~ I
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G H AP HI CAL STAT ISTI CA L METHODS
II> \\ II.
/lillioll,A.M .I.E. E .. ) 1. 1.11. E.
SUMMARY. ,,,, ,I, ,' ... '" .• 11, "'I"") ", II", I'."~' '"," '1"""'" 11",1.,:",,,,,, " !I,)" "",,, .1,.11 ", ," , •.• , " ". 'It"'I'''' "., "."''''''''.~ ,I.""
""'1""'
_,Il> ... ,., _, ",,,II. ,., .1".-.1 ,10, ,I" .,'"'""',It,n •• "".",. ".,,,,' 1""'~Ij,'hl\ ,·"p.r,,,,'" .,11.111','''' rn "'1""·.11.,.,,, ,II
"""'''1'\,,,,,,,,,, ","',,,.
,. ,,,,,.,,,.1 "'_'1"""" "",10 •• 1, .",. ,1, ... "1.,, "h"h "-'1"11" II" 110,·" .. , ... " ~".'"I"h: • • , ., .• ,-.1".
" .• 11 .• ".1 II • • ,-"", .• 1,1.,.1"1'''''''' ·'1 .•• ",,,. 1""'11 "I .• ' .. ,m .• 1 1'''1,,'11, . . . . ",·1 tho ••• ,1,", .. " ,,' 1·".I.,I,bl. I'." .. , , .1 .... ", •. 1 "' .., ... , ""1,1.·,.,,,,. II .. ".·", ."Ih-,.", '''' .. ,,,.,,,,,,, , • .,;"." I.
,.,,"'" ." .. , •• t",· 1 ", •. ". 1 1'1,'",,_
"I".
Ith,,,,
I ... ·" .. ~." ,II .... ,," I'" """,h' '''''~,.h.''"., ....
II" • ''''''I!'' I, '"~ t.,,, ., ... " .1. hl.'.,ld, ,,, I .. ,h •• -' ... · 1 . • "'1.1, •• 11,· 11, .... ,,10' , .. ,,~ • . " I""I~. ",.
,,, "I" " ·"",." .•• 1 ,".·Ik.,. ,.," ,. "I'I'I"~t .1i,,1 110" IOloim 1''''1.· .... · .,1 ,It, "'" ". ,. ,,, "I1,""r"l.;<:
,nl,·r.·., ,It 'I',· I .... ," ,I,,, ... IItoi ,,,,,., "" 'ul ,,,Ill" I
InlrlHludivlI
B
I{():\lll.r "I"·.klln;. \1, .lI'· ·,It'll '''ULI·flU·d\\1111 , \.IItItIlIll).: II" IlI"I. nl'" "f 0;1II111,lr tltlll).:''' . . !lHI \\dll ("fllllll!.! ,III 1410.1 ,'f .... h,l!
'''11101 I. ,-1.' .... 11'.1 .... 11\1'10 . .1 "h,.,\ \ 1\1"""
•. 10,.,1 • '''I!,I I • • 1, IIII! II " ... ,111 111111 II h I,k, II,.
III.tj"r (1) .. I ,,101" h 111 .1 f.11I/\ Llr).:'1· "'"111'1, ;\"
I, .... 11111 ",r1·"'1 ,. ",II,. 1.1, .• ',f II, •• \,'\ 1Il.1,. ,,11I.d ...
,hll. r tr"111 II" l'p" ,11,<11 •.. 01.,1 I,h.ll I'r"I.'rT"'1I ,., II,. 'tll •• 1 1,.0\, It " .... ,".,]'1, • I ... pr"l~ I'll ... I ..
II,. 1'1'".,1 .,11,
("llIrdl,
,I ""
"I ... 11'. 1.,rlll.') 11111011\',11..tlU!"'llll'rt ... Ih, ' \1"1"'111" .,f
tI ,.
,,10 .. r\'l r,.11,01 '111,11 qjc, rl ... 11. II "10-.,, ,iI" ,J,Il .. 1111 I" oi, hll,· :,,101. "11111111111 •. '1' I', .11I\.'IIo·,.j ...
... 1_'1"11 .... h ., "lIhl" I ,.111, It " I'rllll .• nll·
• "1", III. ,I ",tIL. 101 .... '1' lillo:, ~1'1I'IJlIl)! •• ,,,1. \.1111111
lill.! ,I..t.\ .. 1IIt! "If. r •• 1 1,1ItJ.:1I.,t.:"· 11\' \\111' II I), • . ,I~I\.
101., ... .. 111 I . ..
"rl\·",·.<1
h,r. 'I..unpl.·, II .. TU" .. 'I'r"II"hl.· \·.ilil' "f an "I! ... tI. 11'111.1111'11 II • . II,,· tIl'" al \·.Ihl,) , .... IIk.l II1, :'I,~I,': .1Ilt!., r"II~I.n1l
.... 1,1111 , .. cI .... npll\·,· "f Ih. "011'111 whlth ",,),-
\1.111.,1 .. . .111 .. 1, I' r"lllltllh. " pa.,1 \tiu,' , .... tll."
lilt · .... 1.01101 •• 1'01 I~'I.'\I"II 1.11,,\\ .... · Ih,r, "1'"
rt·!·,,).;lI'{. ,I ).:'r''I,h,. ,.I III' tl."oI .. "f ]'r .... 1111(1).; ,11101
. 111.11, "Itt).; 01,'1,', .. II, II ,., th,' 11,,1''1--;1'.,111 ,Ind llJ.:"·'·,
" 1".11 h., •• I"·, II ,1"",,1.:"" ,I I,' • ,,11\',', 1"" lit 111 .. 1' 1.1,
.1.
,11,,1 .tll" ,\ •• rl"I1' • "'11 11I"','h I •• , • •Ir.,,,,, "
""h " /llillll,Utlll .,1 l.d)!111'-
1<"" .. 1,,11, I~ \I .I, I. I"I~ 01 "I I~'PII'.III"". · "I lII.tr,,,I,,.II ... 11,,1. j II" ,h"lr,hllll"U "f ,,"11\1.111 .• 1 ..
III II ... , .. ,1'111 .• ,' ... ,,' ... 01111"'" ,'f 11101,,',,111.,(.. Ir,.", ., 1'",,111.111"11 .\lL1! ,,( 11" ,h., r.hlllinli of 111.\1\ ,,JII.\; ..
III Ih· "'1111],1, II , .. ",.\ "lIqlll'lI1~ I', 1111,1, lh. I, I,., •. '1"tI ,III 1I!..tI p.11'o III 1'''1'111.11''"' h.,. 1)0\"'11" "III
,'1\, "
u\.-,t!. Ih,I' I~. III Ih, .1I1lt'tlltt IIf 1"("rrll,,I">!1 .... 1L" Ii ,.,,, I~· !III. rr. d," ,," ,I,,· ", I "
11,,111'11111.,1, ,Ir,' tll .. rr,hlll.·.1 'IIIII' '''''1'111.'11\'11, ,11101 ,It ,I,.. ~lIlli'II\II\' Wllh
\\1".1t 'I .·:tll I,,· ,I,~.I,I~,I oI'U] tI,hrlol' 1'111"
,,1.· .• 1 Ii .. tnl'IIII"" ,,, kll.,WI, .I~ lh.· . :"" 'flll.ll
1)1~ln"IIII!'n ' I'f Ih, \ •. '" .... ,,111 ) ... ,rchll"'"I.' ,lIIeI ,~ f"u"eI
t.,
.I"I't"'IIIUI. (I" ... I\' I., m.lIl)', .
d.: .. lnltl,""'\" 'If .. h ... r\'.lhl,· '11l;lIltlt1\'~ III 11 1111"
I h. 111.1111 l)oll"r "j I. ,rill/.: d ••
, . !
I', ,,' •. \11,. Ih. I'ml\",dll"I. 1"III,w .1 S"nll." 1)0;11,11111'''11 '''' , ..
I.no .... \du Ih. r Ih' • ,to 1"1\'.' pr,-'" U"Il'. 1'1'",", I" Ih. "I. ,tt ]~'I'IIL1I1"".' ,II, I~' .ll'plll.1 "11111111 ,;.,1111.1, III'· I,. Ih' I'r"III'II' 111 h,uIII 1111 ... 11II1,h Ill' .11" Iholl If Ih, d.,I.\ ... ".,rlll.111\- d ,ndml •• 1 lIIudl I."".ur , ... ,\ .• 01 I~ ... "1 ... · lit, '·.lfI""~ "r,·lit.
11111" It.,,'. I,,"'u '1.lhlll"I.·" ,tII,1 1'"IoI, .. h •• 1 hI th,·"n l".,1 ""r!..,,... III Ih, hd.1 If
,It,·
.1.111 ,.""I 11""11.,1, Oil,' 1 •• 1 .. I', 111.11., "Ii' .. IIII'll •• ,1. 111 ••
I" '" •. 11,d ] If,·d"·I,,,,,,.
1'1" • IIrr. \ 1 .,II,lu,I!· ,... I" tI.·, ,d, wl,.II IIIf.,rlll 1- III'" ,. r"'1U1r,·,' frum till '].11,1 .Iwl .. h,
,'". r
,IJ.:r.q.IHI".,1 ... "IUII'U' " ,.tI"[II.'I' If 11.,1 .... h ... h.r
"11' 11;1" "lilli, ,..111 d.II,1 I., phi II,· .• 11,,111, till \ I,'~'
"f .IIIITI. 1'11111:.," In.,h~, ... (111,'11 .,,, •. 1I11,1.,Ic,1 Ih' roo ,IT • .... I,'" 11,,11\ ,,111,11. III 11 ... ",,].1. ,1 "", •
"1 .. ] .. , ... 01. Ih .• , .\ • IIrn 111111''; ;111.11\ • .; " .. ul'] I .. · r.llh,·r .,\0,"1'01. .11111 "II\'r,.II. " . ,I Iii, .. h '''. ,111\
l'II~."r".'\1II1-: .. \.1'111 "' ,urn 1III'"!.! hI..
I'r.;h.",,1111 1'11- rJ h • '111,1]11 IIlIr. h .• IoI. F"f Ihr .. n , .... ,n pl.,h.lluhl\ 1'.11" r " .1 ';1I.,r. f"r Ih' 1IIl\\.,n . . 1" Ih, I. rlll" .1'I,,'1 I', II ... II f.,r \, rv .1110111 ",11111']'" If"'11 1II1k.h,\'11 I"'I'III.ill"II" ,. \'. n r.,:r".ll 01,"111 ... ~I h lfIWlh.II.lfrl ... ,!ll.lf,.II"w ..
.1 1I.,nl\.,1 ,11'-'1'111111"'11. Ih.· /':1''1,11 '>11 II,. 1'1.,10., 1,,111, ".,,~ r wdl l~·.1 .. lr.lllo:llr 11110 1,1t!" 111.', 11.,1 h. ).:', Ii' r.IIII r, .,h,,,,1 h".\ 1,lri, I'- 'h, c1" ,,11,,"1 11'''111 III" .Ifli ,. wlth'l!, "II I~ 1,,1,·r.II." III ., pr.,. ,,, .,r
•• , ... 1·,1' all ,'''1111'1'1,,,,, "f 1\"1'111 .• 111\' '" I~' )".1"1,,1 .• 1" ",II I~· .hl)1I11 [.1', r
I h, li"n'll\' .,11.1 1.1 ... 111.,1 •• ,,, •• f pr"h,",",\ ]"'1" r
"·,,,1 ... ,,, ,.
hI'''' th, " ... 111111'" "f Ih.• "1Il1ll'1I1 Og,,'" (fr.1I11 whu'h 11 I" 01,11\','",1, 111,1 .11, 'lI']~ rf,. I IIl1d, r .. t.tllthlllo: "f I]" ,·\·,,11111"11 ,,' I'fI,IMhll,ll' l"'I~'f L.11I "'Itl I, •• n"r ... 111,' t"
111\ "rfJ~ I pt"IlllIg .• ,r I', .1 \lr.,,,!.! 1111, qm·I"''''1I
III ,I ... ,1IT1·,·. ";'''lIlt .HI,III!'t I ' 11I,,,k . II,. ro I"To ,
'11 Ih.· f"II"\OIIIJ.: 111)1 .... ,,, I'TnI",,· ,I h." I.gT'IIIHd
"f .11111'1.·. gr.'phl(.:.II ... 1.11, .. 11, ,.I IIh IIt'~I .... uIII III d"III"'hlral.· ';""\1' lIlil, r,lIt hlllll.tll"lI, I.f proh.1 h.lltl 1'.11" I'
'IIII' lIitilu~r:1I11
In ""IH'-\lllg ,I 1J1;1 ... ~ "f Illlnwnr •• 1 n'~nll~ "TH'
1'''UIIIIIlIIlIl!\·..i} ,&.:r"lIp irl"lIf1' ,II T. "IIh~ 1"~'·lhlr.
0111.1 p. rh,II''' .ITT"",(("'· IIH' T""'III1I11:; ,.:r"III'''' HI . I~'· !101m,&.: "l"oI"T of Ill.lg'IHI",I.· ,\ I"gll ,II "'10-11 ... '11 •• f 1111 ... Ulo-.I ", .. uhll .. · I" ,L:f"Up ft~lI!h \O.!t .. h f.1I 1"'11"'11 ,i"liml" l)ttlwd.lfj,"" ,Inri I ••. nT;II1l.:' Ih,· ... · . ..;r.'ul .... In :I""·.lIrI,n.t; "T,I"T ,'f 1l1;ig'llllu,!t·, In Ihh " .I\, III" ,',,'" .11111'11111 "f ,\001.1,1 11'lIIld 1-..
lII.ul,· lIll>fI- '''lIlprl·h'·II'i,hl.· . . Hld .III\' "'1j.,:l1Ifit'.tnl ddf, f., ... , I"'''I'''''n "Ih' j.,'TOUp .iIld .III"IIWT w'mld t ... flIUo .II'I',IT'1I1 h'r "\,IItII,I, ... l1l'p ... Ih.-II .,
t .. ,\, TIIIII,'111 II, 1, •• rlUlI'lIl 11".1'" n'ttllr"d I" T"'IUI~I 11,,11 ... liIh f"r ,I, rn,,1>;11I",J .Ifln.·" ftln t'''', .0101 II
II.h ' ... ·nll.lI I" ,"n ... n',· r.1I1 1II,lt'·fI.ll" .Hld I '''''liT . TIlt' I'r"I.I. In \\"uld I., I" d, ... ,I'.·r h"w 111,111\' "'I'r~ "I ~lIlh would h.· r, 'pllfI'd. :11111 h""
1".111\ ,.I ",1< It ... h"lIld I~ 1I1,IIIUf,t, Illn ,I
1'1 .. IIT ... I ... 1. \' 1I11J.:III 110' I" 1.1\"'" .1 .... 11111'1.· "I 'I'· It "I r,III,I"1II. ,IHoI III. ,1"'l1n' lit. If 111,11'-,.111,11 1 .. 1..:1.1 .. I., II" n",'T, ~t 111.11 .. I~ .. h"WIi in . ,,111111l1'"
I Iud U) 111 [,d,l. I 1.\'",.· Ill. n·f"r,·. 11t.1I lilt'
I.. .:'11 ',f .1 m.m ,." ,rd.-, I .... 'i .... tit 111.1 \ .. It 111.111\, i~ ,In Itil' I, 1.1\\""11 'i7! 111 .Hld 'i ...
!
lit.)"
II ... ItI I ..
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I.,
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.... 111111 .. ·'
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... "1·1 .. • .. 111.11 II ... ,1 .• 1.1 I .. ~f.'ttl'lo·,I II1!" hru,"ld,r
, ... ~. j" ,1:·.IIlPI.·. 11110 111"11 "111i h,'~hl ...
t. 1\1 .. II
'iN!
III ;lIul h,! til 'lwll~'(II" '/lI)O'~ in .11111"t! 111. ,11101 _ ..
"It .
as shuwll III ".IUIllIl I J) rhl ....,,~ J~' 1'1"". d .h ... h"w/I III FI":. I (;t), will r,'
, · . It
h\, 1_" , .. ~ I'''',.INU: •. lJlc.awlIla 1949
!,IH.IT r" pr, ""111 ... ,I ~'1 .. ul' III d,d..t t.\ II:> h'ldll 1."1111: Ilr"r'orl,u"oll 10 IIw IlIltnb • .'r "I 111'11 " ltltlll Iltl' ~ruul' •• 11,,1 'h,' ... Ii.: ... IIf Iht' !'III.IT d"IUllo II ..
j.!'rllllp 11\..I1I1I'1.ITIo·... :O-Ul It .1 hg"IH' .... \"'n"wlI .,,. "
Ilht"J.ir,'III. ollul I ... \.IIII.d,J.· I"r ... h" " III!.:" 110 •
" t .. ,JI . ur 111' .... 1 fr"qu. nl ,·.llu" ,1111." III lit, ...
1,1 ... h .lhlll1l I,'illi .. lIl1illt,· dhl,.'r~llIlI. flr ... ·.III,.r. 'Itlu T ,,,i,' of 1!1t' ,\1"tI.·, III., wltnl. I[ .h .. ". Ih.
dhlnlmll"l1 "f 1I1t1,1·,ellI.", 111 Ih.· .... trlll'l, lin
""111.' "r,,"I. Ill-. II 111.1\' !.It. IIlI,r. \ "rn •
.!U,
Itt 10 1'101 lit, h'lj.!'ht',f
111.1").:"1" .• 111 l'III.lf. !,r"IH,rll"II."I .. lit, I" rlllll.I!.:",· .,( '"I,ll ,,]0 ... n',IIIII'h •. h ~I\'. n 111 1',11,1. I .... 11111111 III .11,,1 .. 11"\'" III Fllo:' J 1
,~ ~'\l~ ...
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h,.; ' 11"/".:"",, u ... f /lcu, .• ,,', '''~ I" tll'I .. I,,,/, ...
", 1t~,.'Jo/ "" " 'I "" If, ,,",( Iltr ..
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J ,'I u.1" "fI 0/.'" (I~r ,. ... ,. ... , .... . " """ "." • • "}o'Jo/, / • ..",." ..
I ""
I"~ ,,, " .. ,( ,,:' ",
The' O,.::i\ C
III pr.,o..IIO·. Ih.· ,.:rllup l> .. u".I,Lr ... of Ih.: llbo" "
f,:r,lIn an' (;ho""11 :Irh Ir.lflh· s" .• -:> I" 1I1.1\"', .1 pn· ... llt.lhl" f'l-!ur,' •. tI,,1 wlll'r".lo; I( I .. 1)0 "'11,11' I ..
J
Itt ... ...,h;11 propurtlon of nl~n havt' lw:ighh ~tll'een,
lIiIy. 'lhl in a.nd 6q1 in, It is not f'uy to ~ what prupnrtion woula haw hf'lgttts ~1~n
Us
in Md 67 In (s.;t\'). or what proportton C'X~ed70ln in tw-'Kht.
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o
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I I I I I I
(b)I
.. •
0.. .. , •
.U1U ... ' (..n)
"'I:
I 0(1' JJ"'trtU.,, llos/"K.( .... ""d 0,11' oj/A,m, .. ",.,.; 'UII""'r~ UI ... ~ .. 'J·r~.u .. , .... 1...4 .... dn
J~lIlrouJ co."I"",,,,. ,}II'II"" t ,.""p,,",lu'" "1 Mt
u/.,."I$
T" wh't, thiS kllld of problem It IS b.:U("r to If)fllI'U!t: thl' cumulatlv\' r~
..
rc.;-ntagc of mt'n, as,huwn III Tabk I, I..olumn (5). For t'xampll',
II:'~. Iff Iht, mt'" had ht'IKhts bdwt.:t:n 571 in 4lld 60t In and 9 2-" bt't""'t'f'n 57' In and oJ' 10, ,Uld so un ~ot'ct" that nu man IS n-corded willi h.'IKht I.,!os Ihan 57' m, and that o.8~. of tht· mcn
... fl' ,'ncuulllI'ft'd O\','r th,' rang.· 5711n 10
bo t
1.1\,Ih,'fl'forl' Iht, cumulalivl' l~rCt'l\lagcs must be 1,lotll'd al thl' ('dgt'!'i of th(' class IIItf'l'Va..IS, as
!>hown III flj{. I (b), This curv(' is an "Ogtv,·."
,md provuks dlfiNt'nt Information from the
-
j..-
HISIUKr,un I' or ,'xampl,', till' proportion of mt'n hil\'ing ht'l,I(hr.... less Ihall tl7 m I" 541'" ami thai k-.J Ih ... n b~1Il II; 2t,~ •• Ihl'rdurt' th,' prol)"r uon uf m,'n bo:-l\'I~'n h"Ighls 65 In and "; III I' Ih" dlfft'H'nc.'
5.1 - .Ill ,... .10· •.
11m, nll'an, that if un.' "tandartl d"SIKIl HI SUII IS illh'lId~d tu fit ml'lI bel ween 65 In anti "7 III m hf:lght, 1111' number tu be rl'qunntlon,'d ~holiid
be .l6". of th., t013I. and ... 111, l lk, .... 1:'1· II
!K't'fllS hardly wurth whll. 1ll •• kIllK SU1I~ III hun.
fur statures less Ihan ,1.1>0\11 hum Vf o\.r iJtII and IheSt' men could boo hlh'd tIIchvHJu.llh
OIW valuabl(' prllJ>l·rty "f th,' {)gIV'· IS Ihdl II IS 1.llrly IIUk·nSIIIV,· to Ih. (hulc.· IIr d.J.ss mlt'rv.d~.
(Jul'IloKrolJII gn,ups) .tllIl Ih,'n forI" "m(~'lh ... toUI I h., oat a whIch was cuar ... 'lwd h\" ... rrvuplnJ,:
'''1 ,h ,'
i"usloJ,'Tam.Thiscxarnplf' ha"!llwwll .... 11"'1 \·.dll.IUI,·IIII"fIll"
lIOn can ho' obl"m"d fr(lln Ih, .• ppll' .Itlllli "I v"ry (·I,·ml'lIl.!r)· M,ltIStl('"J [(JOIJj.. illlt! .1 [nt[,
common ~'n~·. and th"fl ha. .. bI'f'l1 n .. /l,.t! I"
test ttl<" l1 .. la for normalilY. "r l"onfu",' '111\ ... It
... ·llh pn.'lhrllnns b;lM'd on th,' ~ormal Ih .. lro-
blltl"n
Th. (~I\'" I~ lI.Irl1t"ulariv u ... fur f"r .11l,Ih· ... "'1!
data ... hoso· l\,plr.11 \"Iltl" (~t!ld"J 10"1111 .. I ,I" • I, ... , 10 ilnl·xtn·If).· \".Iltl,· Fllr ,·x,lmpl,. HI 111"'1""111111.:
"IC'ctriral ~wllch,!'. Ihr ... llrh r,'","'lallr .. (".11' nev .. r bot· It·ss th,UI I hi' r"<;;I!>la", I' ,.1 Ihl' ("II/ldm I','"
furrrul\~ Ihl' ... llch IMrt,. bUI .! .... ·.I\ .. III.,,.
d.·pt·ndlng 11])1111 th,' ("n(1111I1O of th. "II1I,1! t
"urI,"·... In .. urh ·il ra~ ,h,· 111 ... 111,,',1111 '"
ulbynllnf'tflt.ill or .. "k,'''''''' Fog .I ial .1IIt! 1111
~"'\'~ .. hi' ... lilt minimum n· .... I.In,. '1!l11.
cI.·arl)' . ... hlch I" 01 cour'ot·, a Wiof. ful Il.Ir.1I11I11 r for JudKing' tl ... 'Iualot\, "f Ih,' d,'~ ~/l
If a h·dll1l\[lh' ,1lt·lllpl"Y'·d "'" Ih,11 th" ,Ir"m,
JX.1IIlIS lit z,cro and IUQO~ ar,' Illli pl"ttnl lilt
ag,V('
KIV,· ... au ('xlrap"I.II,·c! vallI.· fnt Ih,· 1111111 mum r{'''I~tanr,· whlrh l~ m'lo'I1",tlvt' In Ih," h."r, flf 11I ... lugr.11l1 das .. Illt.·rvals. (III liar 1'o1tlth ... 1 Thl.!> h a t , Jo1;"".ob], lI·dll1lfl"'·.f"
.111"1'1 ht·(·l\u ... • oth.'fWI ... · th,' ,Irh,tr.tr\' ('holc" /,f .1.1l'>"1111,'1\,,\1 ... ould ."h.IT.lrd\" fi, Iht' p"lIll .. f IA"«
cumul.l.II\"\· "bSI.'rv,lllOn .. ,It th,' "dKI' "f Ih.· I" .. , pillar, whf'fI,:t!' II 15 Olu ... h ""lIer II) I. I th\ 1"I"'ft
data ... ·IJ(l1t Ih.· clil1lC" "f th,~ 1"11111 b,· ,"!(Ir ..
polalltln. ~Irndar r"marks apI'''' 10 lilt' wo pOint It , ... \"I'ry 10'" rUCI 1\',' I" ,'xl,,·nnl.·!U
","ilh ,l(fflUpll1l( data doff. rontl". ,tIul 1I1~'T\"
how sll~htly th,' O~I\"'''' aff,ct.d Graphiral Groupioft of flula
h ,,",\1'" a ~'TI'at (Io'al vf 11m.' and labo.'ur I ..
r('Curd t';lch ohs.·f\'atwn dlrl'Ctly un Ihe )(r3ph pap'r 10 hf' USed tOf lh,' HI~llJt;:r.lm, by makll1j1(
a bold dot uppoSllc' lilt· appropn,'II' 1)01111 un Ih.·
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h ... I .... Q . thus fomlmg rud.mrntarv column!ll of fIt!. :.is ubSo'n'atlons art· Tt'peated. Tlus me·thud a ... ,h.· I{rt·.11 ac"'aJlta~"(' that on,' (;lLn J(.'t. when ullh':I"nl data has be"'n coU,octcd. as thl' dls- nhullOn of dOls b"gllls to sUg'g"st a lh·fuutt'
"rill It IS th"1l ,'.ISV to mark th., dots off
!II .. ",'"Llhl!' groups ai\d con.struct a Hlst~ram IJ: .... tI un th.· numbt'r of duts falhng Inl" tadl
·TUUp . .t" ... hlJ .... n III Fl/{. z. (\\thl'r.· a dut hJI&
In .1 /{r"up buundary, 011,' half nf an obst:rvatlon .11I+1I1d ",unt III (':teh ,I.,'f',.1l1p.) TIm, IS called I 1.I"t Dmb"4.m. and tht' intl-rmedtalf' step of
lrit~'ng the }-hslo~r.\m b lIot lwct:ssary fur
"nstructmg lUl 0g1\·1·. as th,' 101:\1 number of
\"IS cll(;{lunh·r,·d up to .1 Kl""'11 boundary call
~ 0;0','1\ ,hrt--:tl),. Llk"~'I""', hy ub ... 'rvlllg qUa.tl· Itl.·S I" th,· lI,·a.J'eo\t {'11II\f't'T\ICIII UIIII. Iht, dot"
"rill 1'1.·.t1l culul11l1s and hiwl! tl\l' "'-PP"'ar3Jll;"
.f Ililoto~'1"am PlllMS. whIch then·foTt·, 11t'I,d not .. rlr.IWII
\1U,tl .. r ulh-anl..Ll-:l· of "olk'O(""~ "xp"nmcntal Lit •• 11\ dill dl.lj{T.HlIlo. ,~ that It lihow:-. up any Jr.ll III pt'rfunnMu':I' du,' til wIlnmllK lip of
·'IUlPUlL'lIt . .. " . rhl'" bo·t:umcS appart'llt wh,'n 1111' 1I1It!, tilt' CI!!UIlUb "f dots n"t belli'" tLllcd
III ... r.II"!"1II lllaJll1l'r. hut Ihal OIlt'S hand IS
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m,·a.~lIrt·!IU:I1I ... 1ll.'I1IIt)!1.·d ,· .• rlu·r. alld the sc,,[u-
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(Obviously Ih l, SWllt:h nm'!t b!' "ivcII Itnlt' to (:001 down 1:l\·IWI.~'1I l'Xpt'rJI1ll'IHS ami I;trl(;tly ,;p.:aKlIll!. tht' o~rY.'tlon<; should lJt· m,utl' 011 ablml thl' samt· nih'.) TIl!' d.ua h ret urd.·d 11" bifid dot". or utlwr mark .... lu. olh'd "I thl: .Ippr"pnalt- 11111.·, ,I~ ,Imwlt 111 FI,I(. J . .ill<l IUII- '1IIut.· ... ,I "; •. llh'r 1>"1,1..'1",1111 wh ... h I ... IIII,n(Io·'[
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"wlIch r.·",,,t.ll\! ,. uh .... ·rn·t1. d,·I .... ·II'\.-rl. I" ,I gr"al ,·XI.'II( 1111 till' r.·I.' ... ,· UI1\,' .11 wh:ch Ih,·
"h"'·"·all"ll w; .... mad.·
TIlt' IJlt'lh"d of ITt'alllll;; lilt' d,II:' I .. til .l1vltl, Ihl' !\',I.t!r.'11l lilt" ,,111 I all],· ",·rth.11 "trlJh';'l/ Ihill Ih.' d"" ,·Itrl"",·t! ,,111 h.' '·IIn ... loI,·r,·'\ In 11.1\"
,,,·curr.,tt .11 Plu.t!hl\, th,' ",HIli' r.-l.I\I\.· Wilt Th .. n •• Hh ... tnp of d.lt., "In I" lr •. tl<d ., .... ,
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r"qulft d FII-: ~ thl .... 1;;1\, ~ .1 \'. nd.'aT p:C'lurc of tilt' I",rf(.rlllanl' Ilf !lit' ... ~I1. h For I'xampll', al).ml 1\\'0' 111111llt'· ... ah, r "'''110 11l1I~
on. Ih l· , ... Itb w"uld I .... ·
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I"~ It, 1 .. ·low thl" \.dll.· .11101 5""~ .d,.,\',· 1.11..·
w .... ·. Ih,' dWIICI' that IIII' r. ~1~1.11I'-'· would ,·:l.ct·l·d 0.47 mil i ... :l1J<1U1 on.' In IW"III\, 1"·I.III!'.
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l'kfurc lr;lvlng the l'ubjKt orDot and Scatter J)lat,'T:mui, Ihere
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one dlsadvantag~ that ,hould~ mrntionl'({, namely that lX"Cause one can ICe
Ihe dI3!,'Tam taking ,hape, on(' i, inclined 10 ('heat, or ,hall we say, be blasrd in one', judg- ment, and C:\5t the dOls Into where one thmlu lhe)' should g<~, A great deal of. self-discipllne has to be t'xl'rclsed,
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af ploll'"1 paullJ ., I., ~df(J of Ow doJS ,tOl,.",.J.,Arlthmellcal Probability Paper
Prub.1hlhty Paper IS sImply :\ spc<:ial graph rapt r for construclmg ~I\,(,l', in which the wrt,,::al scale for '·Pcrc.'ntagc IIf Tota.] O"""'n'a-
Illms' IS 5trdcht.-d, at th,' rxtro'miti('s m a p ... rticular way. This scalt· IS callrd thi' Prob- ahlIJly ~alt' ht'causc thl' ~"'I' rcpT'('5c1l1S a
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populatIOn IIf a large numbo'r of II1dlVldudls fwm whIch OIW can tll'duCI' tht' odds IIf all obst.'rvallvn falling above or below a pMtlcular value, Lt'I II bot' l'mplial'lU'd al IInC,' th,1[ II IS not eSSo.'nllJ.1 to usc "p,'('\al prubahlilty p'II~'r to do thl.., indced ~\' ha,'c Sl't'n In th~ pn\'IOU" ,,"'ctUIfl th .. 1 the common Ogwe can be u ... ·tl
The prt'fix, . Anthmdlcal' ml'all!' Ihat th, scale for th{' vanabl., IS hll'·Llr. whlk' wIth l..(*'.Ir ithmic Probability Papo.'r. Ih,' !OClik fur Ihl' van"bl.,
is I~Llrith'flIc : the prvb'lblilty scale L','IOg tho
5affi(' as for the aTlthmt'tlcal p.tper. ObVIOUS]"
ont' could u* a IOJ;::anthlfllc 3Calc for Ih,
"ariable, In th<o COIl'ilnlctlon of the comm"l1 OgiH!, If stich a sca.le uffl·ro.'<I ... c1carH plCtun' vf the data,
Most OgIV1!S MC S-shapcd curVI''', and bt'Cvnw difficult tv read at the extremeS. If th\· <;ca!\. I'"
expaOlkd over thC'sc S('('tl!!IIS, th(' readabIlity til tht' graph is ItIcreascd, but thiS dtJCs not nlt'an that the r.'lIabillty of th(' data
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increaSed. Inexactly the l\:lmc way. msp('CtIllf,:' the po-oJ!IVII of an amnl('t('r Jkllnter with a p'lwcrful magrllfYIn,t.:
lens d()('s not IIIcn.'a.5tc' thl' pn'(;I"IUn of a currl'lIt meaSUrt'ffiI'nt, bo.'CauSl' lilt' callilr.llloll rna}' n<>, bo.' r,'lIabl\', 'nils ITII'an" th.!.t wllt'll O~I\,"S ,If,
plotted lIll pr"babihtv pal',,'r. IInl' must 1>- ('xtrrmrlv cautions :thullt makrn/o:: u ... · uf t.'xtr ...
polall'Cl mfurmatlon al Ih., I'XifllneS of prub abIlity !o('alt~, 50:\\', uUlsld.· ttw r,IOf.(e .,f 5"~ til Q5°.,
AI thiS stagl' II l'i con\'('lIIt'i11 10 I'mph:c.u."
tht' COTrI'Ct mt Ihod of pl()tlIO~ d.ll:& un pr.jI.Mblht, p .. 1.plI.'r. S,IlCt' Ih,' CUT\'(' 1~ re,IJlv .Ill 0";1\,,', Ih., POlllls cvrft'SIl<lOdlll~ to n l!1lu],\{Jv,· ,k:rtJul"'"
data IIlIISt bot: plotl"t\ at till' bI'Jund,lr,,'" Ilf tilt liistOf;'ram J.:roup .... a ... hv'A'lI In FIg .. ' ,.lId n,,1 .11 tht, c.'lur .. 1 ,·.Ihle ... 'If thl J,'Tllul>S WhICh, by th, wa\'. I" ;1 ('omm')IJ ,'rror, ~JIlrt.' thll.,r\· IS ntl 7 .• :r ..
or 'tOO~~ 1111 Iht, prnbabihtv $Cal .... d.ll,I fvr Ih.,.-"
points mU~1 llt'cl's''''Inly bf' "mltt('d.
If t)14' I'r"tt"d fWJIIltS LIJI ('xaCllv tin ,I strai~hl IIIit.'. th., d:\I.1 IS normally ,illotrlhult-d. bo.'cauSo· the prob.1.hihtv '\('ail' ha., bo't'n sl")('('Iallv ~trt'lchl'd
to make Ihl'" '>0 l\allirally 'Jl1I' 11("" nut ,'I(I'M'(;1 t'l.:perimt'lllall>OIIlIS
t .,
fit a ~tr'llt:ht JIllt' pt'rf.'CtJy but tht· IlImlt'c! ('xtelll of d"\'I;II\OIl allvwahl, may flllt bo· appn'Cl;'1tHt, and onl' shtlllid h,I\', at least tWI'nly poInts to plot Ilo"fun' tlra.wlIl;.;' any serillus cunclu"lon'l al'MIllt normality,ThIs i~ d('arly t1,'lIlon"tra"'t.1 III Fig, 5, which shows data plotted on probab:.bIY paf'l'r. fr .. m rectangular and triangular pupulallUlls,
tot , .... ,
IX'Ople wlluld ft'd justlfiffi 111 dr.lwlIlg a stral,t.:hl hnl' Ihrough th,' pOint ... S"'\'n h}' I·uht'r "f Ih.
S ct'll Hl'iIW,rrams and might, Ih"rt:furf'. bot' I,d CTTOIlI'OUl'I), 10 b,'ht'\'(" tlMt both populatIOn.;
WI'ft' normall\' dl.;lrJbutt·d
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"ruh.lhllily ,,1 Ih,' flr-t rUIII! fllr Ih,' r"ct:U1/{u!"r d • .;tr,lmlll,n cump.,ro·d with thf' IlH'r.· ,,"rmal In.m"u].lr "",', f.,r ,·,,,ampl,·. I" :,)Pn fllr II ...
" 1.t,lIl~ul.lr . . 1/.:'.UI1 .. t J.I"~ for till' tnan),(ular
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'I h,' P'ljlUI.'ftl\ "f prIlL.tlullt}' 11.11.'( I .. tlu,'
.11 IlU .. m.,lI 1l"·""IH'·. t., th .. t·.I~· wII" ... llIc!.
r,m.!""1 Jnlln'III1',II "h ... ·t\·.III • .os 0.:,111 1)0' h.l"ultod .,lIhIlUj,(h tho ,"111111./11 (:.,.::''''. C,III h.' II ... 01 i l l
~·x.l1·t!\ th.· ... Llll.· ... IV (Thh kl111y,lni".· 111.1\
!'oWt· a 11,1 "I 111111' ;iI1.! labuur wilt II .. uppllt'., "f Ih.· sp"n,II gor'lph paptr an; I\ot a\·,\IIah",.)
1.<'1 u" '·"""101, r th,' '.I~· "f (,ur Ilr .. 1 (';\,11111'1"
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Ttlt' fir .. , :I~"l1mpli"l1 III 1'1(' lI!ad,' IS Ihal ",Ith ,,1ll-\·f\,.,U>t" lI ... s the SoIme
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In otht'r w"rds Ihat "a(:1! of tht' 10'11 (lb~ r\· ... tions r.'prt·- ... ·l1t~ .,h,ml Ih,' !o':llnt· lI\Unlx'ror tn.'n III th,' p"f,'llf PUPU!.III')O H1 (ITO. Thi .. mo..an" th.u "arh III d,,',dual "h"'n'dtL"n in the ...unpl,· 11> oI.S."Ulm'tilt!f"pr, .... ·111 tll.9 nlt'n or to". uf th,' lut.,1 fIl.· ..
HI tt ... l\,lft'llt p"pulalion.
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!>I'(:l>nd .I .. :.urnl,ltVH h that ":u_h s,lmplo:ItIJlvulu,11 IS l}1m,d "f (h.· 10°. of till" p.ln·n! pupul.lliun it tS ., .... um.-d to f.'prt' ... .-nl , Ihal IS, ,hal 1114' majl/fit)' vf tILt- til 1 heIghts of mt-It
t'MI be- ronsld,·n·tI III hi, clush'r('d round th,'
-...1mpl..: \ .du.'
\ tlurd <Ls .. umptlon llhal, fr"lII prt'I,OU"
'11,,-=rJl'nfc "r uther cj,n'ild.'ratIVlb, th.· d.lta can
t.· cxpeo'tt-d to D' normally (il .. tnbllh'J) I"
~·.uu.lblt. but nut ":.lit·ntlal. :1'; II 111,':'11 .. thai IISIU/<: probabthl}' p.a.p,·r. Ih(' h ... 1 .. tralKht 1m"
,-;'Ill h,. tlr ... n Ihrough lilt' 1)(JlIlh. alld .. u allow ..
{,urly :.Lnall sampl.,:. 10 b ... u~ .. J.
rh.· So.·omd as. .. uml'twn IS Ihr k<,y Ir1 II", 1II.·th".! (.f plott lilt{, b..'i.:.IUS(· It nwans Ihat If th,'
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"rol. r uf m.lJo.!lIl1ud.-. • 'OILit HI lurll ('orrf'spond ..
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I\· .·
gruups of p"puloi- tlllll. In tJlher word:.. ,·.Ieh 1t,lIl1plt' mlill-ulual I~ .t .... uln.·d to f.dl 1l'·.Ir til'" ('''I"rl' Hf th.· ~rnul',uul tllt·r.fur.· III Ihl' "\(:ultpk .h(~'I1. hoi" 5d ..
"f Ih, P"I'Ui.111tl1l bduw H In tin,' boundar\' of
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.. f 111<' 1,,1..1 ]Mr"111 p"put.I(lun wuuld bt· ,'1\-
,,,"nt.r.d, ,I lid .11 r.·.uhlllg' th\' $o:·cond. 15~.
""11101 lL.I\' /), .• II J!.I"~·II. 111..1.1,. lip uf th .. fir .. t C'''II[l (III" .. ) pili:' h,llf .. f Ih.· lit· \(1 ,,'TuUP ("iv,,1.
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rur "'11 1111 lL\'1(1 11:11 ... In th,· ... ulll'l.·.Ih.·)' :.IItJUld
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"tl8l'r\'oitwll should 'K'('ur al 100 III ~ •. EX.llIlpl,·
"'UI}~' tllt' h"I~hh vf "'n m,·n.I.lk .. n .11 r;lllrlum.
.... ·'·n· as l'>h()wn III T:thJt· 11. and thai II W.I" knu..,>'11 tiLat a' normal rllilrruutllm ("I'ulol ho.. "'IIo,{"fl'd Ill<' prop"rllQIl .. f Im'n wllh h,"ghl:' h.-Iwel'lI
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ill llll' lullu ... ·"';.: ""r- o:nl .. ltc~
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The :\urmal lJi .. lrihulion
,,", much has b""n ... !III .11>/,111 Il~lmK f"f ll'!fmnlily. and wl\( Ih,'r or lI .. t 1111111'1(111<11 ... i!
be tXprt"h-d 10 foil ... a normal liL:.tr,ooll"n that .t "hort dl'-l.·USSlun I,f Ih. pruIN·rtl>' ...
"pprvlJn ... l~ al thiS .. tag,·.
:\,. nk'ntl1Olll'd ·pr.·\·luu<;l .... the S.,rmal 1)1"
IrtbUllvll IS a (/mc"pllon "f .In II.L .... d p"pU!.,tl1111 vf Inc.!n-Iduab. from Ih,' pl.llnl \,f v.< ... If lII,uil.- nl.ltlloil an.llylo'''. It I" b.L ... ·11 "n lilt' a"~lIntl'!L<'1I thaI d,'\'lallvns vf 11ll!;\"Idu;,I ... frolll Ih.- 111,'.111
\'alil", ub.·y I hr.'" laws
(I) TIll' prub.J.bdll\· "f SIII.l11 tI'·\!.ltl"'!'> fr"l11 th.· ltI ... an voilu, IS 15"
.,10
r titall Ih,'pr"h"blhtr tlf I.lr~l· rl.·vI,llum,
(2) Thl' proh.tb,hlr vi" a ( t ((.\111 d. \'10111<>11 ahu,',' thl' nlt'an ,·.lIu.· ,:' • <jll.tl t.1 Ih.
prob:tl>llLl\' of ~I
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If
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Irn.lJ.:tI1l· .1 ' :Snfnlal . HI ... to~r,611I. th,' fu~t1.11'0' nll',Ul" that Ihe ("(·nlra! I'tllar~ wnd Itl p,·.11.
!\I'ar Ill,. mran . th.· :,o .. ·olld law 1Il,'an" Ih.1I Ih' hl"OKr ... m IS ll),lII'1nll'trt("al •• hom! til.· m. an _ anti Ih. third. Ih:u Ih., t'(Jhllllll~ val1l:.h hurly qUI! kh a .. rill' lirst.IIIC'· from tiLl' 11lt'3n in('fo ... If ".,','
![Alle Sätze bestehen aus einer IP: immer L-L%, L-H%, H-L% oder H- H% wählen. H* oder L* pro akzentuiertes Wort unter dessen primär betonter Silbe. Beispiel: [(meine blühenden Blumen)]L-H% H*](data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==)