isds chapter 2 outline - updated 0810

8/16/2019 ISDS Chapter 2 Outline - Updated 0810

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ii. Chapter 2: Presenting Data in Tables and

Charts

Objectives:

1. Understand that the variable type

determines the analysis approach.

2. Recognie i! a variable is categorical or

n"meric.

#. recognie i! a n"meric variable is discrete

or contin"o"s.$. Recognie %hich s"mmaries are "sed !or

n"meric data or !or categorical data.

&. Constr"ct a !re'"ency table( bar graph and

pie chart !or '"alitative data.

). Convert ra% data into a data array.*. Constr"ct !re'"ency table( relative and

c"m"lative !re'"ency tables( and histogram

!or '"antitative data.

+. Constr"ct a stem,and,lea! display to represent

'"antitative data.


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-. Types o! ariables / in order to address

statistical '"estions( one m"st 0RT be

able to identi!y types o! variables. ee

page 1 o! te3t 4be!ore the Title Page5 !or

the Roadmap.

The T6O types o! variables are:

1. Categorical ariables 4also 7no%n as

8"alitative5 / have val"es that can

be placed into categories 49es ;o<

0roph=rr< RepDemndep<

De!ective;ot De!ective5.

2. ;"meric ariables 4also 7no%n as

8"antitative5 / yield val"es that

represent '"antities 4%eight( salary(

ret"rn,on,investment( >P-( ? o!

children5.

a. Discrete / res"lt o! co"nting

b. Contin"o"s / meas"rementscan ta7e on in!initely many val"es

%ithin an interval


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@3ample: Ta7en !rom an @3cel

spreadsheet containing data collected

!rom the 0all 2AA) D 2AAA Co"rse

"rvey

AGE* GENDER CLASSIFCREDITHOURS*

INTERNETUSAGE SKIP CLASS

HRSWORK*

BUYONLINE GPA*

19 F JR 67 VERY OFTEN VERY RARELY 20 YES 323

20 F JR 61 VERY OFTEN VERY RARELY 17 YES 3!1

19 F SO 36 SO"EWHAT OFTEN NEVER 0 YES 2#$

19 " SO 30 VERY OFTEN VERY RARELY 20 YES 39#

19 " SO !2 VERY OFTEN NEVER 1$ YES 367

20 " SO $6 VERY OFTEN NEVER 20 YES 329

19 F SO 3! VERY OFTEN OCCASIONALLY 12 YES 336

19 F SR 11$ VERY OFTEN VERY RARELY 1! YES 292

;ote : Col"mns represent variables 4'"estions as7ed on the s"rvey5< Ro%s

represent the observations 4st"dents5< B '"antitative data 4all other

variables are '"alitative5< >P- contin"o"s n"meric data

. Data Collection / 6hen addressing

b"siness '"estion( yo" m"st collect dataon the variable4s5 o! interest.

1. Data !all into t%o categories:

a. Primary o"rce

b. econdary o"rce


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2. Data so"rces are created in one o!

!o"r %ays:

a. data distrib"ted by an

organiation or individ"al<

4internet( databases o! private and

government organiations(

ind"stry jo"rnals( etc.5

b. cond"cting and reporting the

res"lts o! a designed e3periment

4e3ample: a st"dy is designed to

see i! sales increase %hen a

company implements an

advertising slogan5

c. responses !rom a s"rvey 4o"r class

s"rvey5

d. cond"cting an observational st"dy

4!oc"s gro"ps cond"cted by

mar7et researchers to elicitc"stomer pre!erences5


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C. Organiing Categorical Data 42.#5

1. ntrod"ction: Data are "s"ally

collected( entered( and saved into

some !orm o! database. n this !orm(

trends and characteristics are not

easily detectable as there can

sometimes be millions o! pieces o!

data. 6e %ant to s"mmariered"ce

the data to a !orm %hich is more

easily interpreted and %hich %ill aid

in decision,ma7ing.

Eany s"mmaries are !o"nd in

ne%spapers( magaines( internet(

ann"al reports( and research st"dies<

there!ore( it is important !or yo" to

"nderstand ho% these s"mmaries are

constr"cted.

2. "mmary Table , a tab"lar s"mmary o!

a data sho%ing the !re'"ency 4orpercent5 o! items in each o! several

distinct categories.


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@3ample: recorded the n"mber o!

st"dents in each o! the !ollo%ing

academic majors and %anted to

s"mmarie:"AJOR

ACCT

ISDS

PBAD"

ISDS

FIN

PBAD"

PBAD"

ISDS

ISDS

PBAD""KT

"KT

PBAD"

PBAD"

FIN

PBAD"

ACCT

ISDS

PBAD"

ISDS

PBAD"

ISDSPBAD"

PBAD"

"KT

"AJOR FRE% RELATIVE FRE% &'()+,

ISDS 2! 02$3 &2$3,

FIN 9 009$ &9$, "KT 1$ 01$# &1$#,

ACCT 7 007! &7!,

PBAD" !0 0!21 &!21,

TOTAL 9$ 1001* &1001,


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D. is"aliing Categorical Data 42.&5

1. ar >raph / graphical representation

o! data %here each category is

depicted by a bar representing the

!re'"ency or proportion o!

observations !alling into a category.

4;ote: bars do not to"ch5

24

9

15

7

40

0

5

10

15

20

25

30

35

40

45

ISDS FIN MKT ACCT PBADM

ACADE"IC "AJORS

ISDS 2000 - FALL 2001


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(Example from Course Survey)

2. Pie Chart / a graphical

representation o! data %here slices

o! the pie( represented by degrees(

are associated %ith the !re'"encyor proportion o! observations

!alling into a category.


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ISDS 2000 - FALL 2001

ACADE"IC "AJORS

25%

9%

16%7%

43%ISDS

FIN

MKT

ACCT

PBADM

#. Pareto Chart / chart %here verticalbars are plotted in descending order(

combined %ith a c"m"lative

percentage line

The Pareto Principle states that a

majority o! responses e3ist %ithin asmall n"mber o! categoriesgro"ps.


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Concl"sion: +*F o! st"dents have some

agreement %ith the statement that salary

potential matters %hen selecting a major.

@. Organiing ;"merical Data 4ect 2.$5

1. Ordered -rray , a se'"ence o! ra%

data in ran7 order !rom the smallest

to the largest observation.

@3ample: "ppose yo" are provided%ith a data set containing the time in

days re'"ired to complete year,end

a"dits !or a sample o! 2A clients o! a

partic"lar acco"nting !irm:


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9ear,@nd -"dit Time 4days5

12 1$ 1G 1+

1& 1& 1+ 1*

2A 2* 22 2#

22 21 ## 2+

1$ 1+ 1) 1#

Data -rray: 12 1# 1$ 1$ 1& 1& 1) 1* 1+

1+ 1+ 1G 2A 21 22 22 2# 2* 2+ ##

4;ote: yo" can see min12( ma3##(

range21( 1+ occ"rs most o!tenH5

2. 0re'"ency Distrib"tion / sometimes

%e may pre!er to arrange data into

categories or class gro"ps so that

interpretation is more manageable<

ho%ever( the original observations are

lost in the gro"ping process.

- Frequency Distribution is a

s"mmary table o! data sho%ing

the n"mber o! observations in each

o! the de!ined n"merically,ordered

categories 4or classes5.

Creating a 0re'"ency Distrib"tion:


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a. elect ;"mber o! Classes / "s"ally

& to 1& classes. 4Iarger data sets

re'"ire more classes( smaller data

sets re'"ire less classes< this is a

very s"bjective decision / sho"ld

try to avoid the panca7e 4%ide!lat5

and s7yscraper 4tallthin5 e!!ect5

4n this e3ample( letJs "se & classes

!or s"mmariing5

b. 6idth o! Class 4appro35

2.45

1233=

−

==

asses NumberOfCl

RangeWidth

6e %ill ro"nd "p to & as that val"e

is commonly "sed and is easily

read. 4;ote: each category has the

same %idth5

c. Class Iimits / the bo"ndaries !or

each class< These are very


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subjective( m"st be de!ined so that

all observations are incl"ded.

4;ote: %e m"st incl"de the

smallest val"e< ho%ever( instead

o! "sing 12 to begin the class

de!initions( %e begin %ith 1A in

order to !acilitate the ease in

interpretation5

Frequency Di!ri"u!i#n

$#r Au%i! Ti&e D'!'

Au%i! Ti&e (D'y) Frequency

10 * un%er 15 4

15 * un%er 20 +

20 * un%er 25 5

25 * un%er 30 2

30 * un%er 35 1

20


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d. Class Eidpoint/hal!%ay point

bet%een the class bo"ndaries.

#. Relative 0re'"ency Distrib"tion / a

tab"lar s"mmary o! a set o! data

sho%ing the proportion o!

observations in each o! the de!ined

categories.

Relative 0re'"ency nFrequency

,e-'!i.e Frequency Di!ri"u!i#n

Au%i! Ti&e D'!'

Au%i!Ti&e

(D'y)

,e-'!i.eFrequency(Pr#/#r!i#n)

10 * un%er 15 020

15 * un%er 20 040

20 * un%er 25 025

25 * un%er 30 010

30 * un%er 35 005

100


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4Use!"l %hen comparing di!!erent

data sets o! di!!erent sies5

$. C"m"lative Distrib"tion / a tab"lar

s"mmary o! a set o! data that

acc"m"lates in!ormation !rom class to

class. This type o! tab"lar s"mmary

can be constr"cted !rom !re'"ency

and relative !re'"ency distrib"tions.

Cu&u-'!i.e Di!ri"u!i#n * Au%i! Ti&e D'!'

Au%i! Ti&e(D'y)

Cu&u-'!i.eFrequency

Cu&u-'!i.e,e-'!i.eFrequency

n%er 15 4 020

n%er 20 12 060

n%er 25 17 0+5 n%er 30 19 095

n%er 35 20 100


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0. is"aliing ;"meric Data 42.)5

1. tem,and,Iea! Display / separates

data into stems 4leading digits5 and

leaves 4or trailing digits5.

a. Right,most digits are leaves(

remaining n"mbers are stems.

-"dit Data @3ample: 12 1# 1$ 1$

1& 1& 1) 1* 1+ 1+ 1+ 1G 2A 21

22 22 2# 2* 2+ ##

1 2#$$&&)*+++G

2 A122#*+# #

b. Characteristics o! tem,and,Iea!


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415 most e!!ective !or relatively

small data sets

425 can "se to determine

minim"m( ma3im"m( range(

mode

4#5 gives an idea o! ho% the

individ"al val"es are

distrib"ted across the range o!

the data

4$5 Retains all data , each

observation remains distinctly

identi!iable

2. Kistogram / a vertical bar chart in

%hich the rectang"lar bars are

constr"cted at the bo"ndaries o! each

class.

a. Koriontal -3is / represents theval"es o! the random variable 4in

this case( the time o! a"dit in days5


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b. ertical -3is / represents

!re'"encies or proportions< the

height o! the bar represents the

'"antity o! the random variable

!or that partic"lar class5

H./)34

0

2

4

6

+

10

5 ( A8. D:/

F ) * + 8 *

; < :

4;ote: this histogram ill"strates skewed data5

#. 0re'"ency Polygon: 0ormed by

connecting midpoints o! each class.

10 15 20 25 30 35


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H./)34

0

2

4

6

+

10

5 6 7 ( A89. D3:/

F ) * + 8 * ; < :

isds chapter 2 outline - updated 0810

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