Lesson 13 -Descriptive Statistics

7/21/2019 Lesson 13 -Descriptive Statistics

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2003 Thomson/South-Western 2003 Thomson/South-Western

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

%&ample: udson (uto epair%&ample: 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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7 2003 Thomson/South-Western 2003 Thomson/South-Western


uidelines +or Selectin# umber o+ )lassesuidelines +or Selectin# umber o+ )lasses

; ! ? usiness Statistics Lesson 2

all 2010 all 2010


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uidelines +or Selectin# Width o+ )lassesuidelines +or Selectin# Width o+ )lasses

;


7/40 5 2003 Thomson/South-Western 2003 Thomson/South-Western



=+ ,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





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





=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



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.




Dot lotDot lot

.. .. . . .

7070 8080 5050 6060 4040 100100

. . . ..... .......... .. . .. . . ... . . . .. .. .. .. .

)ost ACB



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'..



%&ample: udson (uto epair%&ample: 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



)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.




)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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( ositive elationship( ositive elationship

xx

yy


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( e#ative elationship( e#ative elationship

xx

yy


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o (pparent elationshipo (pparent elationship

xx

yy


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%&ample: anthers ootball Team%&ample: anthers ootball Team


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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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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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


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' 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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%&ample: !arada =nn%&ample: !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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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



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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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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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>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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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.



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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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%&ample: in#er Laes omes%&ample: in#er Laes omes


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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=nsi#hts ained +rom the recedin#=nsi#hts ained +rom the recedin#


;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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o, ercenta#eso, ercenta#es


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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)olumn ercenta#es)olumn ercenta#es


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

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Lesson 13 -Descriptive Statistics