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Lesson 2Lesson 2
Descriptive Statistics:Descriptive Statistics:
Tabular and raphical !ethodsTabular and raphical !ethods
Summari"in# $uantitative DataSummari"in# $uantitative Data
Summari"in# $ualitative DataSummari"in# $ualitative Data
%&plorator' Data (nal'sis%&plorator' Data (nal'sis
)rosstabulations)rosstabulationsand Scatter Dia#ramsand Scatter Dia#rams
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%&plorator' Data (nal'sis%&plorator' Data (nal'sis
The techni*ues o+The techni*ues o+ e&plorator' data anal'sise
&plorator' data anal'sisconsist o+ simple arithmetic and eas'-to-dra,consist o+ simple arithmetic and eas'-to-dra,
pictures that can be used to summari"e datapictures that can be used to summari"e data
*uicl'.*uicl'.
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Summari"in# $uantitative DataSummari"in# $uantitative Data
re*uenc' Distributionre*uenc' Distribution
elative re*uenc' and ercent re*uenc'elative re*uenc' and ercent re*uenc'
DistributionsDistributions
Dot lotDot lot
isto#ramisto#ram )umulative Distributions)umulative Distributions
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41 56 43 75 57 72 44 60 45 82
51 84 52 64 88 57 54 57 52 58
10 5 82 86 45 107 55 87 60 104
67 45 66 86 63 86 51 84 85 5
82 62 46 101 54 107 54 84 82 53
41 56 43 75 57 72 44 60 45 82
51 84 52 64 88 57 54 57 52 58
10 5 82 86 45 107 55 87 60 104
67 45 66 86 63 86 51 84 85 5
82 62 46 101 54 107 54 84 82 53
%&le: udson (uto epair%&le: udson (uto epair
The mana#er o+ udson (uto ,ould lie to #etThe mana#er o+ udson (uto ,ould lie to #et
aa
better picture o+ the distribution o+ costs +orbetter picture o+ the distribution o+ costs +or
en#ineen#ine
tune-up parts. ( sample o+ 70 customer invoicestune-up parts. ( sample o+ 70 customer invoices
hashas
been taen and the costs o+ parts9 rounded tobeen taen and the costs o+ parts9 rounded to
thethe
nearest dollar9 are listed belo,.nearest dollar9 are listed belo,.
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re*uenc' Distributionre*uenc' Distribution
uidelines +or Selectin# umber o+ )lassesuidelines +or Selectin# umber o+ )lasses
; ! ? usiness Statistics Lesson 2
all 2010 all 2010
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re*uenc' Distributionre*uenc' Distribution
uidelines +or Selectin# Width o+ )lassesuidelines +or Selectin# Width o+ )lasses
;
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%&le: udson (uto epair%&le: udson (uto epair
re*uenc' Distributionre*uenc' Distribution
=+ ,e choose si& classes:=+ ,e choose si& classes:
(ppro&imate )lass Width @ A104 - 72B/8 @ 4.7(ppro&imate )lass Width @ A104 - 72B/8 @ 4.7
1010
)ost ACB)ost ACB re*uenc're*uenc' 70-7470-74 2 2
80-8480-84 13 13
50-5450-54 18 18
60-6460-64 5 5
40-4440-44 5 5
100-104100-104 77
Total 70Total 70
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elative re*uenc' and ercent re*uenc'elative re*uenc' and ercent re*uenc'
DistributionsDistributions
elative ercentelative ercent
)ost ACB)ost ACB re*uenc're*uenc' re*uenc're*uenc'
70-7470-74 .0.0
80-8480-84 .28.28 2828
50-5450-54 .32.32 3232
60-6460-64 .1.1 11
40-4440-44 .1.1 11
100-104100-104 .10.10 1010
Total 1.00Total 1.00 100 100
%&le: udson (uto epair%&le: udson (uto epair
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%&le: udson (uto epair%&le: udson (uto epair
=nsi#hts ained +rom the ercent re*uenc'=nsi#hts ained +rom the ercent re*uenc'
DistributionDistribution
; nl' E o+ the parts costs are in the C70-74nl' E o+ the parts costs are in the C70-74class.class.
; 30E o+ the parts costs are under C50.30E o+ the parts costs are under C50.;The #reatest percenta#e A32E or almostThe #reatest percenta#e A32E or almost
one-thirdB o+ the parts costs are in the C50-one-thirdB o+ the parts costs are in the C50-
54 class.54 class.
; 10E o+ the parts costs are C100 or more.10E o+ the parts costs are C100 or more.
=>! ? usiness Statistics Lesson 2=>! ? usiness Statistics Lesson 2
all 2010 all 2010
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Dot lotDot lot
ne o+ the simplest #raphical summaries o+ne o+ the simplest #raphical summaries o+
data is adata is a dot plotdot plot..
( hori"ontal a&is sho,s the ran#e o+ data( hori"ontal a&is sho,s the ran#e o+ data
values.values.
Then each data value is represented b' a dotThen each data value is represented b' a dot
placed above the a&is.placed above the a&is.
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%&le: udson (uto epair%&le: udson (uto epair
Dot lotDot lot
.. .. . . .
7070 8080 5050 6060 4040 100100
. . . ..... .......... .. . .. . . ... . . . .. .. .. .. .
)ost ACB
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isto#ramisto#ram
(nother common #raphical presentation o+(nother common #raphical presentation o+
*uantitative data is a*uantitative data is a histo#ramhisto#ram..
The variable o+ interest is placed on theThe variable o+ interest is placed on the
hori"ontal a&is.hori"ontal a&is.
( rectan#le is dra,n above each class interval( rectan#le is dra,n above each class interval
,ith its hei#ht correspondin# to the intervalFs,ith its hei#ht correspondin# to the intervalFs
+re*uenc'+re*uenc'99 relative +re*uenc'relative +re*uenc'9 or9 or percentpercent
+re*uenc'+re*uenc'..
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%&le: udson (uto epair%&le: udson (uto epair isto#ramisto#ram
arts)ost ACB
2
8
6
10
12
1
18
16
/re*uenc'
70 80 50 60 40 100 110
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)umulative Distributions)umulative Distributions
)umulative +re*uenc' distribution)umulative +re*uenc' distribution-- sho,s the-- sho,s the
number o+ items ,ith values less than or e*ualnumber o+ items ,ith values less than or e*ualto the upper limit o+ each class.to the upper limit o+ each class.
)umulative relative +re*uenc' distribution)umulative relative +re*uenc' distribution----
sho,s the proportion o+ items ,ith values lesssho,s the proportion o+ items ,ith values less
than or e*ual to the upper limit o+ each class.than or e*ual to the upper limit o+ each class. )umulative percent +re*uenc' distribution)umulative percent +re*uenc' distribution----
sho,s the percenta#e o+ items ,ith values lesssho,s the percenta#e o+ items ,ith values less
than or e*ual to the upper limit o+ each class.than or e*ual to the upper limit o+ each class.
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%&le: udson (uto epair%&le: udson (uto epair
)umulative Distributions)umulative Distributions
)umulative )umulative)umulative )umulative
)umulative elative ercent)umulative elative ercent
)ost ACB)ost ACB re*uenc're*uenc' re*uenc're*uenc're*uenc're*uenc'
HH7474 2 2 .0 .0
HH8484 17 17 .30 .30 30 30
HH5454 31 31 .82 .82 82 82
HH6464 36 36 .58 .58 58 58 HH4444 7 7 .40 .40 40 40
HH104104 70 70 1.00 1.00 100 100
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Scatter Dia#ramScatter Dia#ram
( scatter dia#ram is a #raphical presentation( scatter dia#ram is a #raphical presentation
o+ the relationship bet,een t,oo+ the relationship bet,een t,o *uantitative*uantitativevariables.variables.
ne variable is sho,n on the hori"ontal a&isne variable is sho,n on the hori"ontal a&is
and the other variable is sho,n on the verticaland the other variable is sho,n on the vertical
a&is.a&is. The #eneral pattern o+ the plotted pointsThe #eneral pattern o+ the plotted points
su##ests the overall relationship bet,een thesu##ests the overall relationship bet,een the
variables.variables.
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Scatter Dia#ramScatter Dia#ram
( ositive elationship( ositive elationship
xx
yy
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Scatter Dia#ramScatter Dia#ram
( e#ative elationship( e#ative elationship
xx
yy
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Scatter Dia#ramScatter Dia#ram
o (pparent elationshipo (pparent elationship
xx
yy
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%&le: anthers ootball Team%&le: anthers ootball Team
Scatter Dia#ramScatter Dia#ram
The anthers +ootball team is interested inThe anthers +ootball team is interested in
investi#atin# the relationship9 i+ an'9 bet,eeninvesti#atin# the relationship9 i+ an'9 bet,een
interceptions made and points scored.interceptions made and points scored.
xx@ umber o+@ umber o+ yy@ umber o+@ umber o+ =nterceptions=nterceptions oints Scoredoints Scored
11 1 1
33 2 2
22 16 16 11 15 15
33 25 25
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%&le: anthers ootball Team%&le: anthers ootball Team
Scatter Dia#ramScatter Dia#ram
yy
xx
umber o+ =nterceptionsumber o+ =nterceptions11 22 33
:um
bero+1ointsScored
:um
bero+1ointsScored
00
77
1010
1717
2020
2727
3030
00
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%&le: anthers ootball Team%&le: anthers ootball Team
The precedin# scatter dia#ram indicates aThe precedin# scatter dia#ram indicates a
positive relationship bet,een the number o+positive relationship bet,een the number o+interceptions and the number o+ points scored.interceptions and the number o+ points scored.
i#her points scored are associated ,ith ai#her points scored are associated ,ith a
hi#her number o+ interceptions.hi#her number o+ interceptions.
The relationship is not per+ectI all plottedThe relationship is not per+ectI all plottedpoints in the scatter dia#ram are not on apoints in the scatter dia#ram are not on a
strai#ht line.strai#ht line.
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Summari"in# $ualitative DataSummari"in# $ualitative Data
re*uenc' Distributionre*uenc' Distribution
elative re*uenc'elative re*uenc'
ercent re*uenc' Distributionercent re*uenc' Distribution
>ar raph>ar raph
ie )hartie )hart
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re*uenc' Distributionre*uenc' Distribution
(( +re*uenc' distribution+re*uenc' distributionis a tabular summar'is a tabular summar'
o+ data sho,in# the +re*uenc' Aor numberB o+o+ data sho,in# the +re*uenc' Aor numberB o+items in each o+ several nonoverlappin#items in each o+ several nonoverlappin#
classes.classes.
The obGective is toThe obGective is to provide insi#htsprovide insi#htsabout theabout the
data that cannot be *uicl' obtained b'data that cannot be *uicl' obtained b'looin# onl' at the ori#inal data.looin# onl' at the ori#inal data.
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%&le: !arada =nn%&le: !arada =nn
uests sta'in# at !arada =nn ,ere ased to rate theuests sta'in# at !arada =nn ,ere ased to rate the
*ualit' o+ their accommodations as bein#*ualit' o+ their accommodations as bein# excellentexcellent99above averageabove average99 averageaverage99 below averagebelow average9 or9 orpoorpoor..
TheThe
ratin#s provided b' a sample o+ 20 *uests are sho,nratin#s provided b' a sample o+ 20 *uests are sho,n
belo,.belo,.
>elo, (vera#e (vera#e>elo, (vera#e (vera#e (bove (vera#e(bove (vera#e
(bove (vera#e (bove (vera#e (bove (vera#e(bove (vera#e (bove (vera#e (bove (vera#e(bove (vera#e >elo, (vera#e(bove (vera#e >elo, (vera#e >elo,>elo,
(vera#e (vera#e oor(vera#e (vera#e oor ooroor(bove (vera#e %&cellent(bove (vera#e %&cellent (bove (vera#e(bove (vera#e
(vera#e (bove (vera#e(vera#e (bove (vera#e (vera#e(vera#e
(bove (vera#e (vera#e(bove (vera#e (vera#e
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re*uenc' Distributionre*uenc' Distribution
atin#atin# re*uenc're*uenc'
ooroor 2 2
>elo, (vera#e>elo, (vera#e 3 3
(vera#e(vera#e 7 7
(bove (vera#e(bove (vera#e 4 4
%&cellent%&cellent 1 1
TotalTotal 20 20
%&le: !arada =nn%&le: !arada =nn
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elative re*uenc' Distributionelative re*uenc' Distribution
TheThe relative +re*uenc'relative +re*uenc'o+ a class is the +ractiono+ a class is the +raction
or proportion o+ the total number o+ data itemsor proportion o+ the total number o+ data itemsbelon#in# to the class.belon#in# to the class.
(( relative +re*uenc' distributionrelative +re*uenc' distributionis a tabularis a tabular
summar' o+ a set o+ data sho,in# the relativesummar' o+ a set o+ data sho,in# the relative
+re*uenc' +or each class.+re*uenc' +or each class.
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ercent re*uenc' Distributionercent re*uenc' Distribution
TheThe percent +re*uenc'percent +re*uenc'o+ a class is the relativeo+ a class is the relative
+re*uenc' multiplied b' 100.+re*uenc' multiplied b' 100. ((percent +re*uenc' distributionpercent +re*uenc' distributionis a tabularis a tabular
summar' o+ a set o+ data sho,in# the percentsummar' o+ a set o+ data sho,in# the percent
+re*uenc' +or each class.+re*uenc' +or each class.
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%&le: !arada =nn%&le: !arada =nn
elative re*uenc' and ercent re*uenc'elative re*uenc' and ercent re*uenc'
DistributionsDistributions
elativeelative ercentercent
atin#atin# re*uenc're*uenc' re*uenc're*uenc'
ooroor .10 .10 1010
>elo, (vera#e>elo, (vera#e .17 .17 1717
(vera#e(vera#e .27 .27 2727
(bove (vera#e(bove (vera#e .7 .7 77
%&cellent%&cellent .07 .07 77
TotalTotal 1.00 1.00 100 100
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>ar raph>ar raph
(( bar #raphbar #raphis a #raphical device +or depictin#is a #raphical device +or depictin#
*ualitative data.*ualitative data. n the hori"ontal a&is ,e speci+' the labelsn the hori"ontal a&is ,e speci+' the labels
that are used +or each o+ the classes.that are used +or each o+ the classes.
(( +re*uenc'+re*uenc'99 relative +re*uenc'relative +re*uenc'9 or9 or percentpercent
+re*uenc'+re*uenc'scale can be used +or the verticalscale can be used +or the verticala&is.a&is.
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%&le: !arada =nn%&le: !arada =nn
>ar raph>ar raph
12
3
7
8
5
6
4
oor >elo,(vera#e
(vera#e(bove(vera#e
%&cellent
Frequ
ency
Rating
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ie )hartie )hart
TheThe pie chartpie chartis a commonl' used #raphicalis a commonl' used #raphical
device +or presentin# relative +re*uenc'device +or presentin# relative +re*uenc'distributions +or *ualitative data.distributions +or *ualitative data.
irst dra, airst dra, a circlecircleI then use the relativeI then use the relative
+re*uencies to subdivide the circle into sectors+re*uencies to subdivide the circle into sectors
that correspond to the relative +re*uenc' +orthat correspond to the relative +re*uenc' +oreach class.each class.
Since there are 380 de#rees in a circle9 a classSince there are 380 de#rees in a circle9 a class
,ith a relative +re*uenc' o+ .27 ,ould consume,ith a relative +re*uenc' o+ .27 ,ould consume
.27A380B @.27A380B @40 de#rees o+ the circle.40 de#rees o+ the circle.
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%&le: !arada =nn%&le: !arada =nn
ie )hartie )hart
(vera#e 27E
>elo,(vera#e
17E
oor10E
(bove
(vera#e 7E
%&c.7E
$ualit' atin#s
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=nsi#hts ained +rom the recedin# ie )hart=nsi#hts ained +rom the recedin# ie )hart
; ne-hal+ o+ the customers surve'ed #avene-hal+ o+ the customers surve'ed #ave!arada a *ualit' ratin# o+ Kabove avera#e!arada a *ualit' ratin# o+ Kabove avera#e
or Ke&cellent Alooin# at the le+t side o+ theor Ke&cellent Alooin# at the le+t side o+ the
pieB. This mi#ht please the mana#er.pieB. This mi#ht please the mana#er.
; oror eacheachcustomer ,ho #ave an Ke&cellentcustomer ,ho #ave an Ke&cellentratin#9 there ,ereratin#9 there ,ere t,ot,ocustomers ,ho #avecustomers ,ho #ave
a Kpoor ratin# Alooin# at the top o+ thea Kpoor ratin# Alooin# at the top o+ the
pieB. This should displease the mana#er.pieB. This should displease the mana#er.
%&le: !arada =nn%&le: !arada =nn
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)rosstabulation)rosstabulation
)rosstabulation)rosstabulationis a tabular method +oris a tabular method +or
summari"in# the data +or t,o variablessummari"in# the data +or t,o variablessimultaneousl'.simultaneousl'.
)rosstabulation can be used ,hen:)rosstabulation can be used ,hen:
; ne variable is *ualitative and the other isne variable is *ualitative and the other is*uantitative*uantitative
; >oth variables are *ualitative>oth variables are *ualitative; >oth variables are *uantitative>oth variables are *uantitative
The le+t and top mar#in labels deJne theThe le+t and top mar#in labels deJne the
classes +or the t,o variables.classes +or the t,o variables.
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%&le: in#er Laes omes%&le: in#er Laes omes
)rosstabulation)rosstabulation
The number o+ in#er Laes homes sold +or eachThe number o+ in#er Laes homes sold +or eachst'le and price +or the past t,o 'ears is sho,n belo,.st'le and price +or the past t,o 'ears is sho,n belo,.
ricerice ome St'leome St'le
an#ean#e )olonial anch Split (-rame Total)olonial anch Split (-rame Total
HHC449000 16C449000 16 8 14 12 8 14 12
7777
M C449000 12 1 18 3M C449000 12 1 18 3 77
TotalTotal 3030 20 37 1720 37 17
100100
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%&le: in#er Laes omes%&le: in#er Laes omes
=nsi#hts ained +rom the recedin#=nsi#hts ained +rom the recedin#
)rosstabulation)rosstabulation
;The #reatest number o+ homes in theThe #reatest number o+ homes in thesample A14B are a split-level st'le and pricedsample A14B are a split-level st'le and priced
at less than or e*ual to C449000.at less than or e*ual to C449000.
; nl' three homes in the sample are an (-nl' three homes in the sample are an (-rame st'le and priced at more thanrame st'le and priced at more than
C449000.C449000.
)rosstabulation: o, or )olumn)rosstabulation: o, or )olumn
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)rosstabulation: o, or )olumn)rosstabulation: o, or )olumn
ercenta#esercenta#es
)onvertin# the entries in the table into ro,)onvertin# the entries in the table into ro,
percenta#es or column percenta#es canpercenta#es or column percenta#es canprovide additional insi#ht about theprovide additional insi#ht about the
relationship bet,een the t,o variables.relationship bet,een the t,o variables.
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%&le: in#er Laes omes%&le: in#er Laes omes
o, ercenta#eso, ercenta#es
ricerice ome St'leome St'le
an#ean#e )olonial anch Split (-rame)olonial anch Split (-rame
TotalTotal
HHC449000 32.53C449000 32.53 10.41 3.7710.41 3.77
21.6221.62 100 100
M C449000 28.85 31.11 37.78 8.85M C449000 28.85 31.11 37.78 8.85
100 100
ote: ro, totals are actuall' 100.01 due to roundin#.ote: ro, totals are actuall' 100.01 due to roundin#.
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%&le: in#er Laes omes%&le: in#er Laes omes
)olumn ercenta#es)olumn ercenta#es
ricerice ome St'leome St'le
an#ean#e )olonial anch Split (-rame)olonial anch Split (-rame
HHC449000 80.00C449000 80.00 30.00 7.2430.00 7.2460.0060.00
M C449000 0.00M C449000 0.00 50.00 7.5150.00 7.51
20.0020.00
TotalTotal 100 100 100 100100 100
100100