1 ? 1c ? s &92  í ??d9 mmm  ?Bt ?3  ?§ ??1? Elizabeth Newton ( ? 8 ?yDy )?T ?B?s ^? Jacqueline Telford (?i ? ?á ?v D )? Roy Welsch( ? 8 ?yDy )?T b 2 m?¥a? “ Pˉ¥ ±X ?A U¤ b#a ?aμ rb ” A U ? b ? F I n Lé7? ^ZEam? !9?  ?¥b ?l¥ bW?μ?¥ ?3b Pv¥ ? "μH ?b P ? ¥?]?sA U¤÷ b#b 3 Charles Joseph Minard ES 1864 M ?$? g¥m? í ? V¨ d?? http://www.math.yorku.ca/SCS/Gallery/ 4 92s ? ? ? ?V A U  ?B ?¥"' ?b M ? ? ^ ?B ?"'] ?μ"'¥ 1 è H?m ?Q÷m ¨ ?m Us ? ? b ? ??m ^|s ?"'?V ú?? ? ¥H?mb  QCú?? ^Vv  ? T?4 ? ?¥b 5 3 á? ?R s??¥[ "¥f m?H?m M ? q   M ? q   6 Charles Joseph Minard ¨c ESò1¥fmA U  1864 M VESò1 ?a? ó¥ ?¥ ? b V¨ d?? http://www.math.yorku.ca/SCS/Gallery/ 7 1??M  ?′? ? ¥m? ??m ?4? ? °Zm ?=m Qm Q?L QQm ? ?m 8 Iris ? ??m ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à14? ?3:à1 iris[“Sepal W”,“Setosa”] 9 {μ43I|¥ Iris ? ??m ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à14? ?3:à1 iris21b 10 S-Plus?¨o?f ?¥ ? m ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à14?′Pm:à1 x′·m:à1 jitter(x) 11 ? m ? ? HW?  ? ? HW ¨?S ? mYè ^쨥b? m ü ^[ HW1àS ? mb h k¨?]¥ZE ?S? a¥ ? m 12 °Zm ?  n=24 BF  2 ?? R¥ ú? ( 2h{?- )b {31,13,20,21,24,25,25,27,28,40,29,30, 31,23,31,32,35,28,36,37,38,40,50, 17} ? 4 UH?o¨? ??¥ ?  ?¨? ? ?¥ ? b ? ó ? s?¥m?b ? °Zm¥ ?V U"'1 èb ? P¨  7 approx.sqrt(n)“bins” ?T ta t?;á t  t üá  àμ%?b ? A Us? ^ ?¥? ^??¥b ??¥? ^ ??¥b ? ? ?¥?#9?A U ? V? ?¥ù5b ? ?¥é  e??¨ μ ?V? ?$ ×S_? ^à/ ? $ V?? ^?i+ y?b 13 Iris ? ¥°Zm ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb 14 { á wL¥ Iris ? °Zm ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb 15 ?=m Cum.s?f ? ?  ?F  ú? ? ?= 9 ? ?°ZmB" ?A U ? ¥s?? = ÷ L=¥ ? b V[ A? ? ¥ ?′  T  ^ 40à 50W¥ ?b ?? ? ′CB?¨  ]B? ? ? ?′v¥÷ úb 16 Iris ? ¥?=m μ|PH¥ ?3 ^ =Bêl ?¥ ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb 17 ?′? ? ¥ í ?d9 ? ê??   ? (′  “ ü (′ ” ? ?ê ? ê? ??"'?W¥′ ^s??¥ 0.5b ?T n1  ? ?ê ?" ?T n1 } ?b {0,1,2}¥?ê ? ^ 1 n=3 ?[ n+1=4&(n+1)/2=2(?=Q′ ) {0,1,2,3}¥?W′ ^ 1.5 L ! ? ^ ??¥ n=4b ? ù ? K ?R¥′b 18 (′ ? ^?ê ? $ ? ? ??¥? a í ?$  (′  ?T ? ¥s? ^? ¥i Oá? ?l '?ê???¥43 ? M1o]? l¥1 èb ?ê ?  ?T ? s? ^ ?á? ^?? ¥b v?s ? Mμ?v¥′?S s′ b  (′?Y?v??ê ? à tv?Yb · ê?P ê ??b 19 sê ?asê?a?s? ?B? ? ?s?  x p ^ ?M  X¥ psê ?¥′' P(X<x p )=pb n ?? ?s?  S-Plus?  7 qnorm(p) 0<p<1,5 {sê?b  S-Plus?  7 pnorm(q)5 {à qb ?B?"' ??d9 ^|"'′? 6? ? bV U1 X (1) ,…,X (n) b psê ? ^·X ?z?¥ ? ?¥ B?′ ps -B¥ ? ?l????? ? ′b 20 ? ? CDF ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à1 x′:à1 pnorm(x)′b 21 9 ?"'sê ?¥ ?E 1?Vl?v¥ ¨? ? 4?′b 2ó?B?1 è p,9 ? :"'?  *p=np. 3 ?T np? ^? ?éê?/B?? ? | np¥ Ki O |M?¥4?′" x p b 4 ?T np ^? ? k, | ??a? k?? (k+1)? ? ¥ ü (′?? (′ü ^ x p b  ['?μ 6B? ?Eb 22 sê ? ?  psê ?" 100?p?sê ? ?  è ?  {0,1,2,3,4,5,6}={x (1) ,x (2) ,x (3) ,x (4) ,x (5) ,x (6) ,x (7) } n=7 Q1=ceiling(0.25*7)=2 Q1=x (2) =1=25?sê ? Q2=ceiling(0.50*7)=4 Q2=x (4) =3=?′ (50?sê ? ) Q3=ceiling(0.75*7)=6 Q3=x (6) =5=75?sê ? S-Plusó ?]¥s? 9 ?sê ?¥?]ZEb 23 ? ?? S?μs F ? 9?μM]¥???? ??? ¥ ? ?? V ?Mμ?vb í ?μs¥ ?ZE 1aó| ? ?s¥ ?′b ?ê ? ^? 50ê?sê ?b ? 25 50 75ê?sê ??1 1s? Q1,Q2,Q3 , iü ? s? 1?zb Kl′Kv′? ??sê ??1 ? ¥ “?? í ? ”b 2a9 ??′b è ?μ 1sê ?μ Zμ?Sμb 24 ? ?? ? μ "Kv′Kl′b 1sê ?μ  IQR" Q3-Q1b "'Zμ  "'Sμ  ? "' (′Zμ?SμD98¥ ( ′Zμ?Sμ M ? b 25  ?¥ ? ?? ? (′ êμ¥ '′¥"' ü (′ ??ê ? êμ¥ '′¥"'?ê ? ¥?ê ?b 26 ? ??¥9 ? è ? ? {0,1,2,3,4,5,6}={x (1) ,x (2) ,x (3) ,x (4) ,x (5) ,x (6) ,x (7) } (′ =(0+1+2+3+4+5+6)/7=21/7=3, Kl′" 0Kv′" 6b Q1=x (2) =1=? 25??s? Q2=x (4) =3=?ê ? (? 50??s? ) Q3=x (6) =5=? 75??s? μ"Kv′Kl′" 6 0" 6b IQR=Q3 Q1" 5 1" 4, s 2 " [(0 2 +1 2 +2 2 +3 2 +4 2 +5 2 +6 2 )-7(3 2 )]/(7-1)=[91-63]/6=4.67 s=sqrt(4.67)=2.16 27 "'Zμ?Sμ s 2 ? so ?¨ ? í ??s?¥ ? ??b ???s???¨sê ?ó ? ?? ÷%ᥠí ?b ? ? ? ?v"'  50 ¥ ? ′ ?? (′ 0.67s¥ uW = ,  68 ¥ ? ′ ??¥ uW (′ 1s,  95 ¥ ? ′ ??¥ uW (′ 2s,  99.7 ¥ ? ′ ??¥ uW (′ 3sb ? ?s? ?  IQR" ( (′ +0.67s)-( (′ -0.67s)=1.34s 28 S? ? á wL ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb ?m??à1 x′:à1 dnorm(x)′b 29 Q ?Lm ? í ?¥ V j?A U ?V??? Qm¥ s′ ?  ?F  2 ú? ? Qm¥sê ? IQR=Q3-Q1 ?" Q3 1.5?IQR /?" Q3 1.5?IQR HL?SLi O |v?s′ c? =b =??¥4?′$ a1 V ? ^ s′ , ¨?? ???|V Ub 30 Iris ? ¥Qm ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à1 iris21′b 31 QQm 1?"'s?? ? ?s? | ? ??b? i? ? ′1 psê ?' p=(i- 0.5)/n,0<p<1b ['?¨ i/(n+1)b  1 I 1? ?:1 i/n$  ? ?s??¤M] psê ?b è ??? ?s? S-Plus?  7 qnorm(p) V {2Tb ? ?sê?m vs.üsê? s ? ? b S-Plus:plot(qnorm((1:length(y)-0.5)/n),sort(y)) E?LYV ??s?¥?B?? ?sê?b 32 Iris ? ¥ QQm ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à1S? ?sê ?′:à1 iris21′b 33 ? ?MD ? s? V[YV?? TVCd? ? è ? s? V ?? ^ò?¥ V ?1? ?s? ?á? ? ^?¥b oμV??? V[YV ? MD ?é???b ?Ts? ^? ê ¥ ?  * 1·H¥á?31_ ú l êbènMDZE ^ ?MD x log x( è ?s ú f?) e?? ??) ) nm 4.11b 7ZMD 4 B?? D¥ l êT¨ ?è $¨? { ??Q ? b ?μ ê ?  V[¨· ? e x ? üZ x 2 M Db 34 V B ??s?? 3?¥? ?à qm ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à1S? ?sê ?:à1 x′b 35 ?M] ? é? ?MDa¥? ? s?m ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à1S? ?sê ?:à1 log(x)′b 36 M] ? ¥°Zm ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb 37 M  ? í ? ? ??"?8?μ ?÷M 1?  H 2T¤?M  ? b ?Toμ ?M 31? 2T¤? ?M  ? b ?B??1M  x 6B??1M  yb á ì V[¨- -D¥ZE??sM  x y? ?tZE? ?ís x? y-W¥1"ù5b  x? y-W¥'é1" ^ I 1 ?Tμ¥?$ 1"μ <$ ???  V[YV ?B?M ?? 6B ?M $ 38 ?M s ? ? í ? ?_V Vì?¥ ?3}V ?? V ? ?YF?¥ ? qb ìa?? ¥?s1 V[¨?9 ?9s?b 39 1? l ??yT ?i¥ ?s1V 40 ? ? ?¥c ? ? “ .M  ? I n¥ V[? M .àà? ?s ?M -W¥ 1" ” 41 D 3¥y' ?  1990 M? 2000 M¥ Q1?D 3y' ¥ ?°?· e ì¥ L= l ?V 1990 M ¥ &97,000??  2000 M¥ &91,000b ? ? ú l ? ^? l ?í? ¥ àμ I nY 3nb 42 “ :?¥# Y ”?8" ;$ ? 8"é? ? v V[ a üd9¥? L il$ ? ÷ 'a¥) ^?μL P$ ? ?μB?e?¥ “ ?3 ”s3ZE9?μ úùb 43 D 3y'? M -¥s ?d9 1980 1990 M - s ? f1 l ? s ? f2 l ? <=45 0.5 $60,000 0.7 $70,000 >45 0.5 $120,000 0.3 $130,000 (′ $90,000 $88,000 44 2 ? ? ?TDDp V¥y'? M -s1  ?  M -l? 45 ?¥ M ^D 3D 39 ? ? 1980 M] 50  1990 M] 70 b  M ^¥D 31 M o¥a÷μü ¥D 3?¥ b YV M -1?DDp V¥ l ?  ???? ?" M -79é 45 ù? 3q 3¥?Y ên ? ??? è0? I Johnson? Wichern ? ÷¥ Business Statistics:Decision Making with Data.Wiley,First Edition,1997b 46 d9¥K? "S ?ù? ?Y ?1?ó # h? ??1? ü?K4?ù??? ? e ?¥<y íb C L ?Y? ?$ ?·?b YV1?< ? ? e?<y í 'ù?2 ?a e?y íb 47 “ ' úμ?y? μ¥?y ' úüμd9 ” Benjamin Disraeli 48 ? ?′M  ? ¥ í ? YVV?m 'B? V[÷ b#¥ A?ZE A?ZE B-W¥1"$ 49 S & ??m YVV ì? ^ m ?÷ ?^¥ A? 1 ?SE ¥ó? £ ü? k¥é ?$ 50 "'M1" ? ?  x? yL?M1 <¥ ?3?d9 b ?éD98M1" ? pM ?b d? ?b  |′ -1? 1-Wb ? O??? x i ,y i  ?BH°L  H? V [¤?′ r=-1 ^μ| q¥°L r=1 ^? _¥°Lb  ?T x? y-WíL?1"5′ tí? 0b ? nm 4.15 4.16 4.17 a b . 51 M1?8 1"$ ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à1 x′:à1 y′b 52 M1?8 1"$ ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à1 x′:à1 y′b 53 M1?8 1"$ ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à1 x′:à1 y′b 54 M1??yT1" úM1?üè$p?? ^yT1"b?B2 ? M ? V e¥4?ù??9? ^ír¥b B? .M 9?] H?Y? ?M b B?M  V ?o ^μ ó"7?iyT1 "b μú?[ J ?¥SEμú¥′??h qbá ì ? ¤ ? ì-W¥yT1" ?$ ?ù??B?èn¥ .M  ^ HW? b ???r Bù5 ?" M -79Fb???  r Bù5 ?$ μ Hs?¥M1??31 ??3 d è ? t ?0?ü6? ùb 55 M  ? ¥m? ? i Qm ? ? ??m ? ??m ? Brush and Spin plotsF ?? ? ? bW ? m 56 ú ? Qm z}V ??¥ ?  ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb ?m??à1? ?′?à1? ú ?b 57 Iris ??m ?  ?¥ ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb 58 ?¥ S-PLUS? IóDb ? NGC7531?_ ? K1 ?" ? O: c ? -?  323??¥? b u×¥ ?è?"¥?_ ?b ?μ¥? ?YVe?¥ t?C? =b? ¥ê?? 1?M  ??b ?? êa êUSbe? 0 0¤í???ê1μ_1?_b a 2  2USbe? 0 0¤í??? 21μ_1?_b ? 4?' d9 =¥ £ üUS? I H?Z_è¥ ?b ?_ê? ?e?¥  ? ?SêUS1μ ?′1μb ? ?_ ?? $ ü / e? b 59 ? ? ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb 60 ? 3Dm ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb 61 1? ? ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb 62 1? 3Dm ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb 63 H b¥m? í ? ? m?F ? bW? P¤ ? V[ H b ?? V[9 < HW? ¥3 d ? ?b ? Charles Joseph Minard(1781-1870)¥ ÷ ?A U  & ? ¥ + 1812 M,S ¥^?? >?¥ bM?¥mVˉ? q V¨ c?? http://www.math.yorku.ca/SCS/Gallery/ 64 1812 M 6 & ?  S {,S¥ +?   422,000 7 S H ^¨o § -,SHa¥ P§ Lí Niemen?)¥Y¥H}Vb H¥ z}V +? b  +?r$!aB b OXùl ¥ ? S H :/ 100,000 |b  & ?  +V ? Sü|¥ ^L¨B H?¥?%¥HV UiH/S ü  ?S? ? b í?o § H +o :/ 10,000 |b 65 ?Minard¥m U¨ ?¥M  ? ? ? B?~? ? :¥# Y1oμe? ?3¥V ?÷  ??b ? m?μ B?M  ê?=? ü ?b  +¥?Z_b ü| ùW¥? ^ HW¥f ?b  +¥? b ?“? V ? ^?C1?S¥Kz¥d9m Ub ” ? Edward Tufte÷  The Visual Display ofQuantitative Information. Cheshire,CT:Graphics Press,2001,pp.40 66 S-Plus?¥ b  ? óq ? ??m 67 m ? ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à1?:à1 ib 68 E?L á ìüè? k¨BH E?°L ? í ? ?M  ?  ? ? " ? a? b V[YV?ZE¤?bK l=eE ^K訥b E?′YèV U1 ?μV U1 w q? s′? ^ I 1$ 69 ×?L ? | x ? ??sbs? x ?B?z¥?ê ?is? y?D-M?¥?ê ?b? ? ?? (x a , y a ), (x b , y b ), (x c , y c )i¨Kl=eE é? E?b ? ? I n  eZ T ? ?t V}9Kl=eEb 70 E?L  ~?¥?¨ ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à1?:à1 ib 71 ????μ E?L V[¨ ???b ?Tá ì? x ? S? t v¤?¥2Tü?zb I n =w??w¥ù5b I3?μ V[úùá ì 3 ?? ? ¥ E??? ?μzb á ì]"9 ? ? s1?μSμ b?i¨ n-2 ^y1 p3 a? b31  ?1?b 72 ?μm 1.? E?′ 2.?3 dM  3.?  e V ?¥3 dM  4. ?T V?? HW á ì??tm A  ? ^ ?¥7? ^{μ  T ¥b s′??Y x¥′ù ? E?L ?μ?v¥×?T¨ b ×??μ?v?μ¥ y′ E?Lμ?v¥? Yb á ìYVüμ?Y¥ ?M 7 ?1? E???μb 73 1? ? ¥{μ4? ? I |¥?μm ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à1 i:à1? E?¥?μb 74 ? E?′¥ ? ?μm ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à ^ E?′:à ^?μ′b 75 üá ? ¨ wL E? ? b ? |?|V. 2?s ? ?b ? E?′ ^Y? y¥F ? ü (′b ? ?× ^??M  x¥f ?b ? 1?Q? ? üá?b ? BíL?íB1?1 2b 76 plot(temperature,ozone) lines(smooth.spline(temperature,ozone,df=16.5)) ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à1?′:à1 i′b 77 plot(temperature,ozone) lines(smooth.spline(temperature,ozone,df=6)) ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb m??à1?′:à1 i′b 78 HW? m a ê vs. HWm 3á ¨?b V/_  A? ^B? V?? “d9 e? ” =¥ è0b oμ?V?×?a? V[é?Yè¥d9??  è ? (′Sμ?? uWL !_ 79 HW?  ? ?]"¥"?í" ¥ HW?  ¤¥ ? b HW? Yèμ ?/?sF?b 1.×?y í 2. t ]y í 3.1?y í 4. ?y í 5.?ìy í ?M  HW?  {x t ,t=1,2,…T} HW? m X t vs. HW 80 ? üá??? HW?  ? ¥ ? ü (Z T 1.M? ü ( 2.· ?F ? ü ( ?toμ? (′ ^è ? V? ^d9 e?/ ^%?¥ ? (′M?? ¤ H? V[ P¨b íB/ ? V[¨ ?  E t ]b  ? I n1?M?[#?  ? W¥ MoG ? 1M1ü31÷5é¥Z Eb 81  ? ?M? ü ( MA w?B"  ??¥ ? ′ ?13 g ¥ ü ( ′ HWKò¥ ? ?v$1"b 3 g (w)v üáb MA?? ??μ (′¥ '?s1μ  μ ['? eqn4.12,s  ^ x7? ^ y 82 · ?F ?M? ü ( ¨ ?μ¥ ? ? ^?¥ ? ?× vb 0<w<1 H ^ üáè ? Yè 0.2? 0.3b EWMA?? ??μ ?w T 3 d ?T??μ ^?¥ ??′?? L =′/B?¨ ¥??|_ ???? μ¥B?1 èb 83 1M1" ?  HW?  ? $+? HW? ù üt  s ?¥43′?1üt b  lag" 1¥43′?B¨1M1" ???  M1" ? K¨1M1" ? 84 S-Plusütm lag.plot(x) or plot(x[1:(n-i)],x[(i+1):n]) ??mV ^ P¨ S-PLUS R èqá 3 ?¥ S-PLUS(R) ^ Insightful 3¥B??¨ Sb 85 John W.Tukey(1915-2000) ?  ?vD?: L id9DE y ?° ?=MD¥?Z?-B | “bit”? “software” ó?B  “? ?ù5¥B?í ?s?1pù5¥B? ú ?s?÷μN′b ” T1 “d9 ?D? ”¥B?8C?Z?¥m U ZE ?=m?Qm ?_ ? b