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Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
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OCR for page 95
~ ~ ~4
DA:~D is*
~ '~ ~ Of ~ ~ ~ Of ~ ~ ~
All
..
"~- is intoned to su=~ two related top:~. data =d
~~ Ne~:~er ~s ~ topic mth~:n mathematics, ~ey am both, how—er-
phenomena ~~: ~ tbe subbed of math~tA ~ ~ ~ ~
ing' =~ and Hi are the Thai finds ~~t ~~ with
d~ and chance' resistively.
Recent recomme:~s co:~.~mi~ Sc~: cumcula. are una~s
in suggest: ng th at =~: ~:~ and: pm babi] :W should occupy ~ mu ~ more
pm-minent pl=e than has ~en the ca~ tn the pa~*~4 Howewt ~
=~e of the emph.~:s that t - e reco:~-~s place on ka anal~
~87 it :5 ~~: t~ ~~ 5~-~ i~ p8~i0~: 85 ~ =~ 0: ~~0i50
Son (or ev= as ~ bag of tnc~. The task of this =~- Is no: to- u~
8-~n to d~a a~d ~~e in the whoo! cu:~:~_~Nt 370 8~v
81lX=~g attention~'ut to -I this stmnd of I Ideas
in ~ ~ that :~CS clear the oVemU themes and strate~es within whIch
:~:iv:~:~ topics :fi~ their natum! p:~.
A:~.~6 O:~.~ that Is t~,l~c to ln~.~e tea.~g S~ ~~.~:
the expenence of teachers and students. Su~o as Or cumculum :~
detached mom that cx~e o~r Sepias hopes ~~t are d:~w
Ceil in By ~~Sti05 :O t50 $~5 iS ~Ot UtOpl8~, ~~W Cal
presentIv being tested 1s p=~.~y used:! and alds mther ~~n did
6~t O ~~Ct CO~tS =6 S~. ~Q~$S, 1t iS C~V I~
our Am to o~rerIook pmctica:! p - gems and to urge the teaching
~5
.~
OCR for page 96
Char ~,~~~4~.SS TO I, CY
-of s^~t moor that is A ~ quan:~v or ~. ~ :~s :~t
to =~! =~;~n to the d:~ =d Ha ~~e s~ps, ~ well as to
-~he adv=~s, in u~ng Ha and champ in ~~e By: of ma
In wntlng ~~s e~y -I h~ tned to e~ ~ the p~1 ~~r than
the umpian. direction"
{~ in tea~ sumacs ::s ~iV due 1:~ -am to rec~on
of ~e place thm ~~g ~h data prays in ~~ - Il~ and in :
:~.~;.~;~.s at ~s -~.~ngly =~ to te=h momma t~s
th~ ~ of di== use, r~er ~ -to—0 mp=s s:=ly Us- th~+
i~d tO :~r t~ in. -~.~. smn~= ~ ~ ~ tople
News - ~s present Aims economic =d so=~! Aim opin~n
pails, me~=T ~m—m bow I: ~~es and cIln:~] tn~s
=d Ws~ and finance ~. M~v c~s must d~ m~ ~a in
more—se) on the job. :~ =d ambustn~s use Mop fo~= a~
~e remIts of a~icultu~ field teals. E~s a~ concemed mth data
on prompt pe - ~~:~, qu~, and reli~:~:~* Man:ufa=~g wo
~ sked to ~~ and a~ on ~~ ~r ~~ss mntr~+
The :~=lth sciences ~e w:~h da~ on co~ and c~:~s as -~11
as m~ -Gus mom median! rese=~ Bus:~-=s =ns on date of eve~
new. =~' profits' s~ p~:~, ma - t wsea - ' and moue more.
Tte:~e are compelling pumice rea.~.s ~ leam ~:i~ics.
As thew eXampleS s~st data are n~ merely =~' but numb
w`~h ~ conI=~- The number iO.3 in the ~~= of ~ -I =~s
nO inf6~tion, that the bl:~ Aims of ~ bead,.,' is iO.3 wunds e~s
us tO ~m=~t on the hea~ ~ze of t~ child. That 15, d=a I:
our I- Of t:~r.~.~t ~ -and we =n un~d and interim,
h s~~y cams out anthm~1 o~g:~-i=.~.
There a~, there~e, stm~ peda~! as wet:} as paretic reasonS
to teach Ice in We - ~~* Statistics combines mmpu*~1 ac~
tiv~yf in ~ mean:~ setting with the e:~.~e of ;~gme^~t i::~. ~;hoos:ng
methods and I =~:~* Statistics :n the ea~ grades is teach:
not Imp ~r its own 53~$ 5~t ~0 it it ~~ 6~ti~6 ~~' t~ 60~
6~0'p-~tit~-6 ~:~.*~]i~6 ~ 8~7 anthm-~tic and Aching
to p=5i6m Ida
Teache~ who understand that data are :3~mbe:= in a* context we ah
ways provide an ~~e co:~t When posing pr-~ems ~: stude:~:~.
Ca:~ati~g the :~an of five *~umbe~*s is an exercise in anth=*=ic~ It
statist~~ Ca*~ting the :~n pnce of ~ popu:1~:r mus:c ta' ~ five
Ceil 0~10~5 }5 It I;:* ~~-~ combined w:~b ~ look a~t the
D
*I
, the pnces and ~ companson with the price of Other types of
OCR for page 97
:~m
:~7
:~t ~ Used ~~t ~e practice! and ~~ am -of coke
-both data nOt -~.~:.~b- to an =~ emphases on me--
at~- :T~che~ =d developers of Am matena1 mu~ =~se
:~ - attain In pmvIdl~ d~ ~~ are Am; to ~~.. {n ~e
~~ =~57 ~3 - = ~t ~0 - ~8 (~ ~ 80~ ~
be used, ~~=tLen~ hardy arm, -such ~a ~0~ : ~:—-
~ :~- In the bower ~7 data p~ ~ t56 ~5 t56~
~ ~~ ~ p~0 ~~ )~ =~ ~~$ =~ 85 g~
~e cl=s ("Dow Hey chlldren I:~ tn wU: house9~) or ~ as~ =~
5~t t~ ~07 =~7 0: I 50~0 ~~*
The ~~ ~~u Add to provide -~a rather than s~v **
hers ~~Id be -taken Into a=~nt -when planning ln~-
6~ ~ =t j~ ~ 8~ ~~ it* =~ 5~$ tt07 8~0
essence to ~ n~e ~ s~- ~t it :s im:~:~ the the e
required to p*~ce Ha not m~ - add the mat~] idea Cat
and Ie~..
ln Dant=~.~' *A to D~ ~ ~ On imoO=~t :~S of
stOe sch~! ~ ~~s much Amp. m~ 15 ~ :t,{~ ~~;~-
~~:~:~: :~s ~~n t:*,im~g anO c~g atI~:s
to pmduce dam m~* ~~) Oral tearoom Em At: ~tics.
The disunities ass~ed w:~h -Gil production ~~es ~~ the 5=t
:~f =~] w~ ~m ~ As. to c~ *~ *A ~ Cum cul~ maten~ ~
=~:~t p=~6 60~ i~ ~~ 3~6 p=~$ - - =~5 ~t
-~ of d~a bY smdent:~.
Over t1~07 t=~ =~ -I and
share data -ads that prim to their commun:~+ =d school. Com-~:~s
aw an :~! means of ~~g and sbanng ~a.
~me phenomena have predic—le outcomes. drop ~ co:n—m ~
known :~t and the tone ill ta~ to ~~! =n ~ p - ~~ - - m ~~c
tner sma~ m~eme~t em>r me 0!~=
is ce=~ If we to~ the co:n, on the other han~^ we =~ot predict
r it m11 ~~w be~S or talls.
min t-~g tS nOt haphaza~.
. .~ ~ ~ .
~ ~ ~ . ~ + -
~e outcome -is u:~- Yet
Tf we ma~ ~ :~= =:~r -of tosses,
the pr-~::~on ot he~s mil ~ Vew close to one~If This lo-
re~n,\y ls not just ~ theistical con~t but an ~~d ~=
The French natuM~in Bu*~n (~~~) tossed ~ Din 4040
t:*~. Result- 9048 :~- ~ proportion of 204874040 ~ O.~69
of h.~*
Around i9-~0 t~e English statisticlan Ka~ PearSo~n herCi=~y
t08~6 ~ Dig 247000 ti=-~. ~~* i2~9 5-~*, ~ p=~
of O~3005.
OCR for page 98
.~:3O
^~w :w x~Y
e Ash ma~em~man Qua ~~, ~:~6 6v
e ~~s ~~g - ~ :~ il' to~d a-. :~O ~~.
~~:~* 5~67 ~, ~ p~-~= 0[ ~ 5067
Pheno~a h~g unwed: :~: ou - ~ ~ ~ ~~r Ace:
t0= 0f ~~s ant many re~ ~~ ~~ ~7~ "~= A
~ 8 synods ~ ~ haph~- bm ~ des=~on "of 3 HM of o
dI~m 0.m the .~e one ~t :~s =~.~d ~
:Pr~W is ~ bmnch hi..
#
~e ~~ ~ fit - n tn :~ Out of ^~! p~s I=s :~=
areas of smence :~n ~ch ~~m beh~r I; Ash ~ ~~cs
~ ~ sch~l a~ ~~n ~ if - V ~~t
sol~d In- cou=~. Uncertain 1s of course ~ pewter aspect ~ ~]
. ¢~, ~: :s ~~e o~r ~n ..: that is ha~ ~ ~~e :n
cas~ stonings. Den =te :~*, a~ ~f~mili~ ~ m~ stoners'
e tithe e~-~e with ~e order a~t of .*: because
th~r e~s on e~Iv unTIk~y I~ pn~s. Tame weD~d
~~s of ¢~e use ~~ p~! =~#z t. ~
e nch haph~'dIv~
s ha ~ show th~ our i: of chance pro~un~s
cOntmbi.:~s ~e iaws Of pr~fI*t ~
:~* This ~~t u:~*~andi~ ::s very di~cu:It to =~ct by Anal
:~=ion. At=-~s to teach prob~:~v and =~:~$~l tn~0
out ~~e intuitive p~*~:~n are ~ second :~r pitfall in tntro
duclng data and chance into schoo! cumcula*
~ ~ Stu~ ~~l to Unde,:~d pm~il.ity
and i. be~= of m:~s that am not removed by ~~Y
Of fawn I 1Rb.e Indict bCtWCC;n p;~;11~ thtCOor 3~d ~~s
died of the wo~d is d~ at Iem ~n :part to ~~ limited conm~ mth
Is* We mum ~~refow p=~re the whys ~r tte 51~v 0: ch~
by ~~-~d:~g ex=~= -~:h mn~m behavior eady in the :~tics
=:~1~. W~:~v, the stu~ of ~ta provides ~ natural setting ~r
such expenence* The :~ of data analysis ow: Army probability
awl index= is an impotent pn.~:~e for instmetio:n in unce~ai.~^
Artificial chance devices (=ins, dices sp:~) c~ be used to pro
duce data in the cIassroo-m w:~h the i:~:*t of applv:~g data analysis
111s to- d:~ ~~e Body na:~:3~e of thew devices. Un:~aint~Y alto
~~n in d=a—m sources other than chance devices. Repeated meetly"
surements of the ~e quanti*~v (~e by sevem) students~ ~r =ample)
iC~ld: V3~g 37~S N31~l, I, 3,99~ if. thC: hOi~t,5, =:~di~;g
If-* or in of a* group of people. It is perhaps su~si:~g that
OCR for page 99
:~m
e ~~.~s ~ carton A. =~! ~~s or ;n ~m on :~-
:~als =n be Or by—- dance mathem~ that Micros
she o~= of chanced ~ices.
=~e wlm hare ln ~a ls ~ n=t n~ toward I: t~e
conne~n Between S~6cS =6 pro6~li~+ ^M ~ leer see ~e mic
~ rieiitem:te ~oln~z~ion In Swish Resee ~ pro
hers ~~s =~. Finally, ~~ scow Ice Us=
e Car and flacks of p~babd~W to express the c=~= we =n
b^e ~ -=nciu~s Own ~ ~a. ~
mmou~ the uset~ n everyday T~e of~ ~ Pasta o~t ran~
dom~ ~s le6s obvious Can ~e ncce~ of dealing gin data' ~ac-
t~ a- ~ teaching ~~ut chase ~ not abbe £3= goal of
ins - ~~= abbe prob~ilhy ~ to he~ students un~xand t~ -~e
maria mther tMn determm:~c c=~n ex;~3~ins many aspects of
the worm
~~ :~= ~ ~~;~ p~r ~ ~ mng I: ~= mace
JAYS- of her ~= throws. At the =d of ~ touma~t ~e ~e
att~s hVe -A throws am makes =.~ t~* "~..~-
ut th:s c=~ explanat~on need not be And;
pl~ :~g ~ ~~v of O.? Of m~ each ~~t haS
Mimi of about O. id of :~sing t:~e or ~~w of bye ~~*
such ~ ~~e can edgy ~ Mmp~ chance v~.~ti=-
e unde~s~Ong of prob~litv en^~ us to consider the ~
chance rather than seek ~ spheric cause' Wartimes spurious, ~r - ~~'
While the a~nt of ~^ Bilk Ike computing has ho ~ imp
t on :~emat~ as ~ whole, it has revolu:~:ized the pmct~e of
s=~tics.: ~~n obvious 'amp of ~e r~ Is that mOre =~x ~ ~
vses on Ia~er sets of ~m are now ea~. At the computing In
has also bro~t about Ranges :n the nature of Aim p~e. Tn
the pa~ natisticlans c;~ed ~~rd but computatio-~V te
dious a:~s based on ~ Bibs mathematical mode! in order to d
concIusions ~~m adds :: in statistics showed ~ co=~ding
emphas:s on :~=ming to ~ om tenths =1~.
~w the parade= statistic an.~s ls ~ dialogue bet:~n m~!
and data. ~e dam are allowed to criticize or - ~~n talsiG the once
nal moms* Diagnostic methods to ~d this p:~ss aw ~ major 5~::~
of research in sut:~tics. All am compu~tio:~v id ~6 the
most sv~v adopted make heavy use of :~:~c Id. :~n add:tio-~-
OCR for page 100
~e~ ~ ~e
.. w.*~Y
~ on~ imposed ~< Id ~=ladon has ~ to
new meters £br-~=e - m even rune smad Ma se~' ~s band
~:~ nature of so is readily repeated ~:~t~:~ ~es, essay
c:~1i ~n increased emphasis an Qh~¢~ m - - d :~:~al Ma
~ #
The ~= of common As Ied to sow ~ searching among
ma~em~cians' same of w~m -que~lon He nature of a proof ~ on
~ compmer se=~h of possible ca~ mo ~emm ~r Inn ~"
At ~ -~e elemental :~1' b~ borers =d ~s asks Seder eariv
u~ ~ ~awrs Ail impede uMema-~ Of hem and arithmetic
opt M~i~c~' on the mber h=~, have ~co~ cat
and co~m ~ a fling ~* =~g sums of shores
h=d Ads n~ increase un~and:~g, ~ mereb numbs the hit In
~ ~rmm~s it :s n~ Or ~ mU$~:~ to urge ~e u~ of
.~m ~ ~m -ha -inst~.~n - ~t ~a at all I - ~.~.
CoH~ m^w of =~ airea~ ~es ~iversaT ~ of ~lW
~ ~ A ~ [~0 00 0~= (~,0~ is 7 ~
coume, ~ cont~m miner than ~ d~n between ~c~ato~ and
m-uters as technol-+ con6~es ~s arrant) Hem
-~-e ~m basic It ~5i~0 in t~ Milt ~ ~ -i
n~:~e ~ preSents ~ ~-~m of-~a = -~e ~ at Chin
each of ~ =up of chin ~ke the~ ~ ~ ~
~ on ~ te~ of men~ ^~y ~s ;= ~ fit wo~ help us
predict the Iater te~ score?
Qume upon ~ :~e ~ st~nt would be asWd ~ plot the data and then
=~-e the ieast ~:~*~s regression line (~e s~6 Me i;n ~e i)
t~r mlb the co=~tio*n coefficient ~ ~ ~e 640 Pe;~s ~e plot
would be om:itted t-O s~e time. Mo~ ~ms wOwd require at icast ~ ~
ail As ~ this e*~-~cise Mach ~ ba~c lit OnTy ~ ~ wo~M
ask much more ~ them.
But -it it appa=nt th~ the Ma ~:~e two out:liers, l~:~ed as -cows ~ ~
and 19 :n the plm~ How do these =~s :-~e ~e reunion analogist
An -~e software Ante of the kind th~ ~s mdelv Able -en
~} vanities of compilers pr-ovidLes immediate 80070~7-10~ :8D be
viably -dimmed if the comp~r has ~hi-= capability. C~e 19^
although far from the re~i-~n it does not hwe a 1~e i:
on the p-~on of the :~:ine or the flue of tale conflation r. Caw 18,
0~ t60 0~: 53~7 is tint infl~mi~. ~g this ~t m - ~s the
regression line to the Co-ed line in the Fire =~d reduces the m=-~1~n
to ~ ~ 335, ~ut half its original ~1~" Thus the evidence th~ ~
at Fist word predicts 1~r Cilia scores is much weaker if caw IS -is
OCR for page 101
A::
is:
~ 1:~0
:
: ~w
fog:
~ -
. ~
~ Hi:
:
~-
-
:: ~ ~ =~s
- - ~
C~e - -
~ >
:0 10 20 30 40 so 60
= to 03= 0~ ~t ~ ~ ~t =~5 0t 2t ¢~ t~ ~ \~ 50~)
~ i) A~ tAve smm the r~k of ~ =~ tm ~= ~ ~ t~r 3~#
~ 8, Is p=}0~dy m0=~! In the =~= ~m deletIng As ~lot =~IV =0~= ~e
~ ~e v~= 0t ~#~ =:~= 5~*~ 35 ~¢ =~*
., , _. . . _ _. . _ .. .. ~
~^ (~= ~ 876 ~] it 60~l l~ 6~5 3# l: 8~6 3~ ~ 4
off hIoore,:3 most of ~e figures ~:n th:s essay am
I the -I ~:~s our energy ~r ~ d~n of
the da~" {t is -~ for the d~-~n to take the ~ of ~p pr~-
iem mwmg: "Is anything -~:~:~9 OutI>i~ ~+ THAW impo~am
are Chid W's t~+ ~g ~e analogs a~n without ~em.= We are
:~n encouraged to seek actions infer ~t the comext of
the dam-to am' ~r - - ample': :f the child of -a t S is so slow to-n
talking as to be out of place in ~ ~ ~ no~! child I.
¢t 68~0 ~0 {~5 ~5 t~ 8~ ~.t ~5 8~ ^~ it
question that Ieads to new and impotent s~ct matter in stati~-
^~-~d calculation ~s ~s to concentm!e on other =~s
O pTO6~= Sobering rig 8O ~C =~' Int0~CtiH~ the
results :n their cont=~' and asking new mathematics questions s
gested W~ an exe~. But it is elm tme that automated cal=~on can
hide the natu~ of the work that is camed out and impede ~t
~t - ~r the wok ~s appropnate to this cite probing. Too
often, students believe that computers Amp into us about the Amp
8$i it tt~ 5~t W~,(~ I
In a.. cia;~m exercise on tiiampling,18 Ids were Milky to recOrd
the colo~ of ~ Cage sample of M&M candies and to commas the
OCR for page 102
~Q:2
~K~'~ 'To N~Y
~ K ~ 00~6 ~5 ~ ~ ~~ ISIS
the -I ~~n of=~ ~ ~ ~
un~- ~ ne pu~e of ~e emus ~s ~ demon~e from ~ =
:~ ~~ t~ =~ Mars ~= n~' ~n - Hi um~N restated.
yet ~ mme smdew- s~pb bel~ ~~ ~e Co~er Gel ~
co~ bec=~e :t Is on the ~mp=~ ~n ~~ :they~ h~ entered
Em ~ut t~ e~Ivenes$ Hers is ~ m~or Item
him p-itf~t 1n t~g logistics' ~ using pianmng to
Aces and com - ~= m.~o ~e cu~ Aces Me Of
i;~om arm I ~s Amid :~[ nu~ =e to ~m ttelr Ovaries
I; =~= to bel~ ~ ~ "magic b~-
B=ic ~~w ~~:~s a~ n=~d ~~r ~:~! anionic and esteem
t~' wash are Ike :in cheerio automated c~^ Wu
IOnctmn =~ p=~ c~l - ~r the O~ ot ~~:~' brim
mu~ be requested ~e ~ one, while automate o~y the a:.
,~ ch~d mast At. ~r ex.~, the ~~. between divisor
and ~-~ ~n order to use ~ ca1~* ~r Tong divide* ~ Maid must
in- begs tO =~ ~ with ~ ~ ~ 1
c~ there~e - .n to u~ ~.~ In ~~= saw of Ma as soon as
the orations ~ u:~. ~^ ~ -I that mI! mm~e the
.. ~
~ . .
sampte me =c stanuar~ ~~on died—m Beam Ma
be used to bypass mut~ al~=hms already :~.
At ~ more advanced I - ~~: some :his~gra3~s sh~d ~ maw by h=d
w fuming ~ att:~lw software that chooses ~~ps and ~~ws
hip di.~V - m ~e ~ ~~. Pe~s most imp eX-
=~ce mth Hi ciLan-ce devices and phylum simul^~ns such as
braving colored b~s few ~ ~x show p=~ com - ~r s~-.
"~wodds~ .~ have nG mutation. ~~h :~, ~ ~~- tend
to bel~ th~ the =~er pr~ts reality.
t~.~nion Dom physic tO ~ is vm~ I-
A:~V ~~
The practice of
=~ed use his easiest when calculator am mmputers are pan of the
no~! Cl~-m I..*: tO be u.~. as :~, not :~ ~r
~ Cecil ~ r~ ects or u~r ~~s ~
From ~~a ~ Inference
There are w~] ding principles th~ help us see :he my
i=! studY of data and chance as ~ cobe:~t - ~~- ~~e su~ principle
is t-hepm~ress'~ fib* data analy;lS ~ cat-a pro~on to—b-
~ t~ i~f l66 ~i50~5i00 id alit 058~ is 0~i:~6 :~ t6~0
same st~.
~ A ~ _
OCR for page 103
103
~~ =~' - :~h I: o~ des~bi~ :~M sum~
w d~, us~v to =~r scow que~s ~~t mme
~ in ~~ =~ 6~n ~ mn~mne~+
~ Tn~, th~ ~ of :~s - m ~~*
Th1s pm~Sion Of topics I- ~~ ~e T~ ~~: of
the :fi - am ~e :~ of I- of ~e m=~-. It ~~= gives
. A cal =~^ 5~6 3~: in ~
cum=~:~. ~ cO~' the i=er three headings mi: a;~: inch
~ .: the =~t ~ ,~t,3 = - i ~ ~ ~
d=~ Din particular expenen~ m:h chance o=~es—can ~~
gin in ~ -~13~ =~s. S:~:~:~, informal concIus:~s band on Ha
I: ~ encou~ ~~m ~ =~Y stew
The Baby Back ~ ~:s outline is ~at it ~= n~ commas:= ~at
pmb~-~:~ ~s i; in its ~ right' n~ memos ~ ~ pad of Akin
tles~ :~th to =~t Of pro:~il:~ty and b~c m~ematl~ ~~s ~=t
prob~-~li:~y =n be i: in elementmt - ~~ as soOn as ~~s
aw unhasty. There is, how—e~ ~ natum! place Or pr~-~ty in the
p-~io~n of Ii ideas. S~M des~s ~r prOductng ~~ are
d ~, the Illiberal u~ of c~= ~n rehem ~~g Al
rarer =~tive expenm~- H=e is an Oppo~i~v tO prO
vIde mme eX~e w:~h : and to. adv~ ce to: ~ ~~y of
random Elation in ~:~al summaries (~ch as the mean- of s
obSe - ~tio:~- Bulb ~~sice:l random =~tion and sim.~.~icn =n
O~ the other ha~d, Army statistics ::~ce requires wme under~
standing of pi There~fbm it makes =~= that the ~~n on
p-~:lity be be~n ~~se ~ pm~ng ~ta and ink Because
Ot t~¢ =~t CO~t I t6~t $~S C~t in p{~iitY
=d in pr~il:ty based i:~:renceA fo:~1 mathematical treatment of
the~ s^~s should probably be an elective mther th~ ~ core cou=e
~ secondary whOo-l,
DATA ANTI - ~S
Data analysis is descriptive statistics :~m, with n~ methods,
r emphasis on ~,~;hics' and ~ cons:~:t philosophy due to John
It t<~8 ~ 3~6 ~ 0: 7~5 ~~ ~4 Kiwi his wnt~
ings in this area.8 ~ reviewer ~~commend$ paper l: in Volume ~ as
~ good starting I:.
..
..
{~C CS$~C O:t 68~8 I iS tO =~t t~0
OCR for page 104
{:~4
j~/ A^~= ~ ~~:~Y
i~ ~ - ~~s in ~ - ~~ at ~ :
r ~e ~~ are =~:~;~e Of some ~;r-~:~ve=~*
Tnspe~mn of Ma ~~ -as ~~ ~~. :If the data
w~e Dro~d to an~= ~ sn.~-~.~c ~-~.~.~ ts ~ - ~2 In whIch
s~ t~ moods ~ co~.~e~s ~~. ~~e tats
~1=d us m : ~e
=,3~8 ~6 5~ turf ~~ ~8 ~5 t6~ ~ - ~~
my Tyson=' ~ ~ ~~ ~^
In other c~s we do n~ ~ ~~c ', 1n mind: :~" ~t
w ~~ ~e data to ~~ ~~s ~= ~ ~ seek ~ barn
. 0~ then~ dew of Sexy -~a a=}ys~s'"
an~ of ~ Alp- ~~ un~ ]~
The bests c~ns ~ Ma a—ys~s ~ new methods ~~r
w~ as ~~ and ~~s (= scam- plms
8~6 50~i - t pi=5 i; ~~ p= - i0~t turf Em: ~~= 0~
amples it is ma- to ~ Ma analysis as ~ mile=~-on -of clever mols -and
Aim thy I,. g p=~ Ah =3,1\rSCS Of =~,~liOX~ ~~ S~ at
~ daM c~ ~~ 2~ ~~ bY three s
ple pnnc1,~.
1- M~ fmm si~ to m~:~- Lam exact ~ s:~e variable
to relations - ~~= twO va~S and connections among ma~!
Baby
2. When =~ni~ ~~a~- wok hr~ ~r an owr~l pattem and then
for mood -~ati=s :~m ~~ pattem.
'. M - e :~m -I I to :1 m=~$ ~ speckle a~
~~s of the ~u to =m,~= mathem~i~ models Or the Feral:]
fi nd ~:~:~ pn:~-~es sub th~ I=~ng abo ~ ~
mth display1~g the ~~tion of ~ slope van~. My such ~~a are
-either =~= :s how qu~ve van~es such as =~or become
numenc~r measur-~s mlb units. Smci6c methods for data dies
play -God advance in parallel mth the development of =~v qua3~titat~e
con cepts~ "~0w many of-e;~ch color :n ~ bag of M&~:7- can be deter
mi:~d'b~ counting and dip Blah smelts of colored bloc~
~~r ~ stempl.~t ~ Wo~di.~t =~s can reinforce the dist1~-~n
between the ~ O's and the ~ ,~ p:~ce in whole num~. ~ ~em~:lot of two~
d:~:t data lists each Is died as ~ "~- and ~~s the obsewat:~s
by placing their i,5 digits as "~- on the appmpnate stem. He:~'
: t~07 iS ~ ~~Ol 0; tt~0 nu - er 0{ home :~s Babe Ruth hit
each -of his ~~= w:~h the W~kees.
OCR for page 105
Ace:
: 25
: 45
6:: :D
~ ~ 66679
449
-~:1 i~r we =:~e to hi;: lo con~= amp -of Ma mth
:~= -~an ~ ~w ~~= =~s an. -~:~ng of "Wmee~= =d
the ~:~>Y to =~p nu:mbe~ as we~ ~ sin in making =d m~ Is
:~n ~~.
~Ch ~ amo~ ~ av~le vanadons on ~~ and Is
=~ :~e ~me:= as the -numbed ~ng up the ~~a b=~e :~s
Up :~ ~ :~= mth -saw ^ts oh~ ramp A
in or t=~, be* examine ~~ =~= m~ se~'e~ d=~]
places ~~o -cased ~r ~ Am requires ~ ~ unde~g of
order ~r ~~ ;~umbe:~- Cam~! planning ~s ~~nt -to Aid gins
adYe~y -sting students mth Was t~t go be.~d the:r Or
sk:l]~* Bm :t :s so-so -God th~ ~:~ ;~s :n ~e ele~ grades =~
r-~:~-= IBM: con~s and $k~:~:~s £~m the existing mathematics
cumculum ~ app~:ing them ,~n i*~-~*~rg settings.
~en we h=e -d ~ did Nve mu~ :~Ct It and com
mundane our understanding -lo others. Ch:1tLw:n are not natumlly ~~e
to Add data a~ =0w ihan lbey a~ ~ ~l0 to :~ad wo~s T~
must be m - t both the ~~ of io:~g at ~a =:d - ~~c ~~s
tO be ~~= off The st~ is e~d In t~ w..~d pnnc~+ ~~k
~r p~m, t~n for d—I- The—chic ~~es change as we
-~-e throu~ the stages ment:~ in the 6:~ pnnc:~" An example
' i ~0 tt~ p ~~s A ~
· .
In 1961 Yankee outhelder Ro~r Mans b^e 13~e -I
~~ of 60 bome ~s in ~ single season. H:~e is ~ bac~
back mmpanson of :~y bome Mars hit by Ruth (~n the :~-~)
and by M~s du:~g their v== w:th the Ya:~.
:~H \~S
~ i.
5:'
54
97-~66 ~ 1
944
~ ~ v..
:~. 346
:. 368
-I. 39
.
..
...
overall shape of Ru:~s di~:~-tion is `~:~v sv~metnc* Thee
center is at ~~t 46 home mns, in the sense -God he hit -more than 46
OCR for page 128
128
¢~ A~:~:~ ~ ~~Y
~ the Bali an ~ :~ th ~ =n =t of prob~ilitv ~ ~ cxp=~ to
such ~~ or =~e pmbab~= ........
What is new be= 1S not the
~~emadc~ wh;ch r~:ns the ~~' but the :~mrp=~:~on o~f Area
b~V as mp~ ~a su~w a~t -of un=~y ~~r ~~n
~ Ion~:n :~at:w ^=D.~- ~e ~~:~;~ ~~= of the s=:st:tc
:x ts now -~.~d to ~e con~t p - ~~s of ~ - ~ ~ ~
. , . . ~ 4%
~n ~ ~ue Ior A. ~ ~~bti~ ~en combln~ me pnOr tn~on
~~ t~6 ~6 ~~ Ah:: ~0 00~ Jo "6 ~ ~
the ~a (~e d:~;e ~ of ~:s ~~ation uses ~ s::;~]e it
-I Ii pm~s ~~ as ~a~7 t5~em' ~ - ~~t
B—s:= school. ~es :ts Came ~ ~e con~ns of in—cnce an
=pr~d :n w~s ~~ - abbey statements ~~t the u~ p=
:~f t~ p—ability :s 950~ -Gil ~~e ~~e ~~ ~~ t~ ~:~
=d 64~7 ~:~ches
The Brim =~n :s ce=:~y easier to =~ th~ the ~~i~
s=~:~- M~ p=~r 1.~-~ is ion :in m.~ pry
atist~ns ~~Iv amen that Basest m-~ Ad be -need v—n
e pnor p-r~ili~ d:i~n of th~e pammeter Is ~-~*~. ~~t :is
dimmed is whether u01e pnor d-~:~ns are atways ~e, as
~~sia:~s comend. ~~:~n ~~;~:s do not think that m-v A-
J~\e a~=t is ~~vs use~: info~ion and 50 are no! wIlll~g to
A. ~~ u~ of su~e prier -I The ~~y clear
=~:n of a Brim =.~Ysis =n ~d stro~v On assum:;~ns
any the pnor direction that cann~ 'I Ch - ~d ~ the CAMP
~r in: inaction. ~~t i..-: Ba:~;n methods hwe
s~l di~:~s - .
· . ~ # #
Th~ :equl~ ~ Ems ~sp of con~dit10~-~ prow
ability Indeed, ~~s mud underhand 7;~e d:: between the
condit1-~! diminution of the sm:stic gl~ the pamm~r and the con~
Aims distntutio:n of the pamm~r ~~n the a=~:y obse~d ~~e
0t t50 5~ti5~0P 'I is ~~> 5~.
The su~-~w id of
p—nullity is quite natu~, but it dlve~s attention—m randomness
and chance as obw:~d phenomena in the ~~d whose pattems can
be d-~ed mathemat:-~- A:n un~ of the behavior of ra
dom phenomena Is an important goal cf teaching ~~t data and cha:~,
pmbabilltv unde~od as persona:! aswsSment of u-~-~:~ain:ty is at ~st
:~t to achieving th:s go~. ¢c Kline ~~m d~a ana:~s through
randomized designs for ~~a production an'd pmb~il.i.~) tO 1~e ls
cIeare~r—en Pi inference iS the ~^
Two t>~s of :~:~, con:fi~-~-e id and signifiable te~' figs
ure in intr~o—tnst:~ion in ciasSIca! ~81 in~-~- The rea~
coning behind both tVpes of i.- can be i.- In~v :~
~i50~.~8 40~t 68~84 ~~: t=~: 806 specific me~s sbould
OCR for page 129
If::
be w~d ~r u~e seCO~ Go: tO p - ~~ =d ~ -
tl~, a~ no : should ~ m~e to ~~m mom ~~n ~ ~ ~~c
As. Andy :n ~ ~e of s~= ~;em ~ ~~ ~
loach o~s tote ~~= ~ suth an e~ the it m~ ~ better to
ail ~~s ~ te~ ~~.~s all~.
~e m~ beh:—confident ~~ts -is Eve ~~
Cat Wh~ :-s more' news :~s :of ~~:~n po~ ~ Weir ~~s
of ~r preside a Cay sew of ~~es ~r -I :Yow ~s :t
t ~ ~~e ~ o~y ~ )~0 ~~e can =~y mp~t ~ Opinion
~ i85 In.. I? Ran~m sampling pmV:~= ~ pa~of
We ~~, =~g Ire pmv:~e the rest =d co~e
:;~s ~~n - M ~e A... of c~r m-~-
eX~e mth sim:~n Of ~~ dl~. ~ I
between population and ~~' the imp of random ~pl:` and the
=~n -of ~ -Amy distrib~:~ am ~~ to in:fewnce. aims
-A ~~s ~e 06~! i: -of con5~= intervals dunning
t~ emanation of A: and sampling din—~~. The ideas of
~~ i ~ ~~ ~ b~ ~,~,=t aria apt . d~~ Y Of simulated
=:~0 ~ mme ~~ appmach ^~s f~ili~-v -em no~
_. ~,jf;~ jar
Same that :n ~ cage county 300~ of him school ~~;~s ~w -em
to: school. As~ ~ ~~e ~~m =~w of 250 ~~s - :~r theV
throve to ~CO] w~y p—uces 230 Ian observations' ea~ m:th
probability ~ ~ -of being ves~ ~e p~ni~ ~ of ~s =~= in
the =~le vanes—~m -do sump:- S:~=e -id' 1000 ~m:~es
~ ~ he Gil; ng ~ ~ ~~:: on of ~ ~ T~t is app
w~h mean O~ 3 and st= ~~d den i ~~ ~n ~ K 0~ 9 ~
9—K Hi it! · ~ I ~ K at , if
Repeated simulations
at sampl~ o: ~~s s:~s tram :~s po~n demonstmte that ~e
center ~ the w=~:~g -I r-~ai:~s at O-3 a~ that the spread
ls contr~m bY tte size of the =~. Tn ia~ ~~CS (~:t lOOO or
so) the W1~s of the ~:~1e ~:~tic ~ are teddy =~:~d around
the populat:~n -I ~ ~ O.3.
~ in ok as i*: . ~d: K
~~ts can See empincally that
=~s of ~~s ~~e allow good ~~s about the entire populations
But~ how g~d am ~~s based on ~ ~~? ~ =n I the
ans~r b~ describing how the Arid ~ vanes :n repeat-cd sampling. It ~s
~ basic fact of normal Is th~ ~~t 955S of all -~tions
lie within two st:~d dev181:ions -oh I:: side Of the mean. so in
:~6 58~li~g7 93~ 0; 3~ samples of 2~O ~~s ~Ye ~ sample
OCR for page 130
=~t art: ~ N~y
prop: ~ m:~n 85~ O-*~6 0f ~ =0 pi 0~3 - 0 ~ - ~
~~. ~e simulate=: Sh~ ~ ~s is m.
~ pw~ th~ ~ ~~e Of:_5~0 Indents in an—= ~= c~
6~s :~5 ~o drove to s~1. WE ~~s th~ :~e ~ ~~n ~ of
all ~~$ ~n ~~s c=~y - he -no ~s~! ~ c1~= m~p ~ tO~O ~~
O-~. If (= ~s t=~) the vary ~s ~~ut the smog as :n the co~y
we dim ~ i:~5 '-by= ~6 0~ ~~ = 95~0 0t
we are By% ~t ~M the u~ wMadon proposal= ~ I~ in
e :~! O.42 ~ O-~. M~ generaDy~ ~ Swerve ~ ~ O+~£ :s a ~~%
ln~] ~r the -ale ~
of ~ =~ ~~ :~ ~ heart
. As- Spewed ~~= of =e 230 :=e ~, som6 of ~e In
v~s ~ ~ O~ ~6 -am the tree pm~dion Of p' wh~ others do nm~ :~t ln
1;.~e ]~.g =~ 95~: offal! ~~. pm~e ~ 1,~.-~, ~~.~g ~e tme
p* ~8t lS, ~ probability that ~e m~om i: 9 ~ O-06 contains
is- Odd* AS 1S ~~b ~e ~e in crania ln~, ads- p~y
=~= to the pe - ~~e of the mealy. :~n an in~it~V i~ =~r
Of wpeat~ oomph.
The ~ ~~n of the =~t ~~ belon~ t:o ~ stu~ of ~:~
pllng and ~~:~n and ls es=~v an em~l ~~:~:n of
~ ~ ,
~ ~g t=~r30~t}~ S Ot S8~= thm
the size of Char p~tion.
ma- ~s that eme~ - m S~h I~
de~:~s ~ much more tm~t than the ~~! dre~ we ~w
there in the s=~nd sta~ of the a=:~t ~e seco~d st~e helon~ tn-
more at study of in:**
~ _ ~ ~ _ are ~ ~r <~ ~~—'4;;7 ~ ~ ~ ~ ~- ~~~~~~ _ we
~e qu.~it~ive concIuslOn ~.~t
mo~ =~le res~s lie cIose tO the tmth 18 made quant:~=ive bY ailing
an :~wal =d ~ te~ of =nfi~^ The natum of this concIu~n =d
i~ li.~tions both need emp~i:~.
~t are the group:, Of Our =~= State~9 There ~ ontY
~ , - ~ ~
two pO-~31 )~-
I . Me interim O-~2 ~ c, 06 contains the t=e ~~ulati.~-n pi
it*
2. Our simple random sample ~ one of the :f6w mmp:~s :~* - ~~b
~ is not ~~::n O-~6 points o ~e tme p. ~niV 5~D O all Samples
~,:~r~ 5~6 ~ ~~:~C =~.
WE can~t know whet:~: our sample is One of the 930~ ~r whiC~.h the
! catches ~ or one of the unIuc~ 5~. The statement that we are
95~- confdent that the unkno~ ~ Its i:n O.42 ~5 O-06 is sho:~d bor
"We ~t ~~e numbers b~ ~ method that gives co=~t results 95% of
the t:~'
As ~r the limitations on this :~oni:~g, remember that the ma~n
of e~r a.. ~ =~e l:~:~T In~:~s onIV mndom ~:~ling en*~:~.
OCR for page 131
:~31
,,-
- ~
\ SMIPUNG o:~U ~ 10~ O:F ~
\
-
~ :c
It
~~ -
- : ~-
-
~ -
~ -
- ~ - -
~ -
- ~
~ -
. ~eK — :. A
nGURE ~ The : of ~ mn660~= im~ 1:n
: - m ~e =~e 'pulatIcn.
~e Oo~l cu - e lo t
=~ng dl~-n of ~e =~^ prim ~ cenwr~ at ~¢
pop~n :~= p~ ~e do~ aw ~e ~~= of ~ from 25
=~:~` w~ fin :~ - ad :~ ~` ~~ ~ ~
s^* I~ the Ion i; mn 95% of th=e ln:~s wIll cOntmn ~
In pm~e t~e am other sources ~ e~r that =e not a~d ~~.
~ · ~ olis are my? (~6 ~ t0~.~=
using equipment ~at dies resident:~ I Imbue—~ randOm.
Te~e m - eyS ~~t hou~s m~t phones. :~ wh:
ste~ ohen find that ~ m=y ~ 70% of the =~ns who answer the
phone a~ ~~. Men will be untLe=~:~d ~n the sample un-
l=s steps =e t~n to =~t males. ~~e ~~S of ~! Licit Il
Irk mme bias into op;~= polls and other ~~e Su~*
51~fi~e :~
~e p-~e of ~ confidence interns is to est:im~e ~ popula:tio:n
mmeter and to accompany the estimate with an ind:~n of the un
00~)t 600 t~ (~0 Dim; :~ tt~ j3~- Ii tests 60 ~~t
OCR for page 132
OCR for page 134
OCR for page 135
OCR for page 136
OCR for page 137
OCR for page 138
Representative terms from entire chapter:
bome mars
I3:2
~~ ~~ ~~ ~~:
~ u~ p~r but - ~y as* asw~t
of - ~~er ~ ~ or Florence ls patent ~ ~e pop~. ~e mere
~~= ~~t :~h an a~t ~ nee~' ~m not ~ ~~ out-*
comes -I ~ rem I c=~' ~~ ~~s n=~] mph~
tIcat10~* ~~cs ~ sclence felt ~~s—o ta~ ~ the am ts
Who 5~ pt6~6 ~~ 6~6 ~ ~ - ~t ~ tt~ 60~ - 4~7
b~r ~~' ts ~~ as C~i~C~ ~e role of ch=~e va~n
* ~
~ not '*I ~"
I As Is ~ ~~ of Is the qu*=~-n Is ~e Ob~
~6 ~ 1~ ~~ =~ ~~ ~ =~ - ~ ~~= ~7
Hew ~s the reasoning of s=~cance te~s -~ IBM ~n the
wn1~ -of ~ :; =;~3Le.
.
amp: Me Wet:~m era:, Con~s :~d ~~t ~~g men
should ~ ~~n at ~~ ~r w-~ice :~n ~ a~- The 5~t
~ah Iottew was held in 1970. Firm ~-~ ~= ~ ln ran-*
dom o~r and men wew -~ :n the c - -~* -in - ~~h their
A- ~ ~ ~ ~ ~ is. .- ~ .
. .. ..
Atwt me A*, n~s omn:~
tI=s -~ ~at m~ bow Iate ln the year were mom ~ ~ ~
:~o get low~ ~ numWrs ~ so to ~ tnduCt~ D313 anal sAs
(~*e 10) ~ s~ ant ~~n ~n bl~h ~~-e a
draft :number. ~ sadistic that m-~*es ~e st*~h of the as
m=~*ti~ b~-~n -my O:~r (! to 366) and bl~ ~~e ~~ to
36-6 beginning mth I=~ ~ ~ ~s the =~n =~:~" ]:n
—t7 ~ ~ ~226 for the 1-~7O Iotte~. Is chic ~d ~~= that
~?
~ IBM test ~~s Me 158~e by asking ~ ~~I'h.~, I-
Age- SUppOSe ~: the =~ Of s`~mlent that the I~t0—~= t=~>r :~
dom' what 1s the p - ~~li.~y that ~ =~m I=~! would p - ~~e an ~
at :~t as far fmm ~ as the Reseed ~ ~ ~Q-~9 /~- ¢e I
-bililv that ~ mndom I- mI! pmdu~ce an ~ chic ~r—m ~ is :~ss Ohm
(3-Q0~L. ~~. Si0= ~ r' 35 If* Hem ~ as that observed in I970
~6 8~ ~~t 00~[ in ~ =~= i0~7 ~ t3~0 5~8 - ~0
that the -3 lotted was not ha;.
~~m tO did the scane~-~t of dra~ numbers ~si~-~d to each
both date b~ the INTO drain Iotte~* I:t is diffi-~t to see a~ systematic
8530Ci3ti0~ or bind d~e and I-~Y number :n the Id;-.
CI - ~~r ~~s can emp.~e the as-~ciati.~, as in the h~. Bm
-Iliad calculation is needed to :~-~= whether the obse - ~d aSso-~.~-
tlon is Ia=r than Ale reasonably be attnbut-ed to c:~:~ce a:-.
In ~ random assignment of
~ 2 art?? ~
=
I:
.. C.
al!' ~ 4~
:2: ~
~ ~ =4P
41i ?.li
hi: ~
#k
.4'
46
e'.
.~- S.
$~,.4, ~ ,?~4'
-~. he ~ ..
4~ ~ ~
"a'
4~
~1:~0 200: 30:0 4~
~ ? p7~ 0~3 ~: .: ~7 07 ? ~3
~=RS 10 Dam-m ~e I97O dm~ ~ew (~ ~ ~t
~6 00~7 ~.~ t)~t 6?~?~5 ~t ~t 0~6 0; t5¢ )~: =~
i~v ~ 5~ low - 0 ~?~ )~-?~^ =~6 =0 ~ ~ - ~ =~0
~> mat ~g tt-0 =~ ~t ~ ~ ?~t =0A~^
¢e pI0t of mo^IV m~ns conn=ed b~ amp..? 5?~.~5 ~
6~7 t50 t~' ~6 ?3 =-~-~ tt~A'?~, ,5 ~. 0~ t~l 0~6
IRKS p~5 t~ 5~5 ~ a t~ ~0 I've
l ~ ~
70 ~ ~ 22(i ~?~g t58t =~n 50= i~Ct in ~t 708
t0~:~?~6 t~ ~t i~ 4~ ~?~ - ¢?0m~ 50~ ~:~6 6~t 6~t
i: ~ 0~6 ~?5 t6?~t ~0 i0~?~ ~5 ~t :~ ~fi-~: all the
00~ati0n in ~ :~= i0~-li &~ n~: 50 0~Q 0. p~?5
that ~ ~ Kid ~ ~ ~ 6: i~ I t50 =~ 0: =~5 tt~ 00~] pi=~5i5~) ~ 0
0~0 t~ 053~ Ill OK
To reSolve his uncertainty we comp~ th0 obse-ed ~26 to ~ mf~
erence do: the ~m:~li:ng di~tion 0~?~ in ~ t=17 random
imte~ ~ We find that ~ tmIv random Iotte~ w~d ~m~t never p~
ce an ~ as ~r-m zero as the ~ observed in I97~D. The iv
~:~.i0~ t0~5 ~5 - ~t ~ 50~0 0'0~. ~t ~ a ~6 is
~ i - 0 0~.~, ~ 50~g 0~t in: ~ t8~ i0~. emit 00~i~?5 ~8
t5~ t5e ~ 970 ]~?--wa8 6185~+ J~i00 ~i$~6 tt8t ttC C3p
s ma ~ ning the biro dates had ~e:3: hIled ~ month a: ~ lime and
not adequately mt~d. ~r dates remained nea: the top and tended
:~o ~ ~ ~~r (~ ~~ mOre de=~l ~~t the in: ~h
, lnd~ :~ s - ~~ Amp: of ~e :~:
Questions h~ "~Is ~:~s ~ la~ Cam ~ "Is ~:s ~ ~~ :~
t. =~e up onen In anteing ~. It is qulm ~~ lo Eye an
3~r key =~ ~e if o=~me ~ ~ =~n
ton, ~ we if =~w ~e b~h ~~t o~f ~ child ~ t~ di$-
~n of bide we~u of Al ch~. Sm~ ~~d =~ai~ be
`. ~ ~ ~ ... . .... ..~ .. . ~ . ~ ~
w. ~
cucQu~c To Temper: ~ role oT =~e Van=~n and to ~~s "s:~-
m603~= Islam ~ -~= lnd)~ Ou^~e to a. sui - ~e
fee dI:S~: {f probity =*d c~er $~IMion are b
~ 6,¢~r0~6 t~ I, 0~^ 50 by; )~ t56 ]~= 0{ p—Dim
am ~~g ~s~s B~m ~~ £~5 05 - ~~;~ 7,
areas in ~ wh~::l c~:icul~-
~m =e :~ ~~s ~r ~~.
TO m~s of scarf ~~
' =~g ~ te~ =~, ~ co.~g Am. t~d ~~*~s
y c~ ~e ream~*~:~g of s~i6~- te~. ~ :~x~:~ :
seli :s some - ~t deft =d ~~! ~ s~.
.. ~ ~ ~ . ~ . . ~ ~
E~e examples of
:~e u~ o: s~= te~s ~ m~ remo~d tram e~' experience
~= opi~ni.o ~ polls and Si mIlar - ~*~S of co n6~n Ce ~~e nts. .~
fling of dab and chance' =d the ~~nt of q=~:w
=~:ni:~g ill: fib 1s berm* se~ m! con~i~g ~e study of stat:i~
05 in ttO 506~5 `15 ~#7 ~~:~g ~~—uti0~S, 00~00
inte - ~~' and ~ mnt1~uing emph~i.s on u~g these tOols in =~g
about uncertain data-.
Statistic =d pmbabllilV aw she sciences that deal mt:h unce~aintv~
m~ variation :n natural a~d m=~e ~~= o~f ~ - kind. As
such theV are :~= than simply ~ part of ~e :~.~ticS cumculu.~
they At wed in that setting. Pm~ili~ is ~ :~ld Ethic* math
emetics. Statistics' like physic or =~*~' is an ~~t d~-i~
:~::~:~:~e that makes hawk and =~tial use of mathematics.
Stat~= has mme cIa:m to be:ng ~ ~~! me:~od of ::~^
~ gener~ way of thinning that is mOre i:~.t tha~ an-~ of the s~
him fac~ or technigues that mom up- the d:~lin*~.
{f the pu~=
of education is to d - ~~p bmad :~:~! s;kills~ ice meets an
es=n tial ~~e ln teach i ~ and I~) ng. Ed ucat lo n. sb.~u ~ ~ 1.~u ~ ~
~~:~ts to lima—-~ and hill methods, to the pol:~} and social
analv~is of :~:n soc:~' to the probing of natu~ b~ expe:~menta1
s=~ and to the power of abst:~ctio-n and deduction :n mathematics.
Reason:~g Prom ur:~=in cmp:~ data :~s ~ aim: p~} and
pe~ astve i:::*:. meth~+
:135
~:~s :~s ~t to =v the ~~d :~on in I n~:i~al :~-
~,,5 ~r t~r ~ s~e ~~d be prom1~t ln ~ Sch~ ~~.
c~ ~~:~g, bm~y underwood
shad ~ pm of the ~~ =uipm.~t of ~~ educated '~^
can summan::e the ~~e eleme~ of-. ~~ ~ Mows~
A VIA An
~e'- r=~d " the ~e mbiMdual =e Va~*
The dommn Of ~ strict: Bins ~ nature and ln b'~= aF
tal~ 1s qu~te In:*
2- ~~e n=d ~r Am: ~~: p:~^ Stad~= ~ Bedfast empt
Wick r=~r ~= same - e. Looking at the data teas host pnon~.
3. The USA of ~m =~n with vanatmn in m~. ^
of mu=~ of un=-~:~ Saabs we wo:d sel~ ~~
~:~-~s and i: on co~:~n in expenmen~} ~~- ~~M we
lntmduce pl=~ wnat:~n tn~ ~~ pro~:~n bY u~ of r=:
~ ~ . ~
OomIZ=~:~.
< . ~ ~ .
~ . INK
A:
4- ~ q=;~n of van~. ~~m variation ~ de$cri~d
m~:~matic~v by probab-~y
~0 ~~ 05 \~ti0~* I 3~\t~$ 5.~5 ~6 ~.~_
~16 6~3 6~ ~C =~= V8~7 0 Hi am
meas:~-
. A
Magi cal thinking ls not rec~ dne or re~ f rom - ~~V expe
ne~* But it mil :~ot be deVel~d in—Idren ::f lt is n~ Meant in
the cu~.~- Students who min. thelr ~~n mlb wiling and
~ t~ t~ Ii t50\t ]~= quic~
tO 0~ 0~0 808~: tO tO ~=t 3~6 01~= ~~g7 8t i085t W~ t56
answers ~e numen~ 6~. Darien ~s unexp~ and un=:~
. Lis~ to A~r N;~6 :~g the expenen~ of his ma - t
research 6~ mth wphistIcawd marketing ma~no
~ ~ ~ 700 must 5~5 =~0 ~~ 04~) \~ t~ ~t ~~ p=~6 0~
mono Th~+ =.~t numbers as =~s T=~h aria 6~d 1t dI~t to ~~k
tang tt~ ¢~pt 05~>. 750~ 60 ~0t ~ ~ I 85 ~ ti~6 0t 5~6
' ~ =~g ~ ~ b~ ~ d 0$~S O~ ~ 301~! keg ~ ~
it heir s~f~7s~ 5 ~ manufacturers 6~0
thmu~ r~t stoms~ AX . ! once decl~d thal we would d~ all cha~s to- shOw
p:A06~6 m~e around the number : ~r example`, =~s are e:~: up
pC=~t Of ~~ ~ =~t O hi; I~ CrW60~. t,S tO=66 CUt tO
~t 0~0 0 =~ ~~{ MA 0~( ~~$ ,)~; 00~l,6~,~t ~~ ~~.~ ~.~5 tryst. ;~
~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~A
The ab-il~ty to deal in~:ligentIv with v~on and uncena~ is the
} of ~inst~tion ~~t data and chance~ Chew is mme C1r~;C
h i ~~ act;~>r :~mp=~r68' this ~i:~yA N:s6-~t 0t 3~- ~0
TO
=~- ~ lying EMS
salmon
, ~ ~
^~ ~ ~:~y
~ .
Ol _~1~.
Hey nose 1bat ~
~p~b~~ Ed Ins Be Alder lo c_
S1_ ~^ I!. an Men beg i~ion~ of ~ Anon kind
-1 Ages nodded 10 ~~ Philips ~~ ~ untrod
~1~. ages ~~ a Up:
[So #= ~ ] apt ~ a ~ lip Imp ~ -~ dig
~i~1~0~ ~1 wits ~~ a ~_~1 Em ~ egged Am our
sanding ~~ on be ~1 YiSil. In -0 Abe no b~=d~ iffy glitch
amok aft ~ Is paled #~ rely pon~Us$i~, ~1
Her sob as am he car c ~ ~1~- or <~r fins ~= so bail
~ul~^'1 Loire up ~ ~~- Surges to bag In one Sl~l~iSli~
gum me arson age :~u~e0~lsll~ Lions =~ ~ =
~s~ am- oaf e~l=1 imps, ~ b~ Ace _ jug 1~^ 1be 6= (me,-
^u1 20 In ~ Ace
Ni^1 Ed his Allege find it ^^ 1b~ ins1~ion of a quite
so fiend dog bag an egg on Bin gout ~~~ oc~n~.
Tbe of is s-~r into Ding 0~ 1be Ilk of
Lisle ideas in eggs line as ~1 HI goad Bank
go. figs is agent ~~ we an in ~~ Baling ~~ ~ ~~/
ly Angle intelle~u~ said. Bigly ~~ ~~~ Herb
Going 1b~ lining in dee~inisl~ic Splints earn ~ Be Huge
1~> dog not mid Ida ~~# S~1iSli~ Paining. His is
evidence 15~ we ~ denim ~~ ~ ~ If inflect mead.
gay Cab 1 ~u and cb~n=? Satiric and p~iIi~ty a~ ups
~1 in patio. Data analysis in Paul blips ~o legging of basic
m ^ emalics. Bu1> mod impo~1,ilis because Pistil 1bi - fig is
an independent and fun eggs inte~1k~u~ method lbetit dk@erves
allenlionin 1be olcu~iculum.
1 - -- --- ~
.
Bobs. ~~ ~~ ~~ ~ ~~> Ones at, 1 9S9,
p. 30.
2 Beat, Vic. ^~/e ~~' ~ ~ ~ Beg By, MY: Joan
~~ ~ ~` 1982.
3. E^n, Barley -ampules am 1~ thaw of stations: Id 1ho untbin~bl~.-
~ ~ 21 { 1979\ 419~37
4 Hon~S SPEW E. dominion and ~ia1 amid: ~c 1970 dam lollc
171 (1971). 255~261.
Gamma, ken and Plan. Andy ~Di~cul~i~ in lca~i~ basic ~ncepls in ~
ability end slati~io: lmplicalions~r Me ~~F~ ~#~6
~~ 19 {1988), ~3.
6. Oas~i~b, Joseph. awe ~~1islical precision of ~mcdica1 mania p~codu~=s: AD
Elision ~ Yaps acid AIDS a~nli~i~ last day.- Ifs) ~^ 2 ( 1987~.
213-27~
at.
:<
-aid
137
. In, Ma; ~~> ~~ Ha, Jag. ^r /
~~. Pro a, a: he ~~, Pubes ~1986.
S. an, LV all. ~~ ~~ ~ ~ ~ ~ I
~~ ~~ /~ 7~7- ~ ~ ^~ ~ ~ ~~=
~ ~ 7~ anal, a: gab ~ /, 1986
9. ma, Ha. gad =~d Aria he ~ anion of in~.-
~7 ~~ art afar I, 83 ( 1 98S), 92~9-~0.
10. ~~ go, Jan ~ as Ann ~ ^~ go ~~> C^: he War
~ 19~.
11. Aft, Jug; ~~ fin; -^ Jag ~ ~ ~~ #~-
~ ~~ ~lo, ~ ~~ Seymour Page 19~87~.
12. H^~:i=1 ~~ aeon a. ~ ~ ~~ ~~: ~ ^
~ ~~ ^~r I Riot ~ Munch. _~n, a:
Agony ^ Pa, 1990.
13~ , D^id ad age, G. ~~
