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8/16/2019 ISDS Chapter 2 Outline - Updated 0810
1/19
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.$. Recognie %hich s"mmaries are "sed !or
n"meric data or !or categorical data.
&. Constr"ct a !re'"ency table( bar graph and
pie chart !or '"alitative data.
). Convert ra% data into a data array.*. Constr"ct !re'"ency table( relative and
c"m"lative !re'"ency tables( and histogram
!or '"antitative data.
+. Constr"ct a stem,and,lea! display to represent
'"antitative data.
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
2/19
-. Types o! ariables / in order to address
statistical '"estions( one m"st 0RT be
able to identi!y types o! variables. ee
page 1 o! te3t 4be!ore the Title Page5 !or
the Roadmap.
The T6O types o! variables are:
1. Categorical ariables 4also 7no%n as
8"alitative5 / have val"es that can
be placed into categories 49es ;o<
0roph=rr< RepDemndep<
De!ective;ot De!ective5.
2. ;"meric ariables 4also 7no%n as
8"antitative5 / yield val"es that
represent '"antities 4%eight( salary(
ret"rn,on,investment( >P-( ? o!
children5.
a. Discrete / res"lt o! co"nting
b. Contin"o"s / meas"rementscan ta7e on in!initely many val"es
%ithin an interval
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
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@3ample: Ta7en !rom an @3cel
spreadsheet containing data collected
!rom the 0all 2AA) D 2AAA Co"rse
"rvey
AGE* GENDER CLASSIFCREDITHOURS*
INTERNETUSAGE SKIP CLASS
HRSWORK*
BUYONLINE GPA*
19 F JR 67 VERY OFTEN VERY RARELY 20 YES 323
20 F JR 61 VERY OFTEN VERY RARELY 17 YES 3!1
19 F SO 36 SO"EWHAT OFTEN NEVER 0 YES 2#$
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
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
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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
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
5/19
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.
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
6/19
@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,
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
7/19
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
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
8/19
(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.
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
9/19
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.
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
10/19
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.$5
1. Ordered -rray , a se'"ence o! ra%
data in ran7 order !rom the smallest
to the largest observation.
@3ample: "ppose yo" are provided%ith a data set containing the time in
days re'"ired to complete year,end
a"dits !or a sample o! 2A clients o! a
partic"lar acco"nting !irm:
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
11/19
9ear,@nd -"dit Time 4days5
12 1$ 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:
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
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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
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
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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
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
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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
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
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4Use!"l %hen comparing di!!erent
data sets o! di!!erent sies5
$. C"m"lative Distrib"tion / a tab"lar
s"mmary o! a set o! data that
acc"m"lates in!ormation !rom class to
class. This type o! tab"lar s"mmary
can be constr"cted !rom !re'"ency
and relative !re'"ency distrib"tions.
Cu&u-'!i.e Di!ri"u!i#n * Au%i! Ti&e D'!'
Au%i! Ti&e(D'y)
Cu&u-'!i.eFrequency
Cu&u-'!i.e,e-'!i.eFrequency
n%er 15 4 020
n%er 20 12 060
n%er 25 17 0+5 n%er 30 19 095
n%er 35 20 100
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
16/19
0. is"aliing ;"meric Data 42.)5
1. tem,and,Iea! Display / separates
data into stems 4leading digits5 and
leaves 4or trailing digits5.
a. Right,most digits are leaves(
remaining n"mbers are stems.
-"dit Data @3ample: 12 1# 1$ 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!
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
17/19
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
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
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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
8/16/2019 ISDS Chapter 2 Outline - Updated 0810
19/19
H./)34
0
2
4
6
+
10
5 6 7 ( A89. D3:/
F ) * + 8 * ; < :
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