Chap002-JK- Tabular & Graphical Metd

7/23/2019 Chap002-JK- Tabular & Graphical Metd

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Business Statistics: Communicating with Numbers

By Sanjiv Jaggia and Alison Kelly

McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies Inc! "ll rights reser#e$ .



2-2

Chapter 2 LearningObjectives (LOs)

LO 2.1: Summarize qualitative data y !orming!requency distriutions.LO 2.2: "onstruct and inter#ret #ie c$arts and ar

c$arts.

LO 2.%: Summarize quantitative data y !orming!requency distriutions.

LO 2.&: "onstruct and inter#ret $istograms' #olygons'and ogives.

LO 2.(: "onstruct and inter#ret a stem)and)lea!diagram.

LO 2.*: "onstruct and inter#ret a scatter#lot.



2-3

A relocation s#ecialist !or a real estate !irm in+ission ,iejo' "A gat$ers recent $ouse salesdata !or a client !rom Seattle' -A.

$e tale elo/ s$o/s t$e sale #rice 0in

1's3 !or %* single)!amily $ouses.

House Prices in SouthernCalifornia



2-4

4se t$e sam#le in!ormation to:

1. Summarize t$e range o! $ouse #rices.

2. "omment on /$ere $ouse #rices tend to cluster.

%. "alculate #ercentages to com#are $ouse #rices.

House Prices in SouthernCalifornia



2-5

2.1 Summariing !ualitative"ata A frequency distribution !or qualitative data

grou#s data into categories and records $o/ manyoservations !all into eac$ category.

-eat$er conditions in Seattle' -A during5eruary 21.

LO 2.1 Summarie #ualitative $ata b% forming

fre#uenc% $istributions.



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Weather FrequencyRelative

Frequency

"loudy 1 16278.%*

9ainy 2 26278.1&

Sunny 6278.2(

otal 27 2762781.

"ategories: Rainy ' Sunny ' or Cloudy . 5or eac$ category;s !requency' count t$e days

t$at !all in t$at category. "alculate relative frequency y dividing eac$

category;s !requency y t$e sam#le size.

Weather Frequency

"loudy 1

9ainy 2

Sunny

otal 27

2.1 Summariing!ualitative "ata

LO2.1


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o e<#ress relative !requencies in terms o!#ercentages' multi#ly eac$ #ro#ortion y 1=.

>ote t$at t$e total o! t$e #ro#ortions must addto 1. and t$e total o! t$e #ercentages must addto 1=.

Weather FrequencyRelative

Frequency

"loudy 1 16278.%*

9ainy 2 26278.1&

Sunny 6278.2(

otal 27 2762781.

Percentage

< 18 %.*=

< 181.&=

< 182(.=

< 181=

2.1 Summariing!ualitative "ata

LO2.1



2.1 Summariing!ualitative "ata A pie chart is a segmented circle /$ose segments

#ortray t$e relative !requencies o! t$e categories o!some qualitative variale. ?n t$is e<am#le'

t$e varialeRegion is#ro#ortionally

divided into& #arts.

LO2.2



2.1 Summariing!ualitative "ata A bar chart de#icts t$e !requency or t$e

relative !requency !or eac$ category o! t$equalitative data as a ar rising vertically !rom

t$e $orizontal a<is. 5or e<am#le' Adidas; salesmay e #ro#ortionallycom#ared !or eac$ 9egion

over t$ese t/o #eriods.

LO2.2



2.2 Summariing !uantitative"ata

A frequency distribution !or quantitative datagrou#s data into intervals called classes' andrecords t$e numer o! oservations t$at !all into

eac$ class. @uidelines /$en constructing !requency

distriution:

"lasses are mutually exclusive. "lasses are exhaustive.

LO 2.& Summarie #uantitative $ata b% forming fre#uenc%

$istributions.



$e numer o! classes usually ranges !rom (to 2.

A##ro<imating t$e class /idt$:

2.2 Summariing!uantitative "ata

LO2.&

Largest value Smallest value

>umer o! classes

−



2.2 Summariing!uantitative "ata $e ra/ data !rom t$e ?ntroductory "ase $as een

converted into a !requency distriution in t$e!ollo/ing tale.

Class (in $1000s) Frequency

% u# to & && u# to ( 11

( u# to * 1&

* u# to (

u# to 7 2otal %*

LO2.&




uestion: -$at is t$e #rice range over t$is time #eriod %' u# to 7'

uestion: Co/ many o! t$e $ouses sold in t$e (' u#to *' range

1& $ouses

Class (in $1000s) Frequency

% u# to & && u# to ( 11

( u# to * 1&

* u# to (

u# to 7 2otal %*

LO2.&



A cuulative frequency distribution s#eci!ies $o/

many oservations !all elo/ t$e u##er limit o! a#articular class.

uestion: Co/ many o! t$e $ouses sold !or less t$an*' 2D $ouses


LO2.&



A relative frequency distribution identi!ies t$e#ro#ortion or !raction o! values t$at !all into eac$class.

A cuulative relative frequency distribution

gives t$e #ro#ortion or !raction o! values t$at !allelo/ t$e u##er limit o! eac$ class.

"lass !requency

"lass relative !requency .otal numer o! oservations=


LO2.&



Cere are t$e relative !requency and t$e cumulativerelative !requency distriutions !or t$e $ouse)#ricedata.

Class (in $1000s) FrequencyRelative

Frequency Cuulative Relative Frequency

% u# to & & &6%* 8 .11 .11

& u# to ( 11 116%* 8 .%1 .11 E .%1 8 .&2

( u# to * 1& 1&6%* 8 .%D .11 E .%1 E .%D 8 .71

* u# to ( (6%* 8 .1& .11 E .%1 E .%D E .1& 8 .D(

u# to 7 2 26%* 8 .* .11 E .%1 E .%D E .1& E .* ≈ 1.

otal %* 1.


LO2.&



4se t$e data on t$e #revious slide to ans/er t$e!ollo/ing t/o questions.

uestion: -$at #ercent o! t$e $ouses sold !or atleast (' ut not more t$an *' %D=

uestion: -$at #ercent o! t$e $ouses sold !orless t$an *' 71=


LO2.&



2.2 Summariing !uantitative"ata

Cistograms

Folygons

Ogives

LO 2.' Construct an$ interpret histograms

pol%gons an$ ogives.



A histogra is a visual re#resentation o! a!requency or a relative !requency distriution.

Bar $eig$t re#resents t$e res#ective class!requency 0or relative !requency3.

Bar /idt$ re#resents t$e class /idt$.


LO2.'



Cere are t$e !requency and relative !requency$istograms !or t$e $ouse)#rice data.

>ote t$at t$e only di!!erence is t$e y )a<is scale.


LO2.'



S$a#e o! Gistriution: ty#ically symmetric orsHe/ed SymmetricImirror image on ot$ sides o! its

center.


LO2.'

Symmetric Gistriution



SHe/ed distriution Fositively sHe/ed ) data!orm a long' narro/ tailto t$e rig$t.

>egatively sHe/ed )data !orm a long'

narro/ tail to t$e le!t.


LO2.'




LO2.'

A polygon is a visual re#resentation o! a!requency or a relative !requency distriution.

Flot t$e class mid#oints on x )a<is andassociated !requency 0or relative!requency3 on y )a<is.

>eig$oring #oints are connected /it$ astraig$t line.



2-24


LO2.'

Cere is a #olygon !or t$e $ouse)#rice data.



2-25


LO2.'

An ogive is a visual re#resentation o! a

cumulative !requency or a cumulativerelative !requency distriution.

Flot t$e cumulative !requency 0or cumulativerelative !requency3 o! eac$ class aove t$eu##er limit o! t$e corres#onding class.

$e neig$oring #oints are t$en connected.



2-26


LO2.'

Cere is an ogive !or t$e $ouse)#rice data.

4se t$e ogive to a##ro<imate t$e #ercentage o!

$ouses t$at sold !or less t$an (('. Ans/er: *=



2-27

2.& Steman$Leaf "iagrams

A ste!and!leaf diagra #rovides a visualdis#lay o! quantitative data.

?t gives an overall #icture o! t$e data;s center andvariaility.

ac$ value o! t$e data set is se#arated into t/o#arts: t$e stem consists o! t$e le!tmost digits'/$ile t$e leaf is t$e last digit.

LO 2.* Construct an$ interpret a steman$

leaf $iagram.



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2.& Steman$Leaf"iagrams $e !ollo/ing data set s$o/s t$e /ealt$iest

#eo#le in t$e /orld and t$eir associated ages. $e le!tmost digit is t$e stem /$ile t$e last digit is

t$e leaf as s$o/n $ere.

LO2.*

Age 8 %*



2-29

2.' Scatterplots

A scatterplot is used to determine i! t/ovariales are related.

LO 2.+ Construct an$ interpret a

scatterplot.

x )a<is

y )a<is

0 x i'y i3 ac$ #oint is a #airing:

0 x 1'y 13' 0 x 2'y 23' etc.

$is scatter#lot s$o/s

income againsteducation.



2-30

2.' Scatterplots

"inear relations$i#: u#/ard or do/n/ard)slo#ing trend o! t$e data.

LO2.+

Fositive linear

relations$i# 0s$o/n$ere3: as x increases' sodoes y .

>egative linearrelations$i#: as x increases' y decreases.



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2.' Scatterplots

"urvilinear relations$i#

LO2.+

As x increases'y increases at an

increasing 0ordecreasing3 rate. As x increases y

decreases' at an

increasing 0ordecreasing3 rate.



2-32

2.' Scatterplots

>o relations$i#: data are randomlyscattered /it$ no discernile #attern.

LO2.+

?n t$is scatter#lot' t$ere

is no a##arentrelations$i# et/een x and y .



S Some ,-celComman$s

LOs 2.1 2.2 an$2.'

Fie c$art or Bar c$art: select t$e relevant

categorical names /it$ res#ective data' t$enc$oose ?nsert Fie 2)G Fie or ?nsert Bar 2)GBar.

Cistogram: select t$e relevant data' and c$ooseGata Gata Analysis Cistogram.

Scatter#lot: select t$e x ) and y )coordinates' c$oose?n#ut Scatter' and select t$e gra#$ at t$e to# le!t.

Chap002-JK- Tabular & Graphical Metd

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