The Cartoon Guide to Statistics

THE CAPTOON GUIDETO

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LARRY GONICK

& \il/oo LLC OTT SM lT H E."': Oa.t' Collins Reference An lmprint of HarperCollins Publishers

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l|lrHAT I5 STAflSTICS? WE IAUVVLE THROUaH LIFE ,tlAKfNA &OldE5 8A5EV ON |NCOt PLFTE INFORIAATION...

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9UOULV

UAVE THC

I

HAVE TAE 5OU?7

'HOUL? ^OU?? EVERYT}.I|N6 ELSE 15

27 0W CF THg 76 TuiES

'O EXPENSIVE, ANP PONT KNOW WHO,5 PAYIN6.". ARE

T,VE T{AP IT, IT

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5T ATt'TtdtANS 5Tl N6y? T\E NEVER @NE OW WIT}I

ONE aEIORE,,. TAOUaH ON/E KNEW A VEPY

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aENEROUS AU,/UNTANT.,

WA' PRETry

b@V.,, gUT 15,fr\ONVAy THE REaULAR CHEF', NI6[,IT

OFF? ANP WHAT IF ALL TAE AIP I4OLECULES IN TNE ROO^4 FLY U? TO

'V?VENLY TILE (EILIN6?

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oF v5

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tlh{g

cotiFoRT;'LY UNCERfNNTY' V}\IEV OF

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couLP Yau

tsRtN6.{'?} iua. 'tA[ctttAT& ",,

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UNCERTAINTY!

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Lvtot&t r'fil ?5%

doNFrosui;w. :3,YHra Tov, tlAg PRosABILffY Btrv-/EEN iti.Al:,',!2u; u5! P ELt t o

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THI' 15 NOT JUST A A,IATTER OR ORPERIN6 fuU?! STNISTIC' AL'O INVOLVES IANTERS OF LIFE AND DFATII...

HEY- r,tAVE You FveR I{AP lUV EOW I{ERE ON AN o?? Nr6r.{r? t

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IN 1956, THE 9?ME CHALLEN^EF EX?LOVEV, KILLINA ,EVEN A'TRONAW'. TAE VEC'5ION 'AUTTLE TO LAUN'I{ 29.VE6REE WE,iHER I4AP BEEN IAAOE WITI{OUT VOIN6 A ,.IM?LE ANALY'I''N OF PERFORIAANIE PATA AT I.OII TEIA?ERATURE. FOR EXAA4PLE,

DH..TI{47

\INTY, :AL

?ART oF T{E

cugue

l//

A ,I4ORE ?OilT,VE EXM.?LE t5 THE SALK P)LIO VACC\NE. TN 1s54, vAC(,tNE TR'AL' WERE ?ERFORA4EP ON 4OO,OOO CAIL?REN, WIT}.I CONTROL' TO ELIA,IINATE SIA'EV RE ULT,. 'OIAE 6009 STNI'TICAL ANALYSI' OF TAE RE ULT' 'TR'CT FIRA,ILY E'TAVL''HEV TAE VMCINE' EFFECTIVENE S, ANV TOVAY ?OLIO 19

AUi6l

UNKNO\ /N.

Dm

TCHAPTER

2t

DESCRIPflON

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i Atten:

cou6 {..'

9rf g:^fr*" ilg

r*??l el ,ig|1.1D.

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)")';4 o /s' ,.*i6n n$-'r*") l,^rtr rr" ct;qn €gi,!i' d1,i l' c+4 '?^,ftlgib ai 6oo't "\ o763

i"yt.i:;):.F'b 4'g'''-?-'9 ?\' \l' )Jr. lg # ,,

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DATA ARE THE STNISTIIIAN,, RAW ,ttlATERlAL, THE NUfigERt WE V5' TO INTERPRET REALITY' ALL 5T N I5T ICAL PROBL EIAS I NVOLVE EITHER T}tE (OLLECTION' V6'CR,IPTION, ANP ANALYSIS OF PATA, OR TT|INKIN, Agp/W T}4E (OLLE'TION, VESCRIPTION' ANP ANALYSIS OF PATA,

l6 '\

IAN WE REPRE,IENT TUIS CAAI|ICR 4ONIENTRNES ON PATA DE'CHMOA'' }IOUI IN A IIEAP OF PATTERN9 UNPERLYIN6 WE ?ATA IN U'EFUL WAY'? HOW 'AN,IU'IIA/iAR]26 ^EE TAE VNA'' $ASIC NAKEP NUIAVERf,? HO\{ lAN WE 'UA?E?

*

WELL,

10 VE

"l3\{,alsh o,,,

CRIIE VNA, THE FIRf.T T}{IN6 YOU NEEP

TO vE^(RlYE...50

Lgr't L)LLECI 50Me

VAIA!

I'

MTUAL 'OIAE

/W, ,z\

qfurg'dr't I

PATA

FoRb€-r Tr{E

HERE 15 fuTAE REAL PATA: A5 PART OF A ClASSROOrfl

g

92 PENN 9TNE STUVENT' RE?O(rEV T}IEIR WEI6J|T, WITH T}1858 EXPERIA,IENT,

w

t$Le ,

rlrE

6lA lrH ,., Jusr $IORD ficR [T.,,

My

RESUWSz

',#

|^ALE' 140 11, 160 190 15' 16' lr? 190 195 lW 160 1r5 157 lE 170 17' t7' 170 180 175 170 1n Bo B5 190 lr5 170 lr, 21' lro 145 156 155 t50 1r' 150 tso 160 l?, 160 1W 1r' lro 148 155 lr0 140 tso 190 145 tro lu 140 142 176 12? 155 FEIAALE

140 120 170 lw l2l 126 116 l# 150 112 126 1W 120 170 1?1 120 1ls 122 115 lUL ll, lro 'no 116 10s g, 12f 177 110 150 10s

;PRESENT HEAP OF

tls 12, tv7 125

agTTINb RIAHT POWN TO VU'INE'', Wg PRAW A POT PLOfi ONE VOT rc85 WER E'{H STUVENT'' RE?OYTEV WEI6HT,

PER

STUVENT

'*,1 Q,,

ffi

8: (c'

(

G

AL

PATA

100

200

150

Weight in Pounds YOU

'tlAY

hEE

A PROfiLEI4

HEREz

THg CLVIAW AT TfO ANP T" ?CUNW, T}IE STUVENT' TENVEV TO REPORT TI4EIR WEIaHT IN FIVE-?OUND INCPEfiIENT'. TN REAL.LIFE ,ITUNIONS LIKE TH''. ONE, SUCH ROUNPINa OFF CAN OVSCURE 6ENERAL PTtrTERN' IN

VNh,,VW

FE

NOW WE'LL JU'T

WORK AROUNP IT,

t'

TASLE:

YtvtvE

tItE

NU'UBER

rHE L'NEtNro,urn*o'JTul%'iiit':")',ff5'*';ly:Yril?l1g5^I't#! ANv aNEN TNTER'AL #"tr;,;;,!:G" INTERVAL' :y_ oY wevute L\ EMlt ^t*-rN pELATtvE nscuEn;G iuernoto*r'ontw-ror[L Nui/tBER oF 51WENT5' FREQu iicf v'iipev sv "ffi-iffYi|

t.8., IT'|THE

INTER/AL I^IPPOINT

CLAfr

952

97.5-1tZ'4 117,6-'172.4

1?2.5-147,4 147.5-162.4

1b2.6'177.4

17

200 2;15

1y2,6'207.5

207,5-222.4

w

E

KETT

rt{E

I

NTERVAL-

)-ffi'tr^ffi',:;Z'i;i;

rl

V'E INTER/AL'

OF

EQUAL LEN6TH WIT}4 AIiI?POINTg AT

/ONVENIENT ROUNP

A SIAALL PATA 991, v^E A SIAALL NU,1,19ER Ot

FOR

INTERVAL''

3l

s s

.og7 ,o97

1 1

A LARaE 591, VtE

FOR

ct^A"

PATA

^{ORE INTEF/AL'I

,0'11

,011

1'000

irmN:'::f

INTER/AL9:

r; IdARaE OR SiAALL?

NUA/\BER5,

2l

.297

.ryu?.n ?,19i,5:3* :

Na Tl'lE [utvELtNES toR FoRi4f

.196

27

q2

forAL NorE,

,tr22 .09g .20b

19

1s5

177,5-792.4

RELATIVE FREQUENCY

I

11o 125 140 155 170

1tr2.5-117.5

TREQVENCY

f'r{ 9s% SURE rr'5 ffiT Ot IARaE,,,

.&)

ilrB :.K\

*

rN THE FREQUEN4Y rAvLE, wE ARg ,Hatt,N6 Hor{ ,r{ANv ?ATA pofNTt ARE 'ARouNP' ENH vALUe wE cAN 6RA?tt rlt,, ,NFoRt{AfloN, T@. TtlE RE5un,N6 gAR 6RAPH I5 r.4.LLEV A III'TO6PM, EMU aAR CANER' AN ANz 6ENTERE? AT TllE ,lltPPotNT. THE, gAR'i HEthti,T tt fliE Nui{BER 'NTEWAL oF oNA

''

Po.INTS IN TI.IE INTER/AL.

25 20 15 10 5 0

100

150

200

Weight in Pounds

WE CAN

ALfr

VRAW

A RELATTYE NEQUENCY III'TO6PM, PLqrflil{.' THE L@K' EXATTLY THE ,.MtE,

RELANVE FREQUENU A6A'N,T TTIE WEIOIIT, TT EI,rcN FOR THE VEFII,,IL SCALE

)

0.2 0.1

0.0 100

150

Weight in Pounds

11

200

A1 9V

TI

)##t.i^T-fi?S i'#Yir';'-;i#

cHrnut

ER''I',' oF A' o

/K Svrabolic @;,r:f,#::{i,

TI

\l T

;tt

ANY ilCI OF HA9 TWO |'IIPORTANT

tiEASVREirrENT9

?R1?ER1

oi

it'

Tt{E

qvTly

g?REAI Aeour rHAr TI{g

4AN

VALUE' YOU IPEA IN TVE,IE

HyPcrrHgrl

NnRRow

^EE

SPREhD

aAu vt1lc,oR Nit'

Tltut'

n t5

ANP AtTllE vALvEt wE ea'ov PATA ?otNT'' rJuile ro'mi TllE tvl FouRrH flt oA'/) iq iuevluug or

ov'ER\tE"

PATA ?OINT.

AN

ARRAY

PATA: I5 A TA9LE OF

ovS1-;RvNlON PATA

A

v

i J

ANP rY?tcAL vALUE:

ius

xgR€ CLTITeF NEFR

1

VALUE flr

244"'on flz flz /'1

"o' fr n'

A

Sti LL 5Et oF n =5 vNA ?otVTi

rA KES THE tff,lKKEEprN| Aty. FOR AUAiIPLE, WE A'K FNE PEOPIE I{OW A,IANY T1OUR' OF ^UPPu'q, TELEVI'ION THEY WNCH A WEEK,., ANV 6ET THE FOUf,/rIIN6 ARRAY:

; >F

'N

O*0.-,1

2

OV,ERVATION

il T

FBRE

6

PATA VALUE

TI4EN

6

7s

frt -- 5, frz=7, fr?= 7, ft1--79,

ANP

fr, -- 7 '

W}IAT'' THE "CENTER" OF THE^E VNA? THERE ARE MTUALLY SWERAL VIFFERENT WAYS TO TAEASURE IT. WE'LL I.OOK AT JUST TWO OF Tllg,tl.

THg

T}lE

MEA

,ft,

(On "NERN2E")

fiEAN OR AVERME VALUE 15 REPREfiENTEV rT'5 OWAINEP gY A?VIN' ALL TUE PATA ANP

gY V,,,

PIVI?IN6 gY T}4E NUfiBER OF SUta

4-,

a'

tlt

-

oF n

OVSERVATIONS:

nATA

d$

fil *f,2 + .,, *ft,

a-

FOR OUR EXAI.i.?LE,

fr

=5+7+7+W+7 5 =

12 HouRs

=

60 5

-

TIIAT

wE

HAVE

O uuoRTHLNP FOR :''; in u^ioiua rlrE

FoR TAe -----

efin

* fiz + "' * fln wE

6REaY

fl, * flz; |t6'u' ro* tuilnATloN: r r/frl zdomu ,#e*'

ANP REAP tT

:ius

A'

/'i FRO^4 i @Et A5 Svti oF

lTOn!

t t h1 tT_

{Ei.r {rttfiE9 AND YOU'LL iiEvER FoR&er

,O,,. 10

REPEAT,

NERAaE' OR \AEAN,

T}IE

OF

sLni n

IN T}IE A^E

Sa L/n i?l

t5 TtlE mEAN wEtaHT ,TWENT',', 91Ng OT OUR 92 PENN

j7-

.46 t-- {

15

n

fr=i -i--tO*

A ilEI OF PATA /'i

:

9L

'/

=

145,15

PouNDa 16

*EmEDIAN

TO FINP TtlE ,tlEPlAN A PATA 9gT,

VALUE OF

WE ARRANaE THE IN ORPER FRONT

PATA

5

7

TO IAR6E5T. 'IAALLEST TtlE ,tlEPfAN t5 TllE VALUE lN TllE tvltwLi,

t5 ANOTIIER K|NP OF CENTER: THE "TAIV?OINT" OF TIIE PATA, LIKE TTIE "A4EPIAN STRI?" IN A ROAP.

7

77s

/ TI/,E ttlEPIAN

TF THg NUA,IBER OF POINT' 15 €VEN1N W}11(H CASE THERE 15 NO ilII?VLE, WE AVERME THE TWO VALUES AROUNV THE I,IIIVVLE.,, 50 IF THE PATA ARE

?rv7 7

Wg AVERIf2E 5 ANP 7 TO 6ET

5+7 ?6 2

TAIVVLE

5?ME

Tlltl

6tVE5 U5 A 6ENERAL

RULEz ORPER

LAR6E5T,

H 'f,

I'

?OINT'

TO '.IAALLEST

TF THC NUA4BER OF PATA POINT' 15 OPD, THE AIEPIAN TNE NV?LE PATA POINT. TF TIIE NUA4BER OF

THE PATA FRCII4

( 15

EVEN, TIIE,IIEPIAN t5 TltE NERAaE OF THE TWO PATA POINT9 NEARE'T THE TAIP?LE,

FoRT|'|E7l--92'TvVg}]TwE|6}1T5, ws4ANFINPTIIEilEPIANFROi',ITVE oRvEREv'T?,i^-ANP-LqJiFv|^bRfutl:

ivot aouNT To Tllg

f,qo + ftqr

2

--

15

145 + 145 2

? 145

-

12 OOO12?55555 " 1? z Oooo7lryr11bgg 14 r ooo&65555 a 15 z oooo000000756555555557 16 z O7OO45

4b111

OV{,ERVNION' TI{E A{EPIAN

nilEt

Q,,5 1O t 2gg 11 z ooTi|bbgg

17

vEStvES CENTRAL WE'

'81, vE cRtgl

r OOOO55

'?PEAD, FROA4 TI PATA TE

19 z OOOS 19 z OOOOS 2Ot 21

Pot)NPt

FOR IN9 STUVEN.

E)t141'

"5

THERE

? e[iirt AA5 lw$rfiAr2*s'

FoR

ExA,rpLE,rurnn^i,";7iiFl4ak"3#'!:';,,f ,'UALL rvrN ouR rifrl?i-v^LuE' -ZAo or rue v't, ,vp?e^E

r,Hfi;dl'#K;;, ORoVn od're*iN wATlllE, wAT4HrN6 9ATA ARE ?, 5, 7, NOW

V -- 4r,g! ',

,iO'

THE

A4EPIAN

'

uoung ?ER wEeK' fHEN ouR gW 7AE A,IEAN UUCHANASP'

I'

''G

V

5?REAV NU'ttERl( WOULP HISTO6F SKINNY,

vvT

tt

t

owtoul OF TI{E

t! 1

Alto You'RE 9t91og{lr*t' av{e MrnU

H?tbHf'

ANNOVNCEV

VIRaINIA IN 1994 TAE UNIVE R'IT'/ OFRHgroHC ANP (n|^-

THAT

|T'

PEPART^,IENT

oF

STAFI\N, SALARy ,!1uNt/ATrONg bRAwNES', IAEAN THE gALARy

oF

N.B.A.

wA9 l,,,ooo. T}lE C,WL|ER, VIV NOT REPRE'ENT THE /ENTER RAL?H SAIA?^ON, V' BA. IN 5?EECA FROA'I U' OF EARNIN6 POWER OF A ?vvLtt*Ev') ;'nrLoim rALARv wArN'r

ft

THE HI'

Math 112 HOMEWORK #11: Due Tuesda

22 October at class start

Read:

A. Re-read Section 7.6 in your book, as needed. B.

c.

Read the Cartoon Guide's description of statistics. Read the news, looking for the misapplication of statistics.

Write:

A. With your group, revise the 4-5 histograms more accurate, if necessary.

and bar graphs you created to be

B. Anatyze your revised histograms:

a. Add measures of center: mean and median to each histoeram. b. Discuss why the measures of center are different or the iame. *lf one is

higher, what does that mean about these data? lf they are the same, what does that tell you? c. Discuss the meaning of the overatl shape of the graph. d. Make any other comments on what interests you about these data. C. Analyze 3 more histograms from our class data. a. Find the measures of center: mean and median. b. Discuss the relationship between the measures of center. c. Discuss the overatt shape of the graph. d. Make any other comments on what interests you about these data. D. Find a new exampte of a misapptication of statistics in the news. Inctude a copy of the article in your homework. Show the articte to a famity member or frieni. Ask them to read and interpret the statistics in the articte before you say anything. Then tatk with them about the misapptication of statistiis. Write up what happened in your discussion as you exptained the misapptication of statistics. Prepare: A. Prepare for a Quiz on Tuesday on Statistics. a. Accurately read statistics in the news b. Accuratety draw and read histograms created from data c. calculate & compare Measures of center: Mean & Median