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 731
– Insufficient Helmet 153
– No Helmet 816
Total 1,700
3
Helmets Used by Motorcyclists
Vertical
Source: US Dept of Transportation
Bar
900
Graph 816
800
Example 731
700
600
Number of Motorcyclists
500
400
300
200 153
100
0
Proper Helmet Insufficient Helmet No Helmet
4
Helmet Type
x-axis & y-axis Variables
• On a vertical bar Helmets Used by Motorcyclists
graph, the y-axis 900
Source: US Dept of Transportation
variable is normally a 800
731
816
quantitative variable. 700
600
Is it discrete or
Number of Motorcyclists
500
continuous? 400
• On a vertical bar 300
200 153
graph, the x-axis 100
variable is normally 0
Proper Helmet Insufficient Helmet No Helmet
a categorical variable 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
800 751
Number of Motorcyclists
700
600
500
400
300
200 153
100
0
Insufficient Helmet Proper Helmet No Helmet
Helmet Type 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
50
48.6
$,000/yr
40
34.3
30
20 16.1
10
0
High
9th Grade Associate Bachelor Master's Doctoral
Highest Ed Level School Gr Degree Degree Degree 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
300 279
250
Sales per Sq Foot
250
220
200
192
147
150
100
50
0
Retailer
Dillard's Federated Marshall Sears Kohls Nordstrom Target
Field's 12
Sales by Store in $/Ft
Non Pareto
Source: Wall Street Journal
Version of 450
410
Sales 400
357
350
Sales per Sq Foot
300 279
250
250
220
200
192
147
150
100
50
0
Dillard's Kohl's Marshall Federated Nordstrom Sears Target
Field's 13
Retailer
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
What Psychic Phenomena Do Americans Believe In?
600
546
506 Source: Gallup Poll
500
400
385
Number of People
300
283
200 152
100
0
Psychic Healing ESP Ghosts Astrology Channeling
Psychic Phenomena
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 Per Four Per Five Totals
Yes 14 17 22 18 71
No 19 9 8 11 47
No Opinion 0 9 1 1 11
Totals 33 35 31 30 129
19
In Class Survey Results from 2009
3-Level Comparative Bar Graph
Does Intro Stat Believe in Psychic Phenomena? Yes
25 No
Source: In Class Survey 22
No Opinion
20 19
18
17
Number of Students
15 14
11
10 9 9
8
5
1 1
0
0
Class Per Two Per Three Per Four Per Five
20
In Class Survey Results from 2009: Simple Bar
Graph
Does Intro Stat Believe in Psychic Phenomena?
80
71
70
Source: In Class Survey
60
Number of Students
47
50
40
30
20
11
10
0
Yes No No Opinion
Opinion 21
In Class Survey Results from 2009: Pie Chart
Does Intro Stat Believe in Psychic Phenomena?
No Opinion
8.5%
No Yes
36.4% 55.0%
Source: In Class Survey 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 Bureau
4.5
4.4
4.0
3.6
3.5
3.2
3.0
3.0
Inches
2.5
2.5
2.0
1.5
1.5 1.4
1.0
1.0 0.8
0.6 0.7
0.5 0.3
0.0
Month Jan Feb Mar Apr May Jun Jul Aug Sep 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
Lotto 42.7%
23.1%
4-Digit Games Source: Stat Abstract of the US
7.2% 3-Digit Games
13.6% Sample Size: $38.4 bn
28
Spending On NY Lottery
$ %
Type of Game in bn nrst 0.1 nrst 0.1
Instant Games °
3-Digit Games °
4-Digit Games °
Lotto °
Other Games °
Totals °
29
Spending On NY Lottery
$ %
Type of Game in bn nrst 0.1 nrst 0.1
Instant Games 16.4 42.7% 153.8 °
3-Digit Games 5.2 13.6% 49.1 °
4-Digit Games 2.8 7.2% 26.0 °
Lotto 8.9 23.1% 83.0 °
Other Games 5.1 13.4% 48.1 °
Totals 38.4 100.0% 360.0 °
30
NY State Lottery Sales in $bn
18.0
16.4 Source: Statistical Abstract of US
16.0
14.0
12.0
10.0
8.9
Sales in $bn
8.0
6.0 5.2 5.1
4.0
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%
Private
Co/Business
36.1%
Own
Business
13.9%
State/Local Federal
Gov't Government
18.9% 13.1%
Source: Duke University 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 °
Total 122 100.0% 360.0 °
34
Turning a Pie Chart into a Bar Graph
50
What Job Do Students Want After College?
45
44
Source: Duke University
40
35
Number of Students
30
25 23 22
20
16 17
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
800
Number of People
700
636
600
500
400
294
300
188
200
100
0
Acquaintances Breeders Pet Stores Animal Shelters
Pet Source 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
Comcast 15.3 33.3% 119.8 °
AT&T 13.5 29.4% 105.8 °
Time Warner 8.8 19.2% 69.0 °
Verizon 8.3 18.1% 65.2 °
Totals 45.9 100.0% 360.0 °
44
Turning a Pie Chart into a Bar Graph
18
Top Internet Broadband Players # of Subscribers 2009
16 15.3
Source: Gartner
14 13.5
12
Subscribers in Millions
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
No Opinion
380 randomly selected 8%
Chicago residents from August
27 to 31, 2009 on the subject
of the potential Chicago
Olympics of 2016. In favor
47%
The question asked was, “Do Oppose
you favor or oppose Chicago 45%
hosting the 2016 Olympic
games?” The results of the poll
were:
Supply the remainder of the
data labels
46
Could the Pie Chart Become a Bar Graph?
The answer is 200
obviously yes, 180
179
171
160
But the question 140
remains, 120
100
Which Graph looks 80
60
better? Which Graph 40 30
is better for display 20
0
purposes? In favor Oppose No Opinion
This is a matter of
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? 70000
11.4%
12.0%
61,786
• What are they? 60000 57,936
10.3% 10.3%
10.0%
• What’s the conclusion? 50000
51,116 50,979 51,372
8.0%
• Good pie chart? 40000
7.7%
6.6%
• Is this a Pareto chart? 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
Somewhat
Dissatisfied
31.8% Satisfied
27.2%
Very
Dissatisfied
37.3%
49
Turning a Pie Chart into a Bar Graph
Number of %
Level of Satisfaction 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
Number of %
Level of Satisfaction Responses nrst 0.1 nrst 0.1
Very Satisfied 94 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 °
Total 2546 100.0 360 °
51
Turning a Pie Chart into a Bar Graph
1000 950
How Satisfied Are You with US Public Schools?
900
Source: YouGov for the Economist 810
800
Number of Responses
693
700
600
500
400
300
200
94
100
0
Very Satisfied Somewhat Satisfied Somewhat Very Dissatisfied
Dissatisfied
52
Turning Pie Charts to Bar Graphs
What is the most serious problem
facing America?
Neither
Education
4.7%
18.4%
Equally
Health
Serious
Care
55.3%
21.6%
Source: YouGov for Economist 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 1408 55.3 199.1 °
Neither 120 4.7 16.9 °
Total 2546 100.0 360 °
55
Turning Pie Charts to Bar Graphs
What is the most serious problem facing America?
1600
Source: YouGov for the Economist
1400
1408
1200
Number of Responses
1000
800
600
550
468
400
200 120
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% Single
Widowed 22.6%
7.5%
Married
57
61.1%
Turning Pie Charts to Bar Graphs
Marital Status %
(millions of people) nrst 0.1 nrst 0.1
Single °
Married °
Widowed °
Divorced °
Total °
58
Turning Pie Charts to Bar Graphs
Marital Status Count %
(millions of people) nrst 0.1 nrst 0.1
Single 41.8 22.6% 81.2 °
Married 113.3 61.1% 220.1 °
Widowed 13.9 7.5% 27.0 °
Divorced 16.3 8.8% 31.7 °
Total 185.3 100.0% 360.0 °
59
Turning Pie Charts to Usual Bar Graphs
150
Marital Status of Americans Ages 18 & Over
125
113.3
Number of Adults in Millions
Source: US Census Bureau
100
75
50 41.8
25 16.3
13.9
0
Single Married Widowed Divorced
Marital Status
60
Turning Pie Charts to Pareto Bar Graphs
150
Marital Status of Americans Ages 18 & Over
125
113.3
Number of Adults in Millions
Source: US Census Bureau
100
75
50 41.8
25
16.3 13.9
0
Married Single Divorced Widowed
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 y-
axis.
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
250
Number of Graduates
200
150
98
100
45
50
18
0
Continuing Employed Military Other
Eduation
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
250
Number of Graduates
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
4,000
Average Credit Card Debt in $
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 College College College College 1st Yr after
Senior Freshman Sophomore Junior Senior Graduation
69
Mountains to Climb
World's Tallest Mountains
Mt, Location Ht in ft
1 Everest, Tibet 29,035
2 K2, Kashmir 28,250
3 Kanchenjunga, Nepal 28,028
4 Lhotse, Nepal 27,890
5 Makalu, Nepal 27,790
6 Dhaulagiri, Nepal 26,810
7 Manaslu, Nepal 26,760
8 Cho Oyu, Nepal 26,750
70
29,500
World's Highest Mountains
29,035 Source: National Geographic
29,000
28,500
28,250
28,028
Height in Feet
28,000 27,890
27,790
27,500
27,000
26,810 26,760 26,750
26,500
26,000
25,500
ir
al
al
al
al
al
l
t
a
be
hm
ep
ep
ep
ep
ep
ep
Ti
N
s
,N
N
N
N
N
Ka
,
,
st
u,
e,
a,
,
yu
lu
iri
re
al
s
g
,
as
ag
K2
O
ot
un
ak
e
an
Lh
ul
Ev
ho
nj
M
ha
M
e
C
71
ch
D
n
Ka
Quiz #103 Bar Charts
Hints:
You need:
• Complete the Vocabulary
Pencil, Eraser • Then do the front page
Calculator
Graph Paper (for 2 • Place your HW in the HW
graphs: one sheet okay) box
No bags on desk
Clear all lists in Calculator
72