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7/23/2019 Chap 001 COMPLETE �BUSINESS �STATISTICS
http://slidepdf.com/reader/full/chap-001-complete-business-statistics 1/79
Chapter 1Chapter 1Introduction and Descriptive StatisticsIntroduction and Descriptive Statistics
COMPLETE
BUSINESS
STATISTICSbyby
AMIR D. ACZEL AMIR D. ACZEL
&&
JAYAVEL SOUNDERPANDIANJAYAVEL SOUNDERPANDIAN
7th edition.7th edition.
Pre!red byPre!red by L"oyd J!i#in$h% Morehe!d St!teL"oyd J!i#in$h% Morehe!d St!te
Unier#ityUnier#ity
McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. ll rights reser!e".
Chapter 1Chapter 1Introduction and Descriptive StatisticsIntroduction and Descriptive Statistics
7/23/2019 Chap 001 COMPLETE �BUSINESS �STATISTICS
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Using Statistics
Percentiles and Quartiles
Measures of Central Tendency
Measures of Variability
Groued !ata and t"e Histogra#
S$ewness and %urtosis
&elations between t"e Mean and Standard !e'iationMet"ods of !islaying !ata
()loratory !ata *nalysis
Using t"e Co#uter
Introduction and Descriptive StatisticsIntroduction and Descriptive Statistics11'()
7/23/2019 Chap 001 COMPLETE �BUSINESS �STATISTICS
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!istinguis" between +ualitati'e data and +uantitati'e data,
!escribe no#inal ordinal inter'al and ratio scales of#easure#ents,
!escribe t"e difference between oulation and sa#le,
Calculate and interret ercentiles and +uartiles,
()lain #easures of central tendency and "ow to co#utet"e#,
Create different tyes of c"arts t"at describe data sets,
Use ()cel te#lates to co#ute 'arious #easures and createc"arts,
LEARNING OBJECTIVES11
After studying this chapter, you should be able to After studying this chapter, you should be able to::
'(*
7/23/2019 Chap 001 COMPLETE �BUSINESS �STATISTICS
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Statistics is a science t"at "els us #a$e better decisions in
business and econo#ics as well as in ot"er fields,
Statistics teac"es us "ow to su##ari.e analy.e and draw
#eaningful inferences fro# data t"at t"en lead to i#ro'e
decisions,
T"ese decisions t"at we #a$e "el us i#ro'e t"e running
for e)a#le a deart#ent a co#any t"e entire econo#y
etc,
WHAT IS STATISTICSWHAT IS STATISTICS??
'(+
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'('. U#in$ St!ti#ti,# -/o C!te$orie#0
Inferential Statistics Predict and forecast
values of population
parameters Test hypotheses about
values of population
parameters
Make decisions
Descriptive Statistics Collect
Organie
Summarie
Display
!nalye
'(1
7/23/2019 Chap 001 COMPLETE �BUSINESS �STATISTICS
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"ualitative #
Categorical or
$ominal%
&'amples are#Color
(ender
$ationality
"uantitative #
Measurable or
Countable%
&'amples are#Temperatures
Salaries
$umber of pointsscored on a 1))
point e'am
ye# o2 D!t! ( /o ye#'(3
7/23/2019 Chap 001 COMPLETE �BUSINESS �STATISTICS
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$ominal Scale # groups or classes
(ender* color* professional classification* etc+
Ordinal Scale # order matters
,anks -top ten videos* products* etc+.
Interval Scale # difference or distance matters / has
arbitrary ero value+
Temperatures -)0* )C. ,atio Scale # ,atio matters / has a natural ero value+
Salaries* eight* volume* area* length* etc+
S,!"e# o2 Me!#4re5ent'(7
7/23/2019 Chap 001 COMPLETE �BUSINESS �STATISTICS
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! population consists of the set of all
measurements for hich the investigator is
interested+
! sample is a subset of the measurements selected
from the population+
! census is a complete enumeration of every item
in a population+
S!5"e# !nd Po4"!tion#'(6
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Sampling from the population is often done
randomly* such that every possible sample of
e2ual sie -n. ill have an e2ual chance of being
selected+! sample selected in this ay is called a simple
random sample or 3ust a random sample+
! random sample allos chance to determine itselements+
Si5"e R!ndo5 S!5"e'(
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Population -$.Population -$. Sample -Sample -nn..
S!5"e# !nd Po4"!tion#'('8
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Census of a population may be%
Impossible
Impractical Too costly
9hy S!5"e:'(''
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Gi'en any set of nu#erical obser'ations order
t"e# according to #agnitude,
T"e P th percentile in t"e ordered set is t"at 'alue below w"ic" lie P 4 0 # ercent1 of t"e obser'ations
in t"e set,
T"e position of t"e P th ercentile is gi'en by
-n 5 1. P 61)) w"ere n is t"e nu#ber of obser'ations
in t"e set,
'() Per,enti"e# !nd ;4!rti"e#'(')
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The magaine ForbesForbes publishes
annually a list of the orld7s
ealthiest individuals+ 0or* 8))9*the net orth of the 8) richest
individuals* in :billions* is as
follos% -data is given on the ne'tslide.+ !lso* the data has been
sorted in magnitude+
E<!5"e '()'('*
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E<!5"e '() -Contin4ed0 ( =i""ion!ire#
;illions Sorted ;illions<< 1=8> 1=8? 1=81 1=1@ 1@8) 8)
1= 8)1= 8)A8 81A> 8889 8888 8<1= 8??@ 8>88 89
8) <88< <<
<8 ?@ 8) A8 1= A>
'('+
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2ind t"e A)th* =)th and t"e @)th ercentiles of t"isdata set,
To find t"e A)th
ercentile deter#ine t"e data ointin osition -n 5 1. P 61)) B -8) 5 1.-A)61)).B 1)+A+
T"us t"e ercentile is located at t"e 1)+Ath
osition, T"e 1)th obser'ation in t"e ordered set is 88 and
t"e 11th obser'ation is also 88,
E<!5"e '() -Contin4ed0 Per,enti"e#'('1
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T"e A)th percentile will lie "alfway between t"e1)th and 11th 'alues 0w"ic" are bot" 33 in t"is case1
and is t"us 88,
E<!5"e '() -Contin4ed0 Per,enti"e#'('3
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To find the =)th percentile* determine the datapoint in position -n 5 1. P 61)) B -8) 5 1.-=)61)).
B 1>+=+ Thus* the percentile is located at the 1>+=th
position+
The 1>th observation is <8* and the 19th observation is also <<+
The =)th percentile is a point lying )+= of theay from <8 to << and is thus <8+=+
E<!5"e '() -Contin4ed0 Per,enti"e#'('7
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To find the @)th percentile* determine the data point inposition -n 5 1. P 61)) B -8) 5 1.-@)61)). B 1=+@+
Thus* the percentile is located at the 1=+@
th
position+ The 1=th observation is ?@* and the 1@th observation is
also A8+
The @)th percentile is a point lying )+@ of theay from ?@ to A8 and is thus ?@ 5 )+@ -A8 / ?@. B ?@ 5
)+@ < B ?@ 5 8+9 B A1+9+
E<!5"e '() -Contin4ed0 Per,enti"e#'('6
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"uartiles are the percentage points that break donthe ordered data set into 2uarters+
The first 2uartile is the 8Ath percentile+ It is the pointbelo hich lie 16? of the data+
The second 2uartile is the A)th percentile+ It is thepoint belo hich lie 168 of the data+ This is alsocalled the median+
The third 2uartile is the 9Ath percentile+ It is thepoint belo hich lie <6? of the data+
;4!rti"e# > Se,i!" Per,enti"e#'('
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The first 2uartile* "1* -8Ath percentile. is
often called the loer 2uartile+
The second 2uartile* "8* -A)
th
percentile. is often called the median or the middle 2uartile+
The third 2uartile* "<* -9Ath percentile.
is often called the upper 2uartile+ The inter2uartile range is the difference beteen the first and the third
2uartiles+
;4!rti"e# !nd Inter?4!rti"e R!n$e'()8
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Sorted;illions ;illions << 1= 8> 1=8? 1=81 1=
1@ 1@ 8) 8) 1= 8) 1= 8) A8 81 A> 88 89 88 88 8<
1= 8? ?@ 8> 88 89 8) <8 8< << <8 ?@ 8) A8
1= A>
0irst "uartile
Median
Third "uartile
-n51.P61))-n51.P61))
03456137/64487,37
03456174/644864,7
03456197/644867,97
1@ 5 -+8A.-1. B 1@+8A
88 5 -+A.-). B 88
895 -+9A.-A. B <)+9A
"uartiles"uartiles
E<!5"e '(*@ indin$ ;4!rti"e#
Position
'()'
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E<!5"e '(*@ U#in$ the e5"!te'())
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E<!5"e '(* -Contin4ed0@ U#in$ the
e5"!te
This is the loer part of the sameThis is the loer part of the same
template from the previous slide+template from the previous slide+
'()*
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Measures of Variability
&ange
Inter+uartile range
Variance Standard !e'iation
Measures of Central Tendency
Median
Mode
Mean
:t"er su##ary
#easures;
S$ewness
%urtosis
S455!ry Me!#4re#@ Po4"!tion
P!r!5eter# S!5"e St!ti#ti,#
'()+
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• Median Middle 'alue w"en
sorted in order of
#agnitude
74t" ercentile
• Mode Most fre+uently-
occurring 'alue
• Mean *'erage
'(* Me!#4re# o2 Centr!" enden,y
or Lo,!tion
'()1
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Median
Median
A)th Percentile
03456174/644864,7 33 5 0,71041 8 33
T"e median is t"e #iddle
'alue of data sorted inorder of #agnitude, It is
t"e 74t" ercentile,
E<!5"e > Medi!n -D!t! i# 4#ed 2ro5
E<!5"e '()0
Sorted;illions ;illions << 1= 8> 1=
8? 1=81 1=
1@ 1@
8) 8) 1= 8) 1= 8) A8 81 A> 88 89 88 88 8< 1= 8?
?@ 8> 88 89 8) <8 8< << <8 ?@ 8) A8
1= A>
'()3
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Mode B 1=
T"e mode is t"e #ost fre+uently occurring 'alue, It
is t"e 'alue wit" t"e highest fre2uency,
E<!5"e ( Mode -D!t! i# 4#ed 2ro5
E<!5"e '()0
'()7
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Mode B 1=
T"e mode is t"e #ost fre+uently occurring 'alue, It
is t"e 'alue wit" t"e highest fre2uency,
E<!5"e ( Mode -D!t! i# 4#ed 2ro5
E<!5"e '()0
'()6
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T"e mean of a set of obser'ations is t"eir a'erage -
t"e su# of t"e obser'ed 'alues di'ided by t"e
nu#ber of obser'ations,
Population Mean Sample Mean
Arith5eti, Me!n or Aer!$e
∑=
= $
i
i %
6
µ ∑=
=n
i
i % %
6
'()
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E<!5"e > Me!n -D!t! i# 4#ed 2ro5
E<!5"e '()0
Sorted;illions ;illions << 1= 8> 1=
8? 1=81 1=
1@ 1@
8) 8) 1= 8) 1= 8) A8 81 A> 88 89 88 88 8< 1= 8?
?@ 8> 88 89 8) <8 8< << <8 ?@ 8) A8 1= A>Sum B A<=
<,3=34
7>?
6 === ∑=
n
ii
% %
'(*8
7/23/2019 Chap 001 COMPLETE �BUSINESS �STATISTICS
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,ange
!ifference between #a)i#u# and #ini#u# 'alues
Inter2uartile ,ange
!ifference between t"ird and first +uartile -"< # "1.
ariance
*'erage@of t"e s+uared de'iations fro# t"e #ean
Standard DeviationS+uare root of t"e 'ariance
∗ !efinitions of oulation 'ariance and sa#le 'ariance differ slig"tly,
'(+ Me!#4re# o2 V!ri!bi"ity or
Di#er#ion
'(*'
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Sorted;illions ;illions ,anks << 1= 1 8> 1= 8 8? 1= < 81 1= ? 1@ 1@ A 8) 8) > 1= 8) 9 1= 8) = A8 81 @ A> 88 1) 89 88 11 88 8< 18
1= 8? 1< ?@ 8> 1? 88 89 1A 8) <8 1> 8< << 19 <8 ?@ 1= 8) A8 1@
1= A> 8)
0irst "uartile
Median
Third "uartile
034561×37/64487,37
034561×74/644864,7
034561×97/644867,97
1@ 5 -+8A.-1. B 1@+8A
88 5 -+A.-). B 88
895 -+9A.-A. B <)+9A
E<!5"e '(*@ indin$ ;4!rti"e#
&ange 8 Ma)i#u# A Mini#u#
8 7= A 6? 8 >?
Inter+uartile &ange 8 Q> A Q6
8 >4,97 A 6<,37 8 66,7
'(*)
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V!ri!n,e !nd St!nd!rd Dei!tion
0 1σ
µ
σ σ
3
3
6
3
6
3
3
6
=
−
=
−
=
=
=
∑
∑ =∑
0 1 %
$
% $
$
i
$
i
$ %i
$
Population ariance
( )
( )
s % %
n
% %
nn
s s
i
n
i
ni
n
3
3
6
3
6
3
3
6
6
6
=−∑
−
=
−∑
−
=
=
=
=∑
0 1
Sample ariance
0 1
'(**
7/23/2019 Chap 001 COMPLETE �BUSINESS �STATISTICS
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1= #=+@ 9@+81 <8?
1= #=+@ 9@+81 <8?
1= #=+@ 9@+81 <8?
1= #=+@ 9@+81 <8?
1@ #9+@ >8+?1 <>1
8) #>+@ ?9+>1 ?))
8) #>+@ ?9+>1 ?))
8) #>+@ ?9+>1 ?))
81 #A+@ <?+=1 ??1
88 #?+@ 8?+)1 ?=?
88 #?+@ 8?+)1 ?=?
8< #<+@ 1A+81 A8@
8? #8+@ =+?1 A9>
8> #)+@ )+=1 >9>89 )+1 )+)1 98@
<8 A+1 8>+)1 1)8?
<< >+1 <9+81 1)=@
?@ 88+1 ?==+?1 8?)1
A8 8A+1 ><)+)1 89)?
A> 8@+1 =?>+=1 <1<>
A<= ) 8>A9+= 191<)
% %− % 0 1 % %− 3
%3
( )
( )
( )
?3,66??B36,6><
??B36,6><6<
?,3=79
6<
3,6BB93696>46<
34
3?<BBB696>4
634
34
7>?696>4
6
6
??B36,6><6<
?,3=79
16340
?,3=79
6
10
3
3
3
6
3
6
3
3
===
==−
=
−=
−
−=
−
∑=−
=
==
−=
−
−=
∑
∑
=
=
s
%
s
n
n
n
i %
n
% %
s
n
i
n
i
C!",4"!tion o2 S!5"e V!ri!n,e'(*+
' *1
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E<!5"e@ S!5"e V!ri!n,e U#in$ the
e5"!te
S!5"e V!ri!n,e
'(*1
' *3
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E<!5"e@ S!5"e V!ri!n,e U#in$ Minit!b
S!5"e V!ri!n,e
'(*3
' *7
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!i'iding data into grous or classes or inter'als
Grous s"ould be;
Mutually e'clusive
ot o'erlaing - e'ery obser'ation is assigned to only onegrou
&'haustive
('ery obser'ation is assigned to a grou
&2ual#idth 0if ossible1 2irst or last grou #ay be oen-ended
'(1 Bro4 D!t! !nd the i#to$r!5'(*7
' *6
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Table wit" two colu#ns listing; (ac" and e'ery grou or class or inter'al of 'alues
*ssociated fre2uency of eac" grou
u#ber of obser'ations assigned to eac" grou
Su# of fre+uencies is nu#ber of obser'ations
for oulation
n for sa#le
Class midpoint is t"e #iddle 'alue of a grou or class or
inter'al,elative fre2uency is t"e ercentage of total obser'ations
in eac" class
Su# of relati'e fre+uencies 8 6
re?4en,y Di#trib4tion'(*6
' *
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' f -'. f -'.6n
Spending Class -:. 0re2uency -number of customers. ,elative 0re2uency
4 to less t"an 644 >4 4,6=>
644 to less t"an 344 >? 4,349
344 to less t"an >44 74 4,393
>44 to less t"an B44 >6 4,6=?
B44 to less t"an 744 33 4,634
744 to less t"an =44 6> 4,494
6?B 6,444
' f -'. f -'.6n
Spending Class -:. 0re2uency -number of customers. ,elative 0re2uency
4 to less t"an 644 >4 4,6=>
644 to less t"an 344 >? 4,349344 to less t"an >44 74 4,393
>44 to less t"an B44 >6 4,6=?
B44 to less t"an 744 33 4,634
744 to less t"an =44 6> 4,494
6?B 6,444
()a#le of relati'e fre+uency; >4/6?B 8 4,6=> Su# of relati'e fre+uencies 8 6
E<!5"e '(7@ re?4en,y Di#trib4tion'(*
' +8
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' F -'. F -'.6n
Spending Class -:. Cumulative 0re2uency Cumulative ,elative 0re2uency
4 to less t"an 644 >4 4,6=>
644 to less t"an 344 =? 4,>94
344 to less t"an >44 66? 4,=B6>44 to less t"an B44 6B< 4,?64
B44 to less t"an 744 696 4,<3<
744 to less t"an =44 6?B 6,444
' F -'. F -'.6n
Spending Class -:. Cumulative 0re2uency Cumulative ,elative 0re2uency
4 to less t"an 644 >4 4,6=>
644 to less t"an 344 =? 4,>94
344 to less t"an >44 66? 4,=B6
>44 to less t"an B44 6B< 4,?64
B44 to less t"an 744 696 4,<3<
744 to less t"an =44 6?B 6,444
T"e cumulative fre2uency of eac" grou is t"e su# of t"e
fre+uencies of t"at and all receding grous,T"e cumulative fre2uency of eac" grou is t"e su# of t"e
fre+uencies of t"at and all receding grous,
C454"!tie re?4en,y Di#trib4tion'(+8
' +'
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* histogram is a c"art #ade of bars of different "eig"ts,
Didt"s and locations of bars corresond to widt"s and locations of data
grouings
Heig"ts of bars corresond to fre+uencies or relati'e fre+uencies of datagrouings
i#to$r!5'(+'
'(+)
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0re2uency istogram
i#to$r!5 2or E<!5"e '(7
6005004003002001000
50
40
30
20
10
0
Dollars
F r e q u e n c y
13
22
31
50
38
30
Histogram of Dollars
'(+)
R " ti i t'(+*
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,elative 0re2uency istogram
Re"!tie re?4en,y i#to$r!5
E<!5"e '(7
6005004003002001000
30
25
20
15
10
5
0
Dollars
P e r c e n t
7.06522
11.9565
16.8478
27.1739
20.6522
16.3043
Histogram of Dollars
NOTE: he re"!tie
2re?4en,ie#!re e<re##ed
!# er,ent!$e#.
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Skeness Measure of t"e degree of asy##etry of a fre+uency distribution
S$ewed to left
Sy##etric or uns$ewed S$ewed to rig"t
Eurtosis Measure of flatness or ea$edness of a fre+uency distribution
Platy$urtic 0relati'ely flat1
Meso$urtic 0nor#al1
Eeto$urtic 0relati'ely ea$ed1
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Skeed to left
Se/ne##' +1
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Se/ne##
Symmetric
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Se/ne##
Skeed to right
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Sy55etri, =i5od!" Di#trib4tion
Symmetric distribution ith to Modes
700600500400300200100
40
30
20
10
0
X
F r e q u e n c y
10
15
35
20
35
15
10
Mean B Me dian
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4rto#i#
Platykurtic - flat distribution
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4rto#i#
Mesokurtic - not too flat and not too ea$ed
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4rto#i#
Feptokurtic - ea$ed distribution
' 7 Re"!tion# bet/een the Me!n !nd'(1)
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Chebyshev7s Theorem
*lies to any distribution regardless of s"ae
Places lower li#its on t"e ercentages of obser'ations wit"in a
gi'en nu#ber of standard de'iations fro# t"e #ean
&mpirical ,ule
*lies only to roug"ly mound#shaped and symmetric
distributions
Secifies aro)i#ate ercentages of obser'ations wit"in a
gi'en nu#ber of standard de'iations fro# t"e #ean
'(7 Re"!tion# bet/een the Me!n !nd
St!nd!rd Dei!tion
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6 63
6 6B
>B
97F
6 6
>6
6
<
?
< ?<F
6 6
B6
6
6=
67
6= <BF
3
3
3
− = − = =
− = − = =
− = − = =
*t least of t"e ele#ents of any distribution lie
wit"in k standard de'iations of t"e #ean
!t
least
Fie
ithin
Standard
deviations
of t"e #ean
3
>
B
Cheby#heF# heore5
−
36
6
&
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2or roug"ly mound#shaped and symmetric distributions aro)i#ately;
=?F 6 standard de'iation
of t"e #ean
<7F Eie
wit"in
3 standard de'iations
of t"e #ean
*ll > standard de'iations
of t"e #ean
E5iri,!" R4"e
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Pie Charts
Categories reresented as ercentages of total
;ar (raphs
Heig"ts of rectangles reresent grou fre+uencies0re2uency Polygons
Heig"t of line reresents fre+uency
Ogives
Heig"t of line reresents cu#ulati'e fre+uencyTime Plots
&eresents 'alues o'er ti#e
'(6 Method# o2 Di#"!yin$ D!t!
Pie Ch!rt -i$4re ' 60 Ine#t5ent'(13
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Pie Ch!rt -i$4re '(60 > Ine#t5ent
Port2o"io
Foreign
Bonds
Small Cap/Mid Cap
Large Cap al!e
Large Cap Blend
Ca"egor#
Large Cap Blend
30$ 30.0%
Large Cap al!e10$ 10.0%
Small Cap/Mid Cap20$ 20.0%
Bonds20$ 20.0%
Foreign20$ 20.0%
The Portfolio
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=!r Ch!rt -i$4re '(0 > he 9eb !e#
O22
2006200520042003200220012000
125
100
75
50
25
0
Year
R e g i s t r a t i o n ( M i l l i o n s )
Chart of Registration (Millions)
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Re"!tie re?4en,y Po"y$on -i$4re '('80
56484032241680
0.30
0.25
0.20
0.15
0.10
0.05
0.00
Sales
R e l a t i e F r e q u e n c y
0
re?4en,y i#
Lo,!ted in the
5idd"e o2 the
inter!".
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O$ie -i$4re '(')0
6050403020100
1.0
0.8
0.6
0.4
0.2
0.0
Sales
C
u m u l a t i e R e l a t i e F r e q u e
n c y
0
he oint /ith hei$ht
,orre#ondin$ to
the ,454"!tie
re"!tie 2re?4en,y i#"o,!ted !t the ri$ht
endoint o2 e!,h
inter!".
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i5e P"ot -i$4re '()+0 > S!"e#
Co5!ri#on
&o'Sep (!lMa#Mar (an
120
115
110
105
100
Month
S a l e s
2000
2001
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Stem#and#Feaf Displays
Quic$ way of listing all obser'ations
Con'eys so#e of t"e sa#e infor#ation as a "istogra#
;o' Plots
Median
Eower and uer +uartiles
Ma)i#u# and #ini#u#
Tec"ni+ues to deter#ine relations"is and trends
identify outliers and influential obser'ations and
+uic$ly describe or su##ari.e data sets,
Tec"ni+ues to deter#ine relations"is and trends
identify outliers and influential obser'ations and
+uic$ly describe or su##ari.e data sets,
'( E<"or!tory D!t! An!"y#i# ( EDA
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1 1 8 8 < A A A > 9 8 ) 1 1 1 8 8 8 < ? > 9 9 9 = @ @ < ) 1 8 ? A 9 ? 1 1 8 A 9 A ) 8 < > > ) 8
1 1 8 8 < A A A > 9 8 ) 1 1 1 8 8 8 < ? > 9 9 9 = @ @
< ) 1 8 ? A 9 ? 1 1 8 A 9 A ) 8 < > > ) 8
E<!5"e '(6@ Ste5(!nd(Le!2 Di#"!y
2igure 6-67; Tas$ Perfor#ance Ti#es
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@o
MedianQ6 Q>Inner
2ence
Inner
2ence
:uter
2ence
:uter
2ence
Inter+uartile &ange
S#allest data
oint not
below inner
fence
Eargest data oint
not e)ceeding
inner fence
Susected
outlier :utlier
Q6->0IQ&1
Q6-6,70IQ&1 Q>56,70IQ&1
Q>5>0IQ&1
(le#ents of a o) Plot(le#ents of a o) Plot
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E<!5"e ' *@ U#in$ the e5"!te to ,o54te
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E<!5"e ' * -Contin4ed0@ U#in$ the
e5"!te to ,o54te De#,ritie St!ti#ti,#
This is the loer part of the sameThis is the loer part of the same
template from the previous slide+template from the previous slide+
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U#in$ the Co54ter e5"!te
O4t4t 2or the i#to$r!5
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U#in$ the Co54ter e5"!te O4t4t 2or
i#to$r!5# 2or Bro4ed D!t!
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U#in$ the Co54ter e5"!te O4t4t 2or
re?4en,y Po"y$on# & the O$ie 2or Bro4ed D!t!
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U#in$ the Co54ter e5"!te O4t4t 2or /o
re?4en,y Po"y$on# 2or Bro4ed D!t!
U#in$ the Co54ter > Pie Ch!rt'(7'
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U#in$ the Co54ter Pie Ch!rt
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$
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U#in$ the Co54ter i5e P"ot
Co5!ri#on e5"!te
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S,!tter P"ot#
Scatter Plots are used to identify and reort
any underlying relations"is a#ong airs of
data sets,
T"e lot consists of a scatter of oints eac" oint reresenting an obser'ation,
S,!tter P"ot#'(76
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S,!tter P"ot#
Scatter lot wit"
trend line, T"is tye of
relations"i is$nown
as a ositi'e
correlation,
Correlation will be
discussed in later
c"aters,
NOE'(7