Dot plot th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 tr\u00ecnh b\u00e0y c\u00e1c t\u1eadp d\u1eef li\u1ec7u c\u00f3 quy m\u00f4 nh\u1ecf ho\u1eb7c v\u1eeba, gi\u00fap ng\u01b0\u1eddi \u0111\u1ecdc nhanh ch\u00f3ng nh\u1eadn bi\u1ebft gi\u00e1 tr\u1ecb ph\u1ed5 bi\u1ebfn nh\u1ea5t, m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n v\u00e0 s\u1ef1 ph\u00e2n b\u1ed1 c\u1ee7a d\u1eef li\u1ec7u.<\/span><\/p>\n Trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n ti\u1ebfng Anh v\u00e0 SAT Math, h\u1ecdc sinh c\u1ea7n n\u1eafm v\u1eefng m\u1ed9t s\u1ed1 thu\u1eadt ng\u1eef li\u00ean quan:<\/span><\/p>\n \u0110\u1ec3 \u0111\u1ecdc m\u1ed9t dot plot, h\u1ecdc sinh c\u1ea7n quan s\u00e1t tr\u1ee5c s\u1ed1, \u0111\u1ebfm s\u1ed1 d\u1ea5u ch\u1ea5m v\u00e0 x\u00e1c \u0111\u1ecbnh nh\u1eefng \u0111\u1eb7c \u0111i\u1ec3m n\u1ed5i b\u1eadt c\u1ee7a t\u1eadp d\u1eef li\u1ec7u.<\/span><\/p>\n Tr\u1ee5c ngang c\u1ee7a dot plot th\u1ec3 hi\u1ec7n c\u00e1c gi\u00e1 tr\u1ecb trong t\u1eadp d\u1eef li\u1ec7u. C\u00e1c gi\u00e1 tr\u1ecb c\u00f3 th\u1ec3 l\u00e0 s\u1ed1 nguy\u00ean, s\u1ed1 th\u1eadp ph\u00e2n ho\u1eb7c nh\u1eefng \u0111\u1ea1i l\u01b0\u1ee3ng \u0111\u1ecbnh l\u01b0\u1ee3ng kh\u00e1c.<\/span><\/p>\n V\u00ed d\u1ee5, m\u1ed9t bi\u1ec3u \u0111\u1ed3 th\u1ec3 hi\u1ec7n s\u1ed1 gi\u1edd h\u1ecdc m\u1ed7i ng\u00e0y c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng c\u00e1c gi\u00e1 tr\u1ecb t\u1eeb 0 \u0111\u1ebfn 5 tr\u00ean tr\u1ee5c ngang.<\/span><\/p>\n H\u1ecdc sinh c\u1ea7n ch\u00fa \u00fd kho\u1ea3ng c\u00e1ch gi\u1eefa c\u00e1c v\u1ea1ch chia \u0111\u1ec3 tr\u00e1nh \u0111\u1ecdc nh\u1ea7m gi\u00e1 tr\u1ecb.<\/span><\/p>\n M\u1ed7i d\u1ea5u ch\u1ea5m \u0111\u1ea1i di\u1ec7n cho m\u1ed9t quan s\u00e1t. N\u1ebfu c\u00f3 b\u1ed1n d\u1ea5u ch\u1ea5m n\u1eb1m ph\u00eda tr\u00ean gi\u00e1 tr\u1ecb 3, \u0111i\u1ec1u \u0111\u00f3 c\u00f3 ngh\u0129a l\u00e0 gi\u00e1 tr\u1ecb 3 xu\u1ea5t hi\u1ec7n b\u1ed1n l\u1ea7n trong t\u1eadp d\u1eef li\u1ec7u.<\/span><\/p>\n T\u1ed5ng s\u1ed1 d\u1ea5u ch\u1ea5m tr\u00ean bi\u1ec3u \u0111\u1ed3 ch\u00ednh l\u00e0 t\u1ed5ng s\u1ed1 quan s\u00e1t.<\/span><\/p>\n Dot plot gi\u00fap x\u00e1c \u0111\u1ecbnh nhanh m\u1ed9t s\u1ed1 \u0111\u1ea1i l\u01b0\u1ee3ng th\u1ed1ng k\u00ea c\u01a1 b\u1ea3n:<\/span><\/p>\n L\u01b0u \u00fd r\u1eb1ng m\u1ed1t v\u00e0 trung v\u1ecb l\u00e0 hai kh\u00e1i ni\u1ec7m kh\u00e1c nhau. Gi\u00e1 tr\u1ecb c\u00f3 t\u1ea7n s\u1ed1 cao nh\u1ea5t kh\u00f4ng nh\u1ea5t thi\u1ebft l\u00e0 trung v\u1ecb c\u1ee7a t\u1eadp d\u1eef li\u1ec7u.<\/span><\/p>\n \u0110\u1ec3 l\u1eadp bi\u1ec3u \u0111\u1ed3 ch\u1ea5m, h\u1ecdc sinh c\u00f3 th\u1ec3 th\u1ef1c hi\u1ec7n theo b\u1ed1n b\u01b0\u1edbc sau:<\/span><\/p>\n B\u01b0\u1edbc 1: Thu th\u1eadp v\u00e0 s\u1eafp x\u1ebfp d\u1eef li\u1ec7u.<\/b><\/p>\n V\u00ed d\u1ee5, \u0111i\u1ec3m s\u1ed1 c\u1ee7a m\u1ed9t nh\u00f3m h\u1ecdc sinh l\u00e0:<\/span><\/p>\n 2, 3, 3, 4, 4, 4, 5, 6.<\/span><\/p>\n B\u01b0\u1edbc 2: V\u1ebd tr\u1ee5c s\u1ed1.<\/b><\/p>\n T\u1ea1o tr\u1ee5c ngang bao g\u1ed3m c\u00e1c gi\u00e1 tr\u1ecb t\u1eeb 2 \u0111\u1ebfn 6.<\/span><\/p>\n B\u01b0\u1edbc 3: \u0110\u1eb7t d\u1ea5u ch\u1ea5m t\u01b0\u01a1ng \u1ee9ng v\u1edbi t\u1eebng quan s\u00e1t.<\/b><\/p>\n M\u1ed7i gi\u00e1 tr\u1ecb xu\u1ea5t hi\u1ec7n m\u1ed9t l\u1ea7n s\u1ebd \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng m\u1ed9t d\u1ea5u ch\u1ea5m. N\u1ebfu m\u1ed9t gi\u00e1 tr\u1ecb xu\u1ea5t hi\u1ec7n nhi\u1ec1u l\u1ea7n, c\u00e1c d\u1ea5u ch\u1ea5m \u0111\u01b0\u1ee3c x\u1ebfp ch\u1ed3ng l\u00ean nhau.<\/span><\/p>\n B\u01b0\u1edbc 4: Ki\u1ec3m tra t\u1ed5ng s\u1ed1 d\u1ea5u ch\u1ea5m.<\/b><\/p>\n \u0110\u1ea3m b\u1ea3o t\u1ed5ng s\u1ed1 d\u1ea5u ch\u1ea5m b\u1eb1ng t\u1ed5ng s\u1ed1 quan s\u00e1t ban \u0111\u1ea7u. Trong v\u00ed d\u1ee5 tr\u00ean, bi\u1ec3u \u0111\u1ed3 ph\u1ea3i c\u00f3 t\u00e1m d\u1ea5u ch\u1ea5m.<\/span><\/p>\n Ngo\u00e0i vi\u1ec7c \u0111\u1ebfm t\u1ea7n s\u1ed1, dot plot c\u00f2n gi\u00fap ng\u01b0\u1eddi h\u1ecdc ph\u00e2n t\u00edch h\u00ecnh d\u1ea1ng v\u00e0 \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a d\u1eef li\u1ec7u.<\/span><\/p>\n Trung t\u00e2m th\u1ec3 hi\u1ec7n v\u1ecb tr\u00ed t\u1eadp trung c\u1ee7a ph\u1ea7n l\u1edbn c\u00e1c gi\u00e1 tr\u1ecb. T\u00f9y thu\u1ed9c v\u00e0o d\u1eef li\u1ec7u, h\u1ecdc sinh c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng trung b\u00ecnh c\u1ed9ng ho\u1eb7c trung v\u1ecb \u0111\u1ec3 m\u00f4 t\u1ea3 xu h\u01b0\u1edbng trung t\u00e2m.<\/span><\/p>\n V\u00ed d\u1ee5, n\u1ebfu ph\u1ea7n l\u1edbn d\u1ea5u ch\u1ea5m t\u1eadp trung quanh gi\u00e1 tr\u1ecb 5, c\u00f3 th\u1ec3 nh\u1eadn th\u1ea5y d\u1eef li\u1ec7u ch\u1ee7 y\u1ebfu n\u1eb1m g\u1ea7n gi\u00e1 tr\u1ecb n\u00e0y.<\/span><\/p>\n \u0110\u1ed9 ph\u00e2n t\u00e1n cho bi\u1ebft c\u00e1c gi\u00e1 tr\u1ecb tr\u1ea3i r\u1ed9ng \u0111\u1ebfn m\u1ee9c n\u00e0o.<\/span><\/p>\n N\u1ebfu c\u00e1c d\u1ea5u ch\u1ea5m n\u1eb1m g\u1ea7n nhau, d\u1eef li\u1ec7u c\u00f3 xu h\u01b0\u1edbng \u00edt ph\u00e2n t\u00e1n. Ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu c\u00e1c d\u1ea5u ch\u1ea5m tr\u1ea3i d\u00e0i tr\u00ean tr\u1ee5c s\u1ed1, d\u1eef li\u1ec7u c\u00f3 \u0111\u1ed9 ph\u00e2n t\u00e1n l\u1edbn h\u01a1n.<\/span><\/p>\n Kho\u1ea3ng bi\u1ebfn thi\u00ean l\u00e0 m\u1ed9t th\u01b0\u1edbc \u0111o \u0111\u01a1n gi\u1ea3n \u0111\u1ec3 m\u00f4 t\u1ea3 \u0111\u1ed9 ph\u00e2n t\u00e1n:<\/span><\/p>\n Range = Maximum \u2212 Minimum.<\/span><\/p>\n Dot plot c\u00f3 th\u1ec3 cho th\u1ea5y m\u1ed9t t\u1eadp d\u1eef li\u1ec7u t\u1eadp trung \u1edf m\u1ed9t v\u00f9ng, ph\u00e2n b\u1ed1 t\u01b0\u01a1ng \u0111\u1ed1i c\u00e2n \u0111\u1ed1i ho\u1eb7c l\u1ec7ch v\u1ec1 m\u1ed9t ph\u00eda.<\/span><\/p>\n Nh\u1eefng \u0111\u1eb7c \u0111i\u1ec3m n\u00e0y gi\u00fap ng\u01b0\u1eddi \u0111\u1ecdc hi\u1ec3u s\u00e2u h\u01a1n v\u1ec1 d\u1eef li\u1ec7u thay v\u00ec ch\u1ec9 nh\u00ecn v\u00e0o gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t ho\u1eb7c nh\u1ecf nh\u1ea5t.<\/span><\/p>\n Outlier l\u00e0 gi\u00e1 tr\u1ecb n\u1eb1m c\u00e1ch bi\u1ec7t \u0111\u00e1ng k\u1ec3 so v\u1edbi ph\u1ea7n l\u1edbn c\u00e1c quan s\u00e1t c\u00f2n l\u1ea1i.<\/span><\/p>\n V\u00ed d\u1ee5, n\u1ebfu \u0111i\u1ec3m s\u1ed1 c\u1ee7a ph\u1ea7n l\u1edbn h\u1ecdc sinh n\u1eb1m trong kho\u1ea3ng 5\u20138 nh\u01b0ng c\u00f3 m\u1ed9t \u0111i\u1ec3m 1 n\u1eb1m ri\u00eang bi\u1ec7t, gi\u00e1 tr\u1ecb 1 c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t \u1ee9ng vi\u00ean ngo\u1ea1i l\u1ec7 c\u1ea7n xem x\u00e9t.<\/span><\/p>\n Tuy nhi\u00ean, kh\u00f4ng n\u00ean k\u1ebft lu\u1eadn m\u1ed9t gi\u00e1 tr\u1ecb ch\u1eafc ch\u1eafn l\u00e0 ngo\u1ea1i l\u1ec7 ch\u1ec9 d\u1ef1a v\u00e0o kho\u1ea3ng c\u00e1ch tr\u1ef1c quan. C\u1ea7n xem x\u00e9t b\u1ed1i c\u1ea3nh v\u00e0 ti\u00eau ch\u00ed th\u1ed1ng k\u00ea ph\u00f9 h\u1ee3p.<\/span><\/p>\n Dot plot c\u00f3 li\u00ean quan \u0111\u1ebfn nh\u00f3m ki\u1ebfn th\u1ee9c th\u1ed1ng k\u00ea v\u00e0 ph\u00e2n t\u00edch d\u1eef li\u1ec7u trong SAT Math. H\u1ecdc sinh c\u00f3 th\u1ec3 g\u1eb7p nh\u1eefng c\u00e2u h\u1ecfi y\u00eau c\u1ea7u \u0111\u1ecdc bi\u1ec3u \u0111\u1ed3, x\u00e1c \u0111\u1ecbnh t\u1ea7n s\u1ed1 ho\u1eb7c so s\u00e1nh c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a hai t\u1eadp d\u1eef li\u1ec7u.<\/span><\/p>\n Exercise:<\/b> M\u1ed9t dot plot th\u1ec3 hi\u1ec7n t\u1eadp d\u1eef li\u1ec7u g\u1ed3m c\u00e1c gi\u00e1 tr\u1ecb:<\/span><\/p>\n 1, 2, 2, 3, 3, 3, 5, 6.<\/span><\/p>\n H\u00e3y x\u00e1c \u0111\u1ecbnh m\u1ed1t v\u00e0 kho\u1ea3ng bi\u1ebfn thi\u00ean.<\/span><\/p>\n L\u1eddi gi\u1ea3i:<\/b><\/p>\n Gi\u00e1 tr\u1ecb 3 xu\u1ea5t hi\u1ec7n ba l\u1ea7n, nhi\u1ec1u h\u01a1n c\u00e1c gi\u00e1 tr\u1ecb c\u00f2n l\u1ea1i. V\u00ec v\u1eady, m\u1ed1t l\u00e0 3.<\/span><\/p>\n Gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t l\u00e0 6 v\u00e0 nh\u1ecf nh\u1ea5t l\u00e0 1.<\/span><\/p>\n Range = 6 \u2212 1 = 5.<\/span><\/p>\n Answer:<\/b> M\u1ed1t b\u1eb1ng 3; kho\u1ea3ng bi\u1ebfn thi\u00ean b\u1eb1ng 5.<\/span><\/p>\n Exercise:<\/b> M\u1ed9t t\u1eadp d\u1eef li\u1ec7u g\u1ed3m c\u00e1c gi\u00e1 tr\u1ecb 2, 2, 4, 4, 4 v\u00e0 8. T\u00ednh gi\u00e1 tr\u1ecb trung b\u00ecnh c\u1ed9ng.<\/span><\/p>\n L\u1eddi gi\u1ea3i:<\/b><\/p>\n Trung b\u00ecnh c\u1ed9ng b\u1eb1ng t\u1ed5ng c\u00e1c quan s\u00e1t chia cho s\u1ed1 l\u01b0\u1ee3ng quan s\u00e1t:<\/span><\/p>\n Mean = (2 + 2 + 4 + 4 + 4 + 8)\/6<\/span><\/p>\n Mean = 24\/6 = 4.<\/span><\/p>\n Answer:<\/b> Trung b\u00ecnh c\u1ed9ng b\u1eb1ng 4.<\/span><\/p>\n Khi \u0111\u1ecdc dot plot, n\u1ebfu m\u1ed9t gi\u00e1 tr\u1ecb c\u00f3 nhi\u1ec1u d\u1ea5u ch\u1ea5m th\u00ec gi\u00e1 tr\u1ecb \u0111\u00f3 ph\u1ea3i \u0111\u01b0\u1ee3c t\u00ednh nhi\u1ec1u l\u1ea7n khi t\u00ednh trung b\u00ecnh c\u1ed9ng. Kh\u00f4ng \u0111\u01b0\u1ee3c ch\u1ec9 c\u1ed9ng c\u00e1c gi\u00e1 tr\u1ecb kh\u00e1c nhau r\u1ed3i chia cho s\u1ed1 l\u01b0\u1ee3ng gi\u00e1 tr\u1ecb xu\u1ea5t hi\u1ec7n tr\u00ean tr\u1ee5c s\u1ed1.<\/span><\/p>\n Exercise:<\/b> Hai nh\u00f3m h\u1ecdc sinh c\u00f3 \u0111i\u1ec3m ki\u1ec3m tra \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng hai dot plot. Nh\u00f3m A c\u00f3 c\u00e1c \u0111i\u1ec3m t\u1eadp trung t\u1eeb 7 \u0111\u1ebfn 9, trong khi nh\u00f3m B c\u00f3 \u0111i\u1ec3m tr\u1ea3i r\u1ed9ng t\u1eeb 4 \u0111\u1ebfn 10.<\/span><\/p>\n N\u1ebfu s\u1ed1 \u0111i\u1ec3m nh\u1ecf nh\u1ea5t v\u00e0 l\u1edbn nh\u1ea5t \u0111\u01b0\u1ee3c \u0111\u1ecdc ch\u00ednh x\u00e1c t\u1eeb bi\u1ec3u \u0111\u1ed3, nh\u00f3m n\u00e0o c\u00f3 kho\u1ea3ng bi\u1ebfn thi\u00ean l\u1edbn h\u01a1n?<\/span><\/p>\n L\u1eddi gi\u1ea3i:<\/b><\/p>\n Nh\u00f3m A c\u00f3 kho\u1ea3ng bi\u1ebfn thi\u00ean:<\/span><\/p>\n Range A = 9 \u2212 7 = 2.<\/span><\/p>\n Nh\u00f3m B c\u00f3 kho\u1ea3ng bi\u1ebfn thi\u00ean:<\/span><\/p>\n Range B = 10 \u2212 4 = 6.<\/span><\/p>\n V\u00ec 6 l\u1edbn h\u01a1n 2 n\u00ean nh\u00f3m B c\u00f3 kho\u1ea3ng bi\u1ebfn thi\u00ean l\u1edbn h\u01a1n.<\/span><\/p>\n Answer:<\/b> Nh\u00f3m B.<\/span><\/p>\n Dot plot c\u00f3 m\u1ed9t s\u1ed1 \u0111i\u1ec3m t\u01b0\u01a1ng \u0111\u1ed3ng v\u1edbi c\u00e1c bi\u1ec3u \u0111\u1ed3 th\u1ed1ng k\u00ea kh\u00e1c, nh\u01b0ng m\u1ed7i lo\u1ea1i ph\u00f9 h\u1ee3p v\u1edbi nh\u1eefng m\u1ee5c \u0111\u00edch ri\u00eang.<\/span><\/p>\n <\/p>\n\n
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2. C\u00e1ch \u0111\u1ecdc Dot Plot ch\u00ednh x\u00e1c<\/b><\/h2>\n
2.1. X\u00e1c \u0111\u1ecbnh gi\u00e1 tr\u1ecb tr\u00ean tr\u1ee5c s\u1ed1<\/b><\/h3>\n
2.2. \u0110\u1ebfm s\u1ed1 d\u1ea5u ch\u1ea5m \u0111\u1ec3 t\u00ecm t\u1ea7n s\u1ed1<\/b><\/h3>\n
2.3. X\u00e1c \u0111\u1ecbnh m\u1ed1t, trung v\u1ecb v\u00e0 kho\u1ea3ng bi\u1ebfn thi\u00ean<\/b><\/h3>\n
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3. C\u00e1ch v\u1ebd Dot Plot t\u1eeb m\u1ed9t t\u1eadp d\u1eef li\u1ec7u<\/b><\/h2>\n
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<\/p>\n4. C\u00e1c \u0111\u1eb7c \u0111i\u1ec3m quan tr\u1ecdng c\u1ee7a ph\u00e2n b\u1ed1 d\u1eef li\u1ec7u tr\u00ean Dot Plot<\/b><\/h2>\n
4.1. Trung t\u00e2m c\u1ee7a d\u1eef li\u1ec7u (Center)<\/b><\/h3>\n
4.2. \u0110\u1ed9 ph\u00e2n t\u00e1n (Spread)<\/b><\/h3>\n
4.3. H\u00ecnh d\u1ea1ng ph\u00e2n b\u1ed1 (Shape)<\/b><\/h3>\n
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4.4. Gi\u00e1 tr\u1ecb ngo\u1ea1i l\u1ec7 (Outlier)<\/b><\/h3>\n
5. Dot Plot trong SAT Math<\/b><\/h2>\n
D\u1ea1ng 1: X\u00e1c \u0111\u1ecbnh m\u1ed1t v\u00e0 kho\u1ea3ng bi\u1ebfn thi\u00ean<\/b><\/h3>\n
D\u1ea1ng 2: T\u00ednh trung b\u00ecnh c\u1ed9ng t\u1eeb Dot Plot<\/b><\/h3>\n
D\u1ea1ng 3: So s\u00e1nh hai t\u1eadp d\u1eef li\u1ec7u<\/b><\/h3>\n
6. Ph\u00e2n bi\u1ec7t Dot Plot v\u1edbi c\u00e1c lo\u1ea1i bi\u1ec3u \u0111\u1ed3 kh\u00e1c<\/b><\/h2>\n
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