Chap 001 COMPLETE BUSINESS STATISTICS

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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



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'()



!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::

'(*



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??

'(+



'('. 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



"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



$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



! 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



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'(



Population -$.Population -$. Sample -Sample -nn..

S!5"e# !nd Po4"!tion#'('8



Census of a population may be%

Impossible

Impractical Too costly

9hy S!5"e:'(''



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#'(')



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 '()'('*



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>

'('+



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



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,




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+=+




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+




"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#'('



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



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

'()'



E<!5"e '(*@ U#in$ the e5"!te'())



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+

'()*



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,#

'()+



• 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



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



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



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



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

'()



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



,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

'(*'



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

'(*)



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

'(**



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



E<!5"e@ S!5"e V!ri!n,e U#in$ the

e5"!te

S!5"e V!ri!n,e

'(*1

' *3



E<!5"e@ S!5"e V!ri!n,e U#in$ Minit!b

S!5"e V!ri!n,e

'(*3

' *7



!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



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

' *



' 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



' 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

' +'



* 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'(+'

'(+)



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'(+*



,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#.

' +*

'(++



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

'(3 Se/ne## !nd 4rto#i#' ++

'(+1



Skeed to left

Se/ne##' +1

'(+3



Se/ne##

Symmetric

' +3

'(+7



Se/ne##

Skeed to right

'(+6



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

'(+



4rto#i#

Platykurtic - flat distribution

'(18



4rto#i#

Mesokurtic - not too flat and not too ea$ed

'(1'



4rto#i#

Feptokurtic - ea$ed distribution

' 7 Re"!tion# bet/een the Me!n !nd'(1)



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

'(1*



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

&

'(1+



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

'(11



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



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

=!r Ch!rt -i$4re ' 0 he 9eb !e#'(17



=!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)

'(16



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!".

'(1



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!".

i5e P"ot -i$4re '()+0 > S!"e#'(38



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

aria)le

'(3'



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

'(3)



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

'(3*



@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

=o< P"ot

'(3+



E<!5"e@ =o< P"ot

E<!5"e '(*@ U#in$ the e5"!te to ,o54te'(31



E<!5"e ' *@ U#in$ the e5"!te to ,o54te

De#,ritie St!ti#ti,#

E<!5"e '(* -Contin4ed0@ U#in$ the'(33



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+

U#in$ the Co54ter > e5"!te'(37



U#in$ the Co54ter e5"!te

O4t4t 2or the i#to$r!5

U#in$ the Co54ter > e5"!te O4t4t 2or'(36



U#in$ the Co54ter e5"!te O4t4t 2or

i#to$r!5# 2or Bro4ed D!t!

U#in$ the Co54ter > e5"!te O4t4t 2or'(3



U#in$ the Co54ter e5"!te O4t4t 2or

re?4en,y Po"y$on# & the O$ie 2or Bro4ed D!t!

U#in$ the Co54ter > e5"!te O4t4t 2or /o'(78



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'



U#in$ the Co54ter Pie Ch!rt

e5"!te O4t4t

U#in$ the Co54ter > =!r Ch!rt'(7)



U#in$ the Co54ter =!r Ch!rt

e5"!te O4t4t

U#in$ the Co54ter > =o< P"ot'(7*



U#in$ the Co54ter =o< P"ot

e5"!te O4t4t

U#in$ the Co54ter > =o< P"ot e5"!te to'(7+



$

Co5!re /o D!t! Set#

U#in$ the Co54ter > i5e P"ot'(71



U#in$ the Co54ter i5e P"ot

e5"!te

U#in$ the Co54ter > i5e P"ot'(73



U#in$ the Co54ter i5e P"ot

Co5!ri#on e5"!te

S,!tter P"ot#'(77



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



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



NOE

MANY O E BRAPS

PRESENED IN IS CAPER

CAN =EBENERAED 9I

MINIA= AS 9ELL.

Chap 001 COMPLETE BUSINESS STATISTICS

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