The Bar Graph or Bar Chart
What is it? How to Draw it
What is a Bar Graph?
A bar graph is a graph that displays the
frequency or numerical distribution of a
categorical variable, showing values for each
bar next to each other for easy comparison.
Alternate Name:
Bar Chart
2
Bar Graph Example
In June 2005, the US Dept of Transportation
reported the following data by observing 1700
motorcyclists nationwide at randomly selected
roadway location:
– Proper Helmet
– Insufficient Helmet
– No Helmet
Total
731
153
816
1,700
3
Helmets Used by Motorcyclists
Vertical
Bar
Graph
Example
Source: US Dept of Transportation
900
816
800
731
700
Number of Motorcyclists
600
500
400
300
200
153
100
0
Proper Helmet
Insufficient Helmet
Helmet Type
No Helmet
4
x-axis & y-axis Variables
Helmets Used by Motorcyclists
Source: US Dept of Transportation
900
816
800
731
700
600
Number of Motorcyclists
• On a vertical bar
graph, the y-axis
variable is normally a
quantitative variable.
Is it discrete or
continuous?

• On a vertical bar
graph, the x-axis
variable is normally
a categorical variable
500
400
300
200
153
100
0
Proper Helmet
Insufficient Helmet
No Helmet
Helmet Type
Source: US Dept of Transportation
Categorical Variable
5
Type of Variables on the
Previous Motorcycle Bar Graph
• x-axis?
Categorical Variable.
Name the categories
Proper, Insufficient, None
• y-axis
Discrete Quantitative Variable
What are the units?
Helmets
6
Making a Bar Graph Look Better
• What would make this bar graph look better?
If we ranked the numbers by either increasing or
decreasing value, the appearance would be less
jagged, making a Pareto Chart.
• What is a Pareto Chart?
A bar graph in which the bars are ordered
according to value, in either increasing or
decreasing order.
• Why Pareto Charts? Graph is named for Vilfredo
Pareto, an Italian mathematician & economist.
1848-1923.
7
Vertical Bar Graph as Pareto Chart
Helmets Used by Motorcyclists
Source: US Dept of Transportation
900
816
751
Number of Motorcyclists
800
700
600
500
400
300
200
153
100
0
Insufficient Helmet
Helmet Type
Proper Helmet
No Helmet
8
Education & Annual Income Survey
Educational Level and Annual Income
Highest Educ
Annual Salary
Level
in $,000
9th Grade
16.1
High School Gr
34.3
Associate Degree
48.6
Bachelor Degree
62.1
Master's Degree
71.0
Doctoral Degree
84.1
9
Educational Level and Annual Income
Source: US Census Bureau
90
84.1
80
71.0
70
62.1
60
48.6
$,000/yr
50
40
34.3
30
20
16.1
10
0
9th Grade
High
Associate
Highest Ed Level School Gr Degree
Bachelor
Degree
Master's
Degree
Doctoral
Degree
10
Retail Sales
Sales per Square Foot in $
Store $/Ft
Dillard's 147
Kohl's 279
Marshall Field's 220
Federated 192
Nordstrom 357
Sears 250
Target 410
11
Pareto Chart of Sales At Retail Outlets
Sales by Store in $/Sq Ft
Source: Wall Street Journal
450
410
400
357
350
Sales per Sq Foot
300
279
250
250
220
192
200
147
150
100
50
0
Retailer
Dillard's
Federated
Marshall
Field's
Sears
Kohls
Nordstrom
Target
12
Sales by Store in $/Ft
Non Pareto
Version of
Sales
Source: Wall Street Journal
450
410
400
357
Sales per Sq Foot
350
300
279
250
250
220
192
200
150
147
100
50
0
Dillard's
Retailer
Kohl's
Marshall
Field's
Federated
Nordstrom
Sears
Target
13
Bar Graphs: VERY FLEXIBLE FORMAT
Advantage over Pie Charts
Bar Graphs are easier to make & to read
than pie charts.
How are they similar to Pie Charts?
Both pie charts & bar graphs can display the
distribution of a categorical variable
How are they different from Pie Charts?
A bar graph can also compare any set of
quantities measured in the same units.
14
Psychic Phenomena
Belief in Various Supernatural Phenomena
Phenomenon
# of people
Psychic Healing
546
ESP
506
Ghosts
385
Astrology
283
Channeling
152
15
Pareto Chart of Psychic Phenomena
600
What Psychic Phenomena Do Americans Believe In?
546
506
Source: Gallup Poll
Number of People
500
385
400
283
300
200
152
100
0
Psychic Healing
Psychic Phenomena
ESP
Ghosts
Astrology
Channeling
16
In Class Survey:
Do you believe in Supernatural Phenomena?
Does Intro Stats Believe in
Psychic Phenomenon?
(including psychic healing, ghosts, astrology, ESP, channeling, etc)
Per 1
Per 2
Per 4
Per 6
Totals
Yes
No
No Opinion
Totals
17
In Class Survey:
Do you believe in Supernatural Phenomena?
Does Intro Stats Believe in
Psychic Phenomenon?
(including psychic healing, ghosts, astrology, ESP, channeling, etc)
Per 3
Per 5 Totals
Yes
No
No Opinion
Totals
18
In Class Survey Results from 2009:
Do you believe in Supernatural Phenomena?
Per Two Per Three
Yes
No
No Opinion
Totals
14
19
0
33
17
9
9
35
Per Four
Per Five
Totals
22
8
1
31
18
11
1
30
71
47
11
129
19
In Class Survey Results from 2009
3-Level Comparative Bar Graph
Yes
No
No Opinion
Does Intro Stat Believe in Psychic Phenomena?
25
22
Source: In Class Survey
19
Number of Students
20
15
18
17
14
11
9
10
9
8
5
1
0
1
0
Class
Per Two
Per Three
Per Four
Per Five
20
In Class Survey Results from 2009: Simple Bar
Graph
80
Does Intro Stat Believe in Psychic Phenomena?
71
Number of Students
70
Source: In Class Survey
60
47
50
40
30
20
11
10
0
Yes
Opinion
No
No Opinion
21
In Class Survey Results from 2009: Pie Chart
Does Intro Stat Believe in Psychic Phenomena?
No Opinion
8.5%
No
36.4%
Source: In Class Survey
Yes
55.0%
Sample Size: 129 Students
22
Rainfall In Hawaii
Monthly Rainfall in Inches
Month Inches MonthInches
Jan
4.4 Jul
0.6
Feb
2.5 Aug
0.8
Mar
3.2 Sep
0.7
Apr
1.4 Oct
1.5
May
1.0 Nov
3.0
Jun
0.3 Dec
3.6
23
Monthly Rainfall in Honlulu 2006
5.0
Source: Hawaiian Weather Burea u
4.5
4.4
4.0
3.6
3.5
3.2
Inches
3.0
3.0
2.5
2.5
2.0
1.5
1.4
1.5
1.0
1.0
0.6
0.8
0.7
Aug
Sep
0.3
0.5
0.0
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Oct
Nov
Dec
24
Bar Graph Characteristics
1. Data can be quantitative or categorical
2. Bars can be vertical or horizontal
3. The x-axis represents the category
displayed
4. The y-axis represents the quantitative
values of the variable being displayed
5. Bars are of uniform width and uniformly
spaced
25
Bar Graph Characteristics
6. A consistent measurement scale is used
for each vertical bar
7. Height of bars represent the values of
the variable displayed, the frequency of
occurrence or percentage of occurrence
8. The graph is well-annotated with title,
labels for each bar, vertical scale,
horizontal categories, source
26
Changing Scale – The Squiggle
What is a squiggle?
At least a 2-angle line on a bar graph axis that
abbreviates a scale.
When do you use a squiggle?
Use a squiggle on the changed axis whenever
you change scale in a bar graph.
Horizontal Squiggle
Vertical Squiggle
or
27
Pie to Bar: Spending On NY Lottery
NY State Lottery Sales in $bn in 2002
Other Games
13.4%
Instant Games
42.7%
Lotto
23.1%
4-Digit Games
7.2%
Source: Stat Abstract of the US
3-Digit Games
13.6%
Sample Size: $38.4 bn
28
Spending On NY Lottery
$
Type of Game
Instant Games
3-Digit Games
4-Digit Games
Lotto
Other Games
Totals
%

in bn nrst 0.1 nrst 0.1
°
°
°
°
°
°
29
Spending On NY Lottery
$
Type of Game
Instant Games
3-Digit Games
4-Digit Games
Lotto
Other Games
Totals
%

in bn nrst 0.1 nrst 0.1
16.4 42.7%
5.2 13.6%
2.8
7.2%
8.9 23.1%
5.1 13.4%
38.4 100.0%
153.8
49.1
26.0
83.0
48.1
360.0
°
°
°
°
°
°
30
NY State Lottery Sales in $bn
18.0
16.4
Source: Statistical Abstract of US
16.0
14.0
12.0
Sales in $bn
10.0
8.9
8.0
6.0
5.2
4.0
5.1
2.8
2.0
0.0
Instant Games 3-Digit Games 4-Digit Games
Lotto
Other
Type of Game
31
Turning a Pie Chart into a Bar Graph
What Job Do Students Want After College?
Grad School
18.0%
Own
Business
13.9%
State/Local
Gov't
18.9%
Source: Duke University
Private
Co/Business
36.1%
Federal
Government
13.1%
Sample Size: 122 Students
32
Turning a Pie Chart into a Bar Graph
Job Type
%
# students nrst 0.1
°
nrst 0.1
Fed Gov't
Private Co/Bus
Grad School
Own Business
State/Local Gov't
Total
33
Turning a Pie Chart into a Bar Graph
Job Type
# students % of Total
°
nrst 0.1
Fed Gov't
16
13.1%
47.2
°
Private Co/Bus
44
36.1%
129.8
°
Grad School
22
18.0%
64.9
°
Own Business
17
13.9%
50.2
°
State/Local Gov't
23
18.9%
67.9
°
122
100.0%
360.0
°
Total
34
Turning a Pie Chart into a Bar Graph
50
45
44
What Job Do Students Want After College?
Source: Duke University
40
Number of Students
35
30
23
25
20
22
17
16
15
10
5
0
Private Co/Business
Federal Government
State/Local Gov't
Own Business
Grad School
35
“Would The Bar Graph Make a Good Pie
Chart?”
• Only when Bar Graphs represent parts of
a whole, can it be made into a Pie Chart.
• If the answer is NO, you could write:
– No, because these values are comparative
data only.
– No, because these values DO NOT represent
parts of the whole.
• If the answer is YES, you could write:
– Yes, because these values represent parts of
the whole.
36
Bar Graph & Pie Chart Relationship Summary
• Every Pie Chart COULD be made into a
Bar Graph
BUT
• NOT all Bar Graphs CAN be made into Pie
Charts
Pie Chart  Bar Graph
Bar Graph  Pie Chart
37
Turning a Pie Chart into a Bar Graph
Where Do Pet Owners
Get Their Animals?
Animal
Shelters
14.7%
Acquaintances
43.9%
Pet Stores
9.4%
Breeders
31.9%
Source: USA Today
Sample Size: 1994 Pet Owners
38
Turning a Pie Chart into a Bar Graph
Sourcing a New Pet
%

# of People nrst 0.1% nrst 0.1°
Acquaintances
°
Breeders
°
Pet Stores
°
Animal Shelters
°
Totals
°
39
Turning a Pie Chart into a Bar Graph
# of People
%

nrst 0.1% nrst 0.1°
Acquaintances
876
43.9%
158.2
°
Breeders
636
31.9%
114.8
°
Pet Stores
188
9.4%
33.9
°
Animal Shelters
294
14.7%
53.1
°
Totals
1994
100.0%
360
°
40
Turning a Pie Chart into a Bar Graph
Where US Pet Owners Get Their Pets
in July 2008
1000
900
876
Number of People
800
700
636
600
500
400
294
300
188
200
100
0
Acquaintances
Breeders
Pet Stores
Pet Source
Animal Shelters
Source: USA Today
41
Turning a Pie Chart into a Bar Graph
Top Broadband Players
Market Share 2009
Verizon
18.1%
Comcast
33.3%
Time
Warner
19.2%
AT&T
29.4%
Source: Gartner
Sample Size: 45.9m subscribers
42
Turning a Pie Chart into a Bar Graph
Top Broadband Companies
# of Subscribers
%

in millions nrst 0.1
nrst 0.1
Comcast
AT&T
Time Warner
Verizon
°
°
°
°
Totals
°
43
Turning a Pie Chart into a Bar Graph
Top Broadband Companies

%
# of Subscribers
in millions nrst 0.1 nrst 0.1
119.8
33.3%
15.3
Comcast
105.8
29.4%
13.5
AT&T
69.0
19.2%
8.8
Time Warner
65.2
18.1%
8.3
Verizon
°
°
°
°
360.0
°
Totals
45.9
100.0%
44
Turning a Pie Chart into a Bar Graph
18
16
Top Internet Broadband Players # of Subscribers 2009
15.3
Source: Gartner
13.5
14
Subscribers in Millions
12
10
8.8
8.3
8
6
4
2
0
Company
Comcast
AT&T
Time Warner
Verizon
45
Deciding Which Graph is Better
The Chicago Tribune polled
380 randomly selected
Chicago residents from August
27 to 31, 2009 on the subject
of the potential Chicago
Olympics of 2016.
The question asked was, “Do
you favor or oppose Chicago
hosting the 2016 Olympic
games?” The results of the poll
were:
No Opinion
8%
In favor
47%
Oppose
45%
Supply the remainder of the
data labels
46
Could the Pie Chart Become a Bar Graph?
The answer is
obviously yes,
But the question
remains,
Which Graph looks
better? Which Graph
is better for display
purposes?
This is a matter of
opinion
200
179
180
171
160
140
120
100
80
60
30
40
20
0
In favor
Oppose
No Opinion
Supply the remainder of the
data labels
47
Examining a Bar Chart for Meaning
•
•
•
•
•
•
•
•
•
What’s the question?
What’s the title?
What’s the population?
What’s the sample?
How many variables?
What are they?
What’s the conclusion?
Good pie chart?
Is this a Pareto chart?
12.0%
70000
11.4%
61,786
60000
57,936
10.3%
10.3%
51,116
10.0%
50,979
51,372
50000
8.0%
7.7%
40000
6.6%
6.0%
30000
4.0%
20000
2.0%
10000
0.0%
0
Washington, DC
Seattle, WA
New York, NY
Portland, OR
Austin, TX
48
Turning a Pie Chart into a Bar Graph
How Satisfied are You with US Public Schools?
Source: YouGov for Economist
Sample Size: 2546 Americans
Very Satisfied
3.7%
Somewhat
Dissatisfied
31.8%
Somewhat
Satisfied
27.2%
Very
Dissatisfied
37.3%
49
Turning a Pie Chart into a Bar Graph
Level of Satisfaction
Number of
Responses
%
nrst 0.1

nrst 0.1
Very Satisfied
°
Somewhat Satisfied
°
Somewhat Dissatisfied
°
Very Dissatisfied
°
Total
°
50
Turning a Pie Chart into a Bar Graph
Level of Satisfaction
Very Satisfied
Number of
Responses
94

%
nrst 0.1
nrst 0.1
3.7
13.3 °
Somewhat Satisfied
693
27.2
97.9 °
Somewhat Dissatisfied
950
37.3
134.3 °
Very Dissatisfied
810
31.8
114.5 °
2546
100.0
360 °
Total
51
Turning a Pie Chart into a Bar Graph
950
1000
How Satisfied Are You with US Public Schools?
900
Number of Responses
Source: YouGov for the Economist
810
800
693
700
600
500
400
300
200
94
100
0
Very Satisfied
Somewhat Satisfied
Somewhat
Dissatisfied
Very Dissatisfied
52
Turning Pie Charts to Bar Graphs
What is the most serious problem
facing America?
Neither
4.7%
Equally
Serious
55.3%
Source: YouGov for Economist
Education
18.4%
Health
Care
21.6%
Sample Size: 2546 Americans
53
Turning Pie Charts to Bar Graphs
Number of
Issue
Responses
%
nrst 0.1

nrst 0.1
Education
°
Health Care
°
Equally Serious
°
Neither
°
Total
°
54
Turning Pie Charts to Bar Graphs
Number of
Issue
Responses

%
nrst 0.1
nrst 0.1
Education
468
18.4
66.2 °
Health Care
550
21.6
77.8 °
Equally Serious
Neither
Total
1408
55.3 199.1 °
120
4.7
16.9 °
2546
100.0
360 °
55
Turning Pie Charts to Bar Graphs
What is the most serious problem facing America?
1600
1400
1408
Source: YouGov for the Economist
Number of Responses
1200
1000
800
550
600
468
400
120
200
0
Equally Serious
Health Care
Education
Neither
Issue
56
Turning Pie Charts to Bar Graphs
Marital Status of Americans Ages 18 & Over
Source: US Census Bureau
Sample Size: 185.3m Americans
Divorced
8.8%
Widowed
7.5%
Married
61.1%
Single
22.6%
57
Turning Pie Charts to Bar Graphs
%
(millions of people) nrst 0.1
Marital Status

nrst 0.1
Single
°
Married
°
Widowed
°
Divorced
°
Total
°
58
Turning Pie Charts to Bar Graphs
Marital Status
Count
(millions of people)
Single
%
nrst 0.1

nrst 0.1
41.8
22.6%
81.2 °
113.3
61.1%
220.1 °
Widowed
13.9
7.5%
27.0 °
Divorced
16.3
8.8%
31.7 °
185.3
100.0%
360.0 °
Married
Total
59
Turning Pie Charts to Usual Bar Graphs
150
Marital Status of Americans Ages 18 & Over
Number of Adults in Millions
125
113.3
Source: US Census Bureau
100
75
50
41.8
25
13.9
16.3
Widowed
Divorced
0
Single
Married
Marital Status
60
Turning Pie Charts to Pareto Bar Graphs
150
Marital Status of Americans Ages 18 & Over
Number of Adults in Millions
125
113.3
Source: US Census Bureau
100
75
50
41.8
25
16.3
13.9
Divorced
Widowed
0
Married
Single
Marital Status
61
Steps in Bar Chart Construction
1. Use a straight edge on a piece of graph
paper
2. Make a first-quadrant x-y axis, unless
some of your data is negative
3. Examine the data and determine the
maximum value of the quantitative data.
Your y-scale must be at least this high
62
Steps in Bar Chart Construction
4. Choose an appropriate scale for the yaxis.
5. Mark scale ticks consistently & label
them, until you reach a mark greater than
the highest value of data.
6. Mark of the bar width of each piece of
categorical data you will be using on the
x-axis.
63
Steps in Bar Chart Construction
7. Make sure you place a space between
each of the data bars.
8. Plot each data point by drawing a bar of
the correct width & height for each.
9. Label the top of each bar with a value.
10. Label both x- and y-axes with a title
11. Title the graph
12. Label the source of the data.
64
What Comes After High School?
Life After High School for 481 1980
Graduates of Ithaca High School
Chosen Path after HS
# of Graduates
Continuing Eduation
320
Employed
98
Military
18
Other
45
65
Path After Graduation for Ithaca
High School Graduates in 1980
350
320
Source: Ithaca High School
300
Number of Graduates
250
200
150
98
100
45
50
18
0
Continuing
Eduation
Employed
Military
Other
Chosen Path
66
Chosen Path
Pareto Chart of “Path After Graduation”
Path After Graduation for Ithaca
High School Graduates in 1980
350
320
Source: Ithaca High School
300
Number of Graduates
250
200
150
98
100
45
50
18
0
Continuing Eduation
Employed
Other
Military
Chosen Path
Chosen Path
67
Kids Borrowing Money (Replace)
Credit Card Debt by Grade Level
Average Credit
Grade Level
Card Debt in $
High School Senior
350
College Freshman
1,533
College Sophomore
1,825
College Junior
2,705
College Senior
3,262
1st Yr after Graduation
4,575
68
Credit Card Debt by Grade Level in 2001
5,000
4,575
Source: Nellie Mae Institute
4,500
Average Credit Card Debt in $
4,000
3,500
3,262
3,000
2,705
2,500
2,000
1,825
1,533
1,500
1,000
500
350
Grade 0
Level
High School
Senior
College
Freshman
College
Sophomore
College
Junior
College
Senior
1st Yr after
Graduation
69
Mountains to Climb
1
2
3
4
5
6
7
8
World's Tallest Mountains
Mt, Location
Everest, Tibet
K2, Kashmir
Kanchenjunga, Nepal
Lhotse, Nepal
Makalu, Nepal
Dhaulagiri, Nepal
Manaslu, Nepal
Cho Oyu, Nepal
Ht in ft
29,035
28,250
28,028
27,890
27,790
26,810
26,760
26,750
70
World's Highest Mountains
29,500
Source: National Geographic
29,035
29,000
28,500
28,028
27,890
28,000
27,790
27,500
27,000
26,810
26,760
26,750
26,500
26,000
al
al
yu
,N
ep
O
C
ho
M
an
as
lu
,
N
ep
ul
ag
iri
,
D
ha
ak
M
N
ep
al
al
N
ep
al
u,
N
ep
e,
ot
s
Lh
a,
en
ju
ng
ch
Ka
n
al
l
N
ep
a
hm
Ka
s
K2
,
re
st
,T
ib
e
t
ir
25,500
Ev
e
Height in Feet
28,250
71
Quiz #103 Bar Charts
You need:
Pencil, Eraser
Hints:
• Complete the Vocabulary
• Then do the front page
Calculator
Graph Paper (for 2
graphs: one sheet okay)
• Place your HW in the HW
box
No bags on desk
Clear all lists in Calculator
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