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Collins ReferenceAn lmprint of HarperCollins Publishers

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rGhcrpter I tl|lrHAT I5 STAflSTICS?

WE IAUVVLE THROUaH LIFE

8A5EV ON |NCOt PLFTE,tlAKfNA &OldE5

INFORIAATION...

9UOULV I HAVE TAE 5OU?727 0W CF THg 76 TuiES

T,VE T{AP IT, IT WA' PRETry

b@V.,, gUT 15,fr\ONVAy THE

REaULAR CHEF', NI6[,IT

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FLY U? TO

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^OU??EVERYT}.I|N6 ELSE 15 'OEXPENSIVE, ANP I PONT

KNOW WHO,5 PAYIN6.". ARE

5T ATt'TtdtANS 5Tl N6y? T\ENEVER @NE OW WIT}I

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

aENEROUS AU,/UNTANT.,

t &1 oF v5 LlvE

cotiFoRT;'LY w lTl'lot*E

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THI' 15 NOT JUST A A,IATTER ORORPERIN6 fuU?! STNISTIC' AL'OINVOLVES IANTERS OF LIFE ANDDFATII...

Ill

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FOR EXAA4PLE, IN 1956, THE 9?ME 'AUTTLE

CHALLEN^EF EX?LOVEV, KILLINA,EVEN A'TRONAW'. TAE VEC'5ION TO LAUN'I{

'N 29.VE6REE WE,iHER I4AP

BEEN IAAOE WITI{OUT VOIN6 A ,.IM?LE ANALY'I' OF PERFORIAANIE PATA ATI.OII TEIA?ERATURE.

DH..TI{47?ART oF T{Ecugue l//

A ,I4ORE ?OilT,VE EXM.?LE t5 THE SALK P)LIO VACC\NE. TN 1s54, vAC(,tNETR'AL' WERE ?ERFORA4EP ON

'OIAE 4OO,OOO CAIL?REN, WIT}.I

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TO ELIA,IINATE SIA'EV RE ULT,. 6009 STNI'TICAL ANALYSI' OF TAE RE ULT'FIRA,ILY E'TAVL''HEV TAE VMCINE' EFFECTIVENE S, ANV TOVAY ?OLIO 19

AUi6l UNKNO\ /N.

HEY- r,tAVE You FveRI{AP lUV EOW I{ERE ON

AN o?? Nr6r.{r?

TCHAPTER 2tDm DESCRIPflON

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. Tl^Fy'fE...i Atten:

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!,iie4'g'''-?- ?\' \l')Jr. lg '9 # ,,

") o /s'

€gi,!i' ct;qn d1,i "\ai 6oo't l'

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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 '\

TUIS CAAI|ICR 4ONIENTRNES ON PATA DE'CHMOA'' }IOUI IAN WE REPRE,IENT

?ATA IN U'EFUL WAY'? HOW 'AN

WE ^EE

UNPERLYIN6 PATTERN9 IN A IIEAP OF

NAKEP NUIAVERf,? HO\{ lAN WE ,IU'IIA/iAR]26 TAE VNA'' $ASIC 'UA?E?

* "l3\{,alsh o,,,

WELL, 10 VE CRIIE VNA, THE FIRf.T T}{IN6 YOU NEEP I' 'OIAE

MTUAL PATA

TO vE^(RlYE...50 Lgr't L)LLECI 50Me VAIA!

/W, ,z\

qfurg'dr't

I

g

w',#

'*,1

ffi

;PRESENT

HEAP OF

AL PATA

agTTINb RIAHT

STUVENT rc85POWN TO VU'INE'', Wg PRAW A POT PLOfi ONE VOT PER

WER E'{H STUVENT'' RE?OYTEV WEI6HT,

Q,,

8:(c'

(G

100 150

Weight in Pounds

200

YOU 'tlAY

hEE A PROfiLEI4 HEREz

THg CLVIAW AT TfO ANP T"?CUNW, T}IE STUVENT' TENVEVTO 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'TWORK AROUNP IT,

HERE 15 fuTAE REAL PATA:

A5 PART OF A ClASSROOrfl

EXPERIA,IENT, 92 PENN 9TNESTUVENT' RE?O(rEV T}IEIRWEI6J|T, WITH T}1858RESUWSz

|^ALE'140 11, 160 190170 1n Bo B51W 1r' lro 148

FEIAALE

140 120 170 lw1ls 122 115 lUL

FoRb€-r6lA lrH ,.,

$IORD

Tr{E t$LeJusr rlrEficR [T.,,

,My

15' 16' lr? 190 195 lW 160 1r5 157 lE 170 17' t7' 170 180 175190 lr5 170 lr, 21' lro 145 156 155 t50 1r' 150 tso 160 l?, 160155 lr0 140 tso 190 145 tro lu 140 142 176 12? 155

l2l 126 116 l# 150 112 126 1W 120 170 1?1 120 tls 12, tv7 125ll, lro 'no 116 10s g, 12f 177 110 150 10s

t' TASLE: YtvtvE tItE NU'UBER

L'NEtNro,urn*o'JTul%'iiit':")',ff5'*';ly:Yril?l1g5^I't#!:y_

"ffi-iffYi|

#"tr;,;;,!:G" ^t*-rN ANv aNEN TNTER'AL rHE

pELATtvE nscuEn;G iuernoto*r'on- oY wevute L\ EMlt INTERVAL'

t.8., IT'|THE FREQu iicf v'iipev sv tw-ror[L Nui/tBER oF 51WENT5'

CLAfr INTER/AL I^IPPOINT TREQVENCY RELATIVE FREQUENCY

97.5-1tZ'41tr2.5-117.5

117,6-'172.4

1?2.5-147,4

147.5-162.4

1b2.6'177.4

177,5-792.4

1y2,6'207.5207,5-222.4

95211o I125 19

140 17

155 27

170 s

1s5 s

200 1

2;15 1

,tr22.09g.20b

.196

.297

.og7,o97,0'11

,011

forAL q2 1'000

NorE, w E KETT rt{E I NTERVAL- .ryu?.n ?,19i,5:3* : irmN:'::f *

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

[utvELtNES toR FoRi4f Na Tl'lE ct^A" INTER/AL9:

rl V'E INTER/AL' OF

EQUAL LEN6TH WIT}4

AIiI?POINTg AT

/ONVENIENT ROUNP

NUA/\BER5,

FOR A SIAALL PATA

991, v^E A SIAALL

NU,1,19ER OtINTERVAL''

FOR A LARaE PATA

591, VtE ^{OREINTEF/AL'I

r;IdARaE OR

SiAALL?

f'r{ 9s% SURE

rr'5 ffiT OtIARaE,,,

2l

3l

.&)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,N6gAR 6RAPH I5 r.4.LLEV A III'TO6PM, EMU aAR CANER' AN

'NTEWAL ANz

''6ENTERE? AT TllE ,lltPPotNT. THE, gAR'i HEthti,T tt fliE Nui{BER oF oNAPo.INTS IN TI.IE INTER/AL.

2520151050

100 150

Weight in Pounds

150

Weight in Pounds

200

200

)

WE CAN ALfr VRAW A RELATTYE NEQUENCY III'TO6PM, PLqrflil{.' THERELANVE FREQUENU A6A'N,T TTIE WEIOIIT, TT L@K' EXATTLY THE ,.MtE,EI,rcN FOR THE VEFII,,IL SCALE

0.2

0.1

0.0100

11

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A19V

TI

TI

;- CLTITeF

tt

NEFR xgR€

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v

iJ

ANY ilCI OF tiEASVREirrENT9

HA9 TWO |'IIPORTANT

?R1?ER1 it' Tt{E qvTlyoi rY?tcAL vALUE: ANP

ius g?REAI Aeour rHAr

VALUE' YOU 4AN ^EE

TI{g

IPEA IN TVE,IE

HyPcrrHgrl aAu vt1lc,oR Nit'NnRRowSPREhD

AtTllE vALvEt wE ov'ER\tE" Tltut' n t5

TllE ro'mi rJuile ea'ov PATA ?otNT'' ANP

fl t oA'/) iq iuevluug or tvl FouRrH

PATA ?OINT.

AN ARRAY I5 A TA9LE OF PATA:

ovS1-;RvNlON 1

PATA VALUE flr

244"'onflz flz /'1 "o' fr n'

;>F O*0.-,1

ilT FBRE

A Sti LL 5Et oF n =5 vNA ?otVTi rA KES THE tff,lKKEEprN| Aty.

^UPPu'q, FOR AUAiIPLE, WE A'K FNE PEOPIE I{OW A,IANY T1OUR' OF

TELEVI'ION THEY WNCH 'N

A WEEK,., ANV 6ET THE FOUf,/rIIN6 ARRAY:

OV,ERVATION

PATA VALUE 7s

TI4EN frt -- 5, frz=7, fr?= 7, ft1--79, ANP fr, -- 7 '

W}IAT'' THE "CENTER" OFTHE^E VNA? THERE AREMTUALLY SWERALVIFFERENT WAYS TOTAEASURE IT. WE'LL I.OOK AT

JUST TWO OF Tllg,tl.

THg MEA (On "NERN2E")

T}lE fiEAN OR AVERME VALUE 15 REPREfiENTEVgY V,,, rT'5 OWAINEP gY A?VIN' ALL TUE PATA ANPPIVI?IN6 gY T}4E NUfiBER OF OVSERVATIONS:

626

-,4-tlt a'

-a-

d$SUta oF nATA

n

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

60=

-5fr

FOR OUR EXAI.i.?LE,

=5+7+7+W+75

= 12 HouRs

,ft,

-----FoR TAe efin * fiz + "' * fln wE

ANP REAP tT A':ius Svti oF /'iA5 i @Et FRO^4

lTOn!

t t h1 tT_{Ei.r {rttfiE9AND YOU'LLiiEvER FoR&er

wE HAVE O uuoRTHLNP FOR TIIAT

fl, * flz; :''; in u^ioiua rlrE 6REaY

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

,O,,. 10 REPEAT, T}IE NERAaE' OR

n

\AEAN, OF A ilEI OF PATA /'i 15

sLni-i--tO*fr=i

nSaL/ni?l

IN T}IE A^E OT OUR 92

j7- :

.46 9Lt-- { '/

=

PENN 91Ng ,TWENT',', TtlE mEAN wEtaHT t5

145,15 PouNDa16

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

TO FINP TtlE ,tlEPlANVALUE OF A PATA 9gT,WE ARRANaE THE PATA 7IN ORPER FRONT

'IAALLEST TO IAR6E5T.

TtlE ,tlEPfAN t5 TllEVALUE lN TllE tvltwLi, TI/,E ttlE

W}11(H CASE THERE 15 NO ilII?VLE, WEI,IIIVVLE.,, 50 IF THE PATA ARE

7

/PIAN

5 77s

TF THg NUA,IBER OF POINT' 15 €VEN1NAVERME THE TWO VALUES AROUNV THE

?rv77

TAIVVLE5?ME

Tlltl 6tVE5 U5 A 6ENERAL RULEz

TF THC NUA4BER OF PATA

POINT' 15 OPD, THE AIEPIAN

I' TNE NV?LE PATA POINT.

TF TIIE NUA4BER OF ?OINT' 15

EVEN, TIIE,IIEPIAN t5 TltENERAaE OF THE TWO PATAPOINT9 NEARE'T THE TAIP?LE,

5+7 ?6Wg AVERIf2E 5ANP 7 TO 6ET 2

ORPER THE PATA FRCII4 '.IAALLEST

TO LAR6E5T,

H'f,

(

FoRT|'|E7l--92'TvVg}]TwE|6}1T5,ws4ANFINPTIIEilEPIANFROi',ITVEoRvEREv'T?,i^-ANP-LqJiFv|^bRfutl:ivot aouNT To Tllg 4b111

OV{,ERVNION' TI{E A{EPIAN 15

Q,,51O t 2gg

11 z ooTi|bbgg12 " OOO12?55555

1? z Oooo7lryr11bgg14 r ooo&65555 a

15 z oooo00000075655555555716 z O7OO45

17 r OOOO55

19 z OOOS

19 z OOOOS

2Ot21 "5

f,qo + ftqr

-

2

145 + 145--

2

? 145 Pot)NPt

nilEt

vEStvES

CENTRAL

'81, WE'

vE cRtgl

'?PEAD,FROA4 TI

PATA TE

FOR IN9STUVEN.

E)t141'THERE V

5?REAV

NU'ttERl(

WOULP

HISTO6F

SKINNY,

vvT tt towtoulOF TI{E

THE HI'

t!1

? e[iirt AA5 lw$rfiAr2*s' FoR

ExA,rpLE,rurnn^i,";7iiFl4ak"3#'!:';,,f rifrl?i-v^LuE'r,Hfi;dl'#K;;, or rue v't, ,vp?e^E rN ouR ,'UALL rv-

wAT4HrN6 ORoVn od're*iN wATlllE, -ZAo

uoung ?ER wEeK' fHEN ouR

9ATA ARE ?, 5, 7, ',

,iO' THE A4EPIAN ' ''G UUCHANASP'

gW 7AE A,IEAN I'

NOW V -- 4r,g!

IN 1994 TAE UNIVE R'IT'/ OF VIRaINIA ANNOVNCEV

THAT |T' PEPART^,IENT oF RHgroHC ANP (n|^-

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

wA9 l,,,ooo. T}lE C,WL|ER, THE gALARy oF N.B.A.

/ENTER RAL?H SAIA?^ON, VIV NOT REPRE'ENT THE

EARNIN6 POWER OF A BA. IN 5?EECA FROA'I U' OF V'

ft ;'nrLoim rALARv wArN'r ?vvLtt*Ev')

Alto You'RE9t91og{lr*t'av{e MrnUH?tbHf'

Math 112 HOMEWORK #11: Due Tuesda 22 October at class start

Read:A. Re-read Section 7.6 in your book, as needed.B. Read the Cartoon Guide's description of statistics.c. Read the news, looking for the misapplication of statistics.

Write:A. With your group, revise the 4-5 histograms and bar graphs you created to be

more accurate, if necessary.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 copyof 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 sayanything. Then tatk with them about the misapptication of statistiis. Write upwhat happened in your discussion as you exptained the misapptication ofstatistics.

Prepare:A. Prepare for a Quiz on Tuesday on Statistics.

a. Accurately read statistics in the newsb. Accuratety draw and read histograms created from datac. calculate & compare Measures of center: Mean & Median