0111\u00f3.<\/p>\n
Ch\u00fang ta s\u1ebd c\u00f9ng t\u00ecm v\u1ea5n \u0111\u1ec1 n\u00e0y b\u1eb1ng c\u00e1ch \u0111o th\u1eed th\u1eddi gian l\u00e0m vi\u1ec7c c\u1ee7a 2 v\u0103n ph\u00f2ng A v\u00e0 B, m\u1ed7i v\u0103n ph\u00f2ng c\u00f3 20 nh\u00e2n vi\u00ean. K\u1ebft qu\u1ea3 \u0111o \u0111\u01b0\u1ee3c s\u1ebd \u0111\u01b0\u1ee3c ph\u00e2n chia theo kho\u1ea3ng c\u00e1ch nhau 5 ph\u00fat v\u00e0 bi\u1ec3u th\u1ecb th\u00e0nh bi\u1ec3u \u0111\u1ed3. Nh\u00ecn v\u00e0o k\u1ebft qu\u1ea3 \u0111o \u0111\u01b0\u1ee3c, ch\u00fang ta s\u1ebd th\u1ea5y ngay ng\u01b0\u1eddi l\u00e0m nhanh nh\u1ea5t t\u1ea1i v\u0103n ph\u00f2ng A ch\u1ec9 h\u1ebft 22 ph\u00fat, trong khi ng\u01b0\u1eddi l\u00e0m ch\u1eadm nh\u1ea5t s\u1ebd ti\u00eau t\u1ed1n 44 ph\u00fat. T\u01b0\u01a1ng t\u1ef1 nh\u01b0 th\u1ebf \u0111\u1ed1i v\u1edbi v\u0103n ph\u00f2ng B, ng\u01b0\u1eddi l\u00e0m nhanh nh\u1ea5t th\u1eadm ch\u00ed ch\u1ec9 h\u1ebft 17 ph\u00fat nh\u01b0ng l\u1ea1i c\u00f3 ng\u01b0\u1eddi l\u00e0m t\u1edbi 48 ph\u00fat.<\/p>\n
N\u1ebfu b\u1ea1n mu\u1ed1n \u0111\u00e1nh gi\u00e1 tr\u1ea1ng th\u00e1i l\u00e0m vi\u1ec7c c\u1ee7a 2 v\u0103n ph\u00f2ng n\u00e0y b\u1eb1ng th\u1ecb gi\u00e1c th\u00ec bi\u1ec3u \u0111\u1ed3 Histogam l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 h\u1eefu hi\u1ec7u. Ngo\u00e0i ra, tr\u00ean bi\u1ec3u \u0111\u1ed3 n\u00e0y c\u00f2n bi\u1ec3u th\u1ecb gi\u00e1 tr\u1ecb trung b\u00ecnh v\u00e0 \u0111\u1ed9 l\u1ec7ch ti\u00eau chu\u1ea9n. \u1ede c\u1ea3 2 v\u0103n ph\u00f2ng n\u00e0y \u0111\u1ec1u c\u00f3 th\u1eddi gian l\u00e0m vi\u1ec7c trung b\u00ecnh l\u00e0 32,1 ph\u00fat nh\u01b0ng \u0111\u1ed9 l\u1ec7ch ti\u00eau chu\u1ea9n t\u1ea1i v\u0103n ph\u00f2ng A l\u00e0 5,86 v\u00e0 c\u1ee7a B l\u00e0 7,71. Ch\u00fang ta c\u00f3 th\u1ec3 th\u1ea5y \u0111\u1ed9 l\u1ec7ch ti\u00eau chu\u1ea9n c\u1ee7a B g\u1ea5p t\u1edbi 1,3 l\u1ea7n c\u1ee7a A n\u00ean c\u00f3 th\u1ec3 k\u1ebft lu\u1eadn r\u1eb1ng t\u1ea1i v\u0103n ph\u00f2ng B \u0111ang c\u00f3 v\u1ea5n \u0111\u1ec1 g\u00ec \u0111\u00f3.<\/p>\n
B\u1ea3ng t\u1ea7n s\u1ed1 r\u1ea5t quan tr\u1ecdng v\u00e0 c\u00f3 th\u1ec3 n\u00f3i r\u1eb1ng \u0111\u00e2y ch\u00ednh l\u00e0 n\u00ean t\u1ea3ng trong qu\u00e1 tr\u00ecnh l\u1eadp bi\u1ec3u \u0111\u1ed3 Histogram. B\u1ea3ng t\u1ea7n s\u1ed1 s\u1ebd \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng theo c\u00e1c b\u01b0\u1edbc sau d\u1ef1a tr\u00ean d\u1eef li\u1ec7u \u0111\u00e3 thu th\u1eadp v\u1ec1 chi\u1ec1u cao c\u1ee7a 60 ng\u01b0\u1eddi.<\/p>\n
C\u00e1c b\u01b0\u1edbc x\u00e2y d\u1ef1ng bi\u1ec3u \u0111\u1ed3 Histogaram<\/p>\n
\u2013 B\u01b0\u1edbc 1: Thu th\u1eadp d\u1eef li\u1ec7u S\u1ed1 d\u1eef li\u1ec7u n = 60<\/p>\n
\u2013 B\u01b0\u1edbc 2: T\u00ecm gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t v\u00e0 l\u1edbn nh\u1ea5t Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t x-max = 186 cm, gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t x-min = 160 cm<\/p>\n
\u2013 B\u01b0\u1edbc 3: Quy\u1ebft \u0111\u1ecbnh s\u1ed1 kho\u1ea3ng chia Kho\u1ea3ng chia \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00e1ch l\u1ea5y c\u0103n b\u1eadc 2 c\u1ee7a s\u1ed1 bi\u1ebfn s\u1ed1 (s\u1ed1 ng\u01b0\u1eddi \u0111\u00e3 \u0111o chi\u1ec1u cao) \u221an = \u221a60 = 7,75 \u2192 8 (s\u1ed1 kho\u1ea3ng chia)<\/p>\n
\u2013 B\u01b0\u1edbc 4: Quy\u1ebft \u0111\u1ecbnh \u0111\u1ed9 r\u1ed9ng c\u1ee7a m\u1ed7i kho\u1ea3ng chia \u0110\u1ed9 r\u1ed9ng kho\u1ea3ng chia = (Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t \u2013 gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t)\/ s\u1ed1 kho\u1ea3ng chia = (186 \u2013 160)\/8 = 3,25 Th\u1ef1c t\u1ebf, \u0111\u1ed9 r\u1ed9ng kho\u1ea3ng chia \u0111\u01b0\u1ee3c t\u00ednh theo t\u00edch \u0111\u01a1n v\u1ecb \u0111o nh\u1ecf nh\u1ea5t v\u1edbi m\u1ed9t s\u1ed1 nguy\u00ean. Do \u0111\u01a1n v\u1ecb \u0111o nh\u1ecf nh\u1ea5t \u1edf \u0111\u00e2y l\u00e0 1 cm n\u00ean ch\u00fang ta ch\u1ecdn \u0111\u1ed9 r\u1ed9ng kho\u1ea3ng chia l\u00e0 3.<\/p>\n
\u2013 B\u01b0\u1edbc 5: Quy\u1ebft \u0111\u1ecbnh ranh gi\u1edbi tr\u00ean d\u01b0\u1edbi c\u1ee7a kho\u1ea3ng chia Ranh gi\u1edbi c\u1ee7a m\u1ed9t kho\u1ea3ng chia \u0111\u01b0\u1ee3c t\u00ednh nh\u01b0 sau: Ranh gi\u1edbi d\u01b0\u1edbi = gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t \u2013 \u00bd \u0111\u01a1n v\u1ecb \u0111o nh\u1ecf nh\u1ea5t \u0110\u1ed1i v\u1edbi kho\u1ea3ng 1: Ranh gi\u1edbi d\u01b0\u1edbi = 160 \u2013 \u00bd x 1 = 159,5 Ranh gi\u1edbi tr\u00ean = Ranh gi\u1edbi d\u01b0\u1edbi + \u0110\u1ed9 r\u1ed9ng kho\u1ea3ng chia \u0110\u1ed1i v\u1edbi kho\u1ea3ng 1 : Ranh gi\u1edbi tr\u00ean = 159,5 + 3 = 162,5 Gi\u00e1 tr\u1ecb trung t\u00e2m = (Ranh gi\u1edbi tr\u00ean + Ranh gi\u1edbi d\u01b0\u1edbi)\/2 \u0110\u1ed1i v\u1edbi kho\u1ea3ng 1: (159,5+162,5)\/2 = 161 T\u01b0\u01a1ng t\u1ef1 nh\u01b0 v\u1eady ch\u00fang ta c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c ranh gi\u1edbi c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c kho\u1ea3ng nh\u01b0 b\u1ea3ng d\u01b0\u1edbi.<\/p>\n
\u2013 B\u01b0\u1edbc 6: T\u1ed5ng h\u1ee3p c\u00e1c kho\u1ea3ng \u0111\u1ec3 t\u1ea1o th\u00e0nh b\u1ea3ng t\u1ea7n su\u1ea5t 3. V\u1ebd bi\u1ec3u \u0111\u1ed3 Histogram Sau khi k\u1ebft th\u00fac 6 b\u01b0\u1edbc \u1edf ph\u1ea7n tr\u01b0\u1edbc ch\u00fang ta \u0111\u00e3 c\u00f3 m\u1ed9t b\u1ea3ng t\u1ea7n xu\u1ea5t ho\u00e0n ch\u1ec9nh v\u1edbi \u0111\u1ea7y \u0111\u1ee7 c\u00e1c s\u1ed1 li\u1ec7u. Nh\u1eefng s\u1ed1 li\u1ec7u n\u00e0y s\u1ebd \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e2y d\u1ef1ng bi\u1ec3u \u0111\u1ed3 Histogram.<\/p>\n
\u2013 B\u01b0\u1edbc 7: Quy\u1ebft \u0111\u1ecbnh t\u1ef7 l\u1ec7 Tr\u1ee5c ho\u00e0nh s\u1ebd bi\u1ec3u th\u1ecb gi\u00e1 tr\u1ecb trung t\u00e2m c\u1ee7a c\u00e1c kho\u1ea3ng v\u00e0 tr\u1ee5c tung s\u1ebd bi\u1ec3u th\u1ecb t\u1ea7n s\u1ed1 c\u1ee7a t\u1eebng d\u1eef li\u1ec7u.<\/p>\n
\u2013 B\u01b0\u1edbc 8: v\u1ebd bi\u1ec3u \u0111\u1ed3 d\u1ea1ng c\u1ed9t V\u1ebd c\u00e1c c\u1ed9t d\u1ef1a v\u00e0o gi\u00e1 tr\u1ecb trung t\u00e2m cho t\u1eebng kho\u1ea3ng. Ch\u00fa \u00fd ch\u00fang ta s\u1ebd kh\u00f4ng \u0111\u1ec3 kho\u1ea3ng tr\u1ed1ng gi\u1eefa c\u00e1c c\u1ed9t.<\/p>\n
\u2013 B\u01b0\u1edbc 9: \u0110i\u1ec1n gi\u00e1 tr\u1ecb trung b\u00ecnh Sau khi t\u00ednh gi\u00e1 tr\u1ecb trung b\u00ecnh, h\u00e3y bi\u1ec3u th\u1ecb gi\u00e1 tr\u1ecb n\u00e0y b\u1eb1ng \u0111\u01b0\u1eddng n\u00e9t \u0111\u1ee9t tr\u00ean bi\u1ec3u \u0111\u1ed3.<\/p>\n
– B\u01b0\u1edbc 10: \u0110i\u1ec1n c\u00e1c m\u1ee5c c\u00f2n l\u1ea1i v\u00e0o bi\u1ec3u \u0111\u1ed3 Nh\u1eefng th\u00f4ng tin quan tr\u1ecdng kh\u00e1c c\u1ee7a bi\u1ec3u \u0111\u1ed3 nh\u01b0 s\u1ed1 d\u1eef li\u1ec7u, gi\u00e1 tr\u1ecb trung b\u00ecnh, sai l\u1ec7ch ti\u00eau chu\u1ea9n.<\/p>\n
Nh\u1eefng \u0111i\u1ec1u c\u00f3 th\u1ec3 hi\u1ec3u \u0111\u01b0\u1ee3c t\u1eeb bi\u1ec3u \u0111\u1ed3 Histogram Khi nh\u00ecn v\u00e0o bi\u1ec3u \u0111\u1ed3 ch\u00fang ta c\u00f3 th\u1ec3 th\u1ea5y \u0111\u01b0\u1ee3c m\u1ed9t s\u1ed1 \u0111i\u1ec1u nh\u01b0 sau: \u2013 Gi\u00e1 tr\u1ecb trung t\u00e2m c\u1ee7a ph\u00e2n b\u1ed1 n\u1eb1m \u1edf \u0111\u00e2u? \u2013 \u0110\u1ed9 kh\u00f4ng \u0111\u1ed3ng \u0111\u1ec1u c\u1ee7a d\u1eef li\u1ec7u l\u1edbn hay nh\u1ecf? \u2013 D\u1eef li\u1ec7u ph\u00e2n b\u1ed1 theo d\u1ea1ng n\u00e0o ? (tham kh\u1ea3o ph\u1ea7n 4) \u2013 So s\u00e1nh v\u1edbi gi\u00e1 tr\u1ecb ti\u00eau chu\u1ea9n \u0111\u1ec1 \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c c\u1ee7a c\u00f4ng \u0111o\u1ea1n<\/p>\n
Sau khi t\u00e1c th\u00e0nh bi\u1ec3u \u0111\u1ed3 Histogram, ch\u00fang ta ch\u1ec9 tho\u00e1ng nh\u00ecn l\u00e0 c\u00f3 th\u1ec3 hi\u1ec3u \u0111\u01b0\u1ee3c tr\u1ea1ng th\u00e1i ph\u00e2n b\u1ed1 c\u1ee7a d\u1eef li\u1ec7u. H\u00ecnh d\u1ea1ng c\u1ee7a bi\u1ec3u \u0111\u1ed3 s\u1ebd gi\u00fap ch\u00fang ta n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c v\u1ea5n \u0111\u1ec1 c\u1ea7n gi\u1ea3i quy\u1ebft.<\/p>\n
\u2022 D\u1ea1ng chung: T\u1ea7n s\u1ed1 s\u1ebd l\u1edbn d\u1ea7n khi ti\u1ebfn g\u1ea7n v\u1ec1 ph\u00eda trung t\u00e2m v\u00e0 nh\u1ecf d\u1ea7n khi d\u1ecbch chuy\u1ec3n v\u1ec1 2 ph\u00eda. Khi c\u00f4ng \u0111o\u1ea1n trong tr\u1ea1ng th\u00e1i \u1ed5n \u0111\u1ecbnh th\u00ec d\u1eef li\u1ec7u s\u1ebd c\u00f3 d\u1ea1ng n\u00e0y.<\/p>\n
\u2022 D\u1ea1ng c\u00f3 \u0111\u1ea3o nh\u1ecf t\u00e1ch ri\u00eang: \u1ede d\u1ea1ng n\u00e0y s\u1ebd xu\u1ea5t hi\u1ec7n d\u1eef li\u1ec7u n\u1eb1m t\u00e1ch ri\u00eang v\u1ec1 m\u1ed9t ph\u00eda so v\u1edbi c\u00e1c d\u1eef li\u1ec7u c\u00f2n l\u1ea1i. D\u1ea1ng n\u00e0y th\u01b0\u1eddng g\u1eb7p khi c\u00f3 m\u1ed9t ph\u1ea7n d\u1eef li\u1ec7u b\u1ea5t th\u01b0\u1eddng \u0111\u01b0\u1ee3c tr\u1ed9n l\u1eabn v\u00e0o. N\u1ebfu \u0111\u00e2y l\u00e0 d\u1eef li\u1ec7u do sai s\u00f3t khi \u0111o \u0111\u1ea1c th\u00ec ch\u00fang ta c\u00f3 th\u1ec3 b\u1ecf \u0111i. Nh\u01b0ng n\u1ebfu \u0111\u00e2y kh\u00f4ng ph\u1ea3i d\u1eef li\u1ec7u do sai s\u00f3t th\u00ec n\u00ean xem l\u1ea1i qu\u00e1 tr\u00ecnh \u0111o d\u1eef li\u1ec7u n\u00e0y \u0111\u1ec3 t\u00ecm v\u1ea5n \u0111\u1ec1.<\/p>\n
\u2022 D\u1ea1ng 2 ng\u1ecdn n\u00fai hay cao nguy\u00ean: V\u1edbi d\u1ea1ng 2 ng\u1ecdn n\u00fai th\u00ec c\u00e0ng g\u1ea7n trung t\u00e2m t\u1ea7n s\u1ed1 s\u1ebd c\u00e0ng gi\u1ea3m v\u00e0 h\u00ecnh th\u00e0nh 2 ng\u1ecdn n\u00fai \u1edf hai b\u00ean. D\u1ea1ng n\u00e0y \u0111\u01b0\u1ee3c h\u00ecnh th\u00e0nh c\u00f3 th\u1ec3 do s\u1ef1 tr\u1ed9n l\u1eabn c\u1ee7a 2 lo\u1ea1i d\u1eef li\u1ec7u c\u00f3 ph\u00e2n b\u1ed1 kh\u00e1c nhau. V\u1edbi d\u1ea1ng cao nguy\u00ean, t\u1ea7n s\u1ed1 gi\u1eefa c\u00e1c kho\u1ea3ng h\u1ea7u nh\u01b0 kh\u00f4ng thay \u0111\u1ed5i nhi\u1ec1u. \u0110\u00e2y c\u00f3 th\u1ec3 th\u00ec ph\u00e2n b\u1ed1 \u0111\u00e3 b\u1ecb l\u1eabn nhi\u1ec1u lo\u1ea1i d\u1eef li\u1ec7u kh\u00e1c nhau. Trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y, h\u00e3y th\u1eed ph\u00e2n t\u1ea7ng th\u00e0nh 2 hay nhi\u1ec1u ph\u00e2n b\u1ed1 c\u00f3 gi\u00e1 tr\u1ecb trung b\u00ecnh kh\u00e1c nhau r\u1ed3i v\u1ebd ri\u00eang th\u00e0nh t\u1eebng bi\u1ec3u \u0111\u1ed3. Sau \u0111\u00f3, xem x\u00e9t v\u1ea5n \u0111\u1ec1.<\/p>\n
\u2022 D\u1ea1ng l\u1ec7ch v\u1ec1 m\u1ed9t ph\u00eda hay l\u1ec7ch ho\u00e0n to\u00e0n v\u1ec1 m\u1ed9t ph\u00eda: D\u1ea1ng l\u1ec7ch v\u1ec1 m\u1ed9t ph\u00eda, gi\u00e1 tr\u1ecb trung b\u00ecnh s\u1ebd kh\u00f4ng n\u1eb1m \u1edf gi\u1eefa m\u00e0 thi\u00ean v\u1ec1 m\u1ed9t trong 2 ph\u00eda, bi\u1ec3u \u0111\u1ed3 c\u00f3 d\u1ea1ng b\u1ea5t \u0111\u1ed1i x\u1ee9ng. V\u1edbi d\u1ea1ng bi\u1ec3u \u0111\u1ed3 n\u00e0y ch\u00fang ta c\u00f3 th\u1ec3 ph\u00e1n \u0111o\u00e1n r\u1eb1ng d\u1eef li\u1ec7u \u0111\u00e3 b\u1ecb gi\u1edbi h\u1ea1n m\u1ed9t ph\u00eda (ph\u00eda kh\u00f4ng b\u00ecnh th\u01b0\u1eddng) b\u1edfi m\u1ed9t ti\u00eau chu\u1ea9n n\u00e0o \u0111\u00f3. C\u00f2n d\u1ea1ng l\u1ec7ch ho\u00e0n to\u00e0n th\u00ec d\u1eef li\u1ec7u s\u1ebd d\u1ed3n ho\u00e0n to\u00e0n v\u1ec1 m\u1ed9t ph\u00eda gi\u1ed1ng nh\u01b0 m\u1ed9t b\u1ee9c t\u01b0\u1eddng. D\u1ea1ng n\u00e0y th\u01b0\u1eddng xu\u1ea5t hi\u1ec7n khi c\u00e1c d\u1eef li\u1ec7u n\u1eb1m ngo\u00e0i ti\u00eau chu\u1ea9n \u0111\u00e3 b\u1ecb lo\u1ea1i b\u1ecf. \u0110\u1ed1i v\u1edbi c\u1ea3 2 tr\u01b0\u1eddng h\u1ee3p tr\u00ean, ch\u00fang ta n\u00ean \u0111\u01b0a c\u1ea3 nh\u1eefng d\u1eef li\u1ec7u b\u1ecb gi\u1edbi h\u1ea1n hay b\u1ecb lo\u1ea1i b\u1ecf b\u1edfi ti\u00eau chu\u1ea9n v\u00e0o \u0111\u1ec3 xem x\u00e9t v\u00e0 t\u00ecm v\u1ea5n \u0111\u1ec1.<\/p>\n
So s\u00e1nh kho\u1ea3ng r\u1ed9ng c\u1ee7a d\u1eef li\u1ec7u v\u1edbi kho\u1ea3ng r\u1ed9ng ti\u00eau chu\u1ea9n Vi\u1ec7c so s\u00e1nh bi\u1ec3u \u0111\u1ed3 histogram v\u1edbi gi\u00e1 tr\u1ecb ti\u00eau chu\u1ea9n s\u1ebd cho ch\u00fang ta bi\u1ebft \u0111\u01b0\u1ee3c n\u0103ng l\u1ef1c c\u1ee7a c\u00f4ng \u0111o\u1ea1n c\u00f3 th\u1ecfa m\u00e3n nh\u1eefng y\u00eau c\u1ea7u k\u0129 thu\u1eadt hay kh\u00f4ng. C\u1ee5 th\u1ec3, n\u1ebfu \u0111i\u1ec1n gi\u00e1 tr\u1ecb ti\u00eau chu\u1ea9n ho\u1eb7c gi\u00e1 tr\u1ecb m\u1ee5c ti\u00eau l\u00ean bi\u1ec3u \u0111\u1ed3 Histogram, ch\u00fang ta s\u1ebd th\u1ea5y ngay gi\u00e1 tr\u1ecb trung b\u00ecnh sai l\u1ec7ch bao nhi\u00eau so v\u1edbi ti\u00eau chu\u1ea9n hay m\u1ee5c ti\u00eau, hay d\u1eef li\u1ec7u c\u00f3 n\u1eb1m trong kho\u1ea3ng ti\u00eau chu\u1ea9n hay kh\u00f4ng. T\u1eeb k\u1ebft qu\u1ea3 nh\u1eadn \u0111\u01b0\u1ee3c, ch\u00fang ta c\u00f3 th\u1ec3 d\u1ec5 d\u00e0ng n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c v\u1ea5n \u0111\u1ec1 (n\u1ebfu c\u00f3) c\u1ee7a c\u00f4ng \u0111o\u1ea1n s\u1ea3n xu\u1ea5t \u1edf tr\u1ea1ng th\u00e1i hi\u1ec7n t\u1ea1i.<\/p>\n
\u2013 Tr\u01b0\u1eddng h\u1ee3p l\u00ed t\u01b0\u1edfng: sai l\u1ec7ch c\u1ee7a s\u1ea3n ph\u1ea9m hay c\u00f4ng vi\u1ec7c \u0111\u1ec1u n\u1eb1m trong ti\u00eau chu\u1ea9n, v\u00e0 gi\u00e1 tr\u1ecb trung b\u00ecnh c\u0169ng \u0111\u1ed3ng nh\u1ea5t v\u1edbi gi\u00e1 tr\u1ecb trung t\u00e2m c\u1ee7a ti\u00eau chu\u1ea9n. \u0110\u00e2y l\u00e0 tr\u1ea1ng th\u00e1i l\u00fd t\u01b0\u1edfng v\u00e0 c\u1ea7n duy tr\u00ec.<\/p>\n
\u2013 Tr\u01b0\u1eddng h\u1ee3p kh\u00f4ng c\u00f3 d\u01b0 th\u1eeba \u1edf m\u1ed9t ph\u00eda: Sai l\u1ec7ch c\u1ee7a s\u1ea3n ph\u1ea9m hay c\u00f4ng vi\u1ec7c \u0111\u1ec1u t\u1eadp trung b\u00ean trong kho\u1ea3ng ti\u00eau chu\u1ea9n nh\u01b0ng gi\u00e1 tr\u1ecb trung b\u00ecnh l\u1ea1i b\u1ecb l\u1ec7ch sang m\u1ed9t ph\u00eda. \u1ede tr\u1ea1ng th\u00e1i n\u00e0y, n\u1ebfu th\u00ec c\u1ea7n c\u00f3 thay \u0111\u1ed5i nh\u1ecf trong c\u00f4ng \u0111o\u1ea1n s\u1ea3n xu\u1ea5t c\u0169ng c\u00f3 th\u1ec3 \u0111\u01b0a sai l\u1ec7ch ra kh\u1ecfi kho\u1ea3ng ti\u00eau chu\u1ea9n. Trong nh\u1eefng tr\u01b0\u1eddng h\u1ee3p nh\u01b0 th\u1ebf n\u00e0y th\u00ec ph\u01b0\u01a1ng \u00e1n kh\u1eafc ph\u1ee5c t\u1ed1t nh\u1ea5t l\u00e0 th\u1ef1c hi\u1ec7n c\u00e1ch \u0111\u1ed1i s\u00e1ch \u0111\u1ec3 gi\u1ea3m gi\u00e1 tr\u1ecb trung b\u00ecnh v\u00e0 gi\u1ea3m sai l\u1ec7ch.<\/p>\n
\u2013 Tr\u01b0\u1eddng h\u1ee3p kh\u00f4ng c\u00f3 d\u01b0 th\u1eeba \u1edf c\u1ea3 hai ph\u00eda: Sai l\u1ec7ch c\u1ee7a s\u1ea3n ph\u1ea9m hay c\u00f4ng vi\u1ec7c v\u1eeba \u0111\u1ee7 n\u1eb1m trong kho\u1ea3ng ti\u00eau chu\u1ea9n. \u0110\u00e2y kh\u00f4ng ph\u1ea3i l\u00e0 tr\u1ea1ng th\u00e1i m\u00e0 ch\u00fang ta c\u00f3 th\u1ec3 an t\u00e2m, c\u00f3 th\u1ec3 d\u1ef1 \u0111o\u00e1n \u0111\u01b0\u1ee3c vi\u1ec7c d\u1eef li\u1ec7u s\u1ebd l\u1ec7ch kh\u1ecfi ti\u00eau chu\u1ea9n b\u1ea5t c\u1ee9 l\u00fac n\u00e0o. Trong tr\u01b0\u1eddng h\u1ee3p n\u00e0y, vi\u1ec7c \u0111\u01b0a ra c\u00e1c ph\u01b0\u01a1ng \u00e1n x\u1eed l\u00fd nh\u1eb1m thu nh\u1ecf sai l\u1ec7ch \u0111\u1ec3 t\u1ea1o th\u00eam kho\u1ea3ng d\u01b0 th\u1eeba \u1edf hai ph\u00eda l\u00e0 r\u1ea5t quan tr\u1ecdng.<\/p>\n","protected":false},"excerpt":{"rendered":"
[the_ad_group id=”454″] Gauss (1777 ~ 1855) l\u00e0 nh\u00e0 to\u00e1n h\u1ecdc v\u00e0 nh\u00e0 khoa h\u1ecdc t\u00e0i n\u0103ng ng\u01b0\u1eddi \u0110\u1ee9c, ng\u01b0\u1eddi \u0111\u00e3 c\u00f3 nhi\u1ec1u \u0111\u00f3ng g\u00f3p l\u1edbn cho c\u00e1c l\u0129nh v\u1ef1c khoa h\u1ecdc, nh\u01b0 l\u00fd thuy\u1ebft s\u1ed1, gi\u1ea3i t\u00edch, h\u00ecnh h\u1ecdc vi ph\u00e2n, khoa tr\u1eafc \u0111\u1ecba, t\u1eeb h\u1ecdc, thi\u00ean v\u0103n h\u1ecdc v\u00e0 quang h\u1ecdc. \u00d4ng \u0111\u00e3 ph\u00e1t […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[220,227],"tags":[],"_links":{"self":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/8072"}],"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\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/comments?post=8072"}],"version-history":[{"count":0,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/posts\/8072\/revisions"}],"wp:attachment":[{"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/media?parent=8072"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/categories?post=8072"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/masterskills.org\/blog\/wp-json\/wp\/v2\/tags?post=8072"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}