The Dot Plot
What is it? How to Draw it
Bet you’ve never seen a graph like this
one before. . .
What is a Dot Plot?
A dot plot is a graph that shows the
distribution of a quantitative variable above a
number line with small periods, dots, circles
or x’s. It plots a quantitative variable against
a quantitative variable.
Axes on a dot plot
A dot plot only has an x-axis.
The y-axis is never drawn
Advantage of a dot plot
Moderate amounts of quantitative data can
be quickly visualized
2
What is a Dot Plot?
2 Variables on a dot plot:
x-axis variable is quantitative and identified
y-axis variable is implied since the y-axis is
never drawn.
y-axis variable is ‘the count’ and so is
normally discrete quantitative
3
Making a Dot Plot
• I want to know more about my students who
take Intro Stats so I’ve decided to take a survey
and make a dot plot of the results
• I’d like to find out about the pets they have in
their household.
• The question then becomes:
“How many pets are in your household?”
4
Making a Dot Plot from Live Data
Frequency
Frequency
0 pets
9 pets
1 pet
10 pets
2 pets
11 pets
3 pets
12 pets
4 pets
13 pets
5 pets
14 pets
6 pets
15 pets
7 pets
16 pets
8 pets
17 pets
5
Dot Plot Example
Number of Pets Per Household
for Ms. H's Intro Stat Classes
2009
|
|
|
|
|
|
|
|
|
|
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18
Source: In Class Survey
|
|
|
|
|
|
|
|
x-axis: # of Pets
|
6
Freq
Table
Example
4 Classes
Combined
Totals
Class
0 pets
1 pet
2 pets
3 pets
4 pets
5 pets
6 pets
7 pets
8 pets
9 pets
10 pets
11 pets
12 pets
13 pets
14 pets
15 pets
16 pets
17 pets
18 pets
19 pets
Frequency
37
31
27
8
10
7
2
3
2
1
1
3
0
1
0
0
0
0
0
0
20
21
22
23
24
25
26
27
28
29
30
0
0
0
0
0
0
0
0
0
0
1
pets
pets
pets
pets
pets
pets
pets
31 classes
134
Relative
Freq
27.6%
23.1%
20.1%
6.0%
7.5%
5.2%
1.5%
2.2%
1.5%
0.7%
0.7%
2.2%
0.0%
0.7%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
Mean = 2.52 pets
Median = 2 pets
Mode = 0 pets (37x)
Range = 30 pets
Spread = 0 - 30 pets
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.0%
0.7%
n = 134 students
100%
7
Dot Plot Example 4 Classes Combined
.
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
.
:
:
:
:
:
:
:
:
:
:
:
:
:
:
:
.
:
:
:
:
:
:
:
:
:
:
:
:
:
|
|
0
1
Number of Pets Per Household
for Ms. H's Intro Stat Classes
Oct 6, 2010
:
:
:
:
:
:
:
:
:
.
:
:
:
|
|
|
2
3
4
:
.
:
:
.
.
.
:
|
|
|
|
|
|
|
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 28 30
Source: In Class Survey
.
|
|
.
|
x-axis:
|
|
|
|
|
|
|
|
|
|
|
|
|
|
# of Pets
8
Dot Plot: Statistical Vocabulary Background
Spread (also called Variability)
The spread of data in statistics is the smallest value
in a data set and the largest value
It is always expressed as 2 numbers
Prefer to write smallest then largest number
Units are important
Range
The range of data in statistics is the difference
between the smallest value and the largest value
Take the spread and subtract the two numbers:
large – small
9
Units are important
Dot Plot: Statistical Vocabulary Background
One Measure of Center
One measure of the center of a data
distribution is the median, the place where
the data tends to be ½ above and ½ below.
Units are important
Mode
The mode of data is a place or places with
the largest number of data with the same
value. Units are important.
10
Dot Plot: How to Describe It
Shape
The shape of a data distribution possibilities:
1) Symmetry
Symmetric
Also ‘Fairly Symmetrical’
Skewed Left (negatively skewed)
Skewed Right (positively skewed)
2) Peaks
Single Peaked (unimodal)
Double Peaked (bimodal)
Multi Peaked (multimodal)
NOTE: Data have modes, dot plots have peaks
11
Student Scores in Anderson’s Cr Writing
Name
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Gender 3rd Per
Grade
ID
Teacher
No
Benson, Paul
M Kling
11
0754447
Bishop, Sally
F Smith
12
2310476
Chan, Alex
M Yale
11
4512683
Chaney, Brenda
F Fernando 11
1268130
Darosa, Rick
M Iijima
11
7481322
Dovsten, Stan
M Browne
10
9181322
Dring, Pamela
F Nikola
11
5381421
Gomez, Tom
M Lunceford 12
4681967
Hart, Ron
M Tyler
10
2588132
Ho, DJ
M Cedric
11
4678194
Hughes, Kim
F Dorman
12
5524911
Kennedy, Fred
M Ho
11
6582044
Khangura, Sam
M Horvath
11
9562648
Lace, Bob
M Kwok
11
3219403
Lamar, Candy
F Falck
11
6651060
Lunda, Alice
F Edwards
12
8650602
Nester, Lucy
F Ho
10
9651060
Pomodor, Gorden M Horvath
10
9631068
Prado, Cindy
F Kang
11
7510253
Rice, Dale
M Duerr
12
3651054
Test #10
%
95
57
92
75
83
86
68
66
75
82
92
87
60
75
81
68
58
88
82
82
12
Student Scores in Anderson’s Cr Writing
Anderson's English Class Test 101 Scores
. . .
. :
|
|
|
|
|
50 55 60 65 70
Source: Teacher Records
.
:
|
75
.
. : . .. . :
.
|
|
|
|
80 85 90 95
x-axis: Score in pts.
|
100
13
% of Population Over 65
1 Alabama
13
26 Montana
13
2 Alaska
5
27 Nebraska
14
3 Arizona
13
28 Nevada
11
4 Arkansas
15
29 N Hampshire
12
5 California
11
30 N Jersey
14
6 Colorado
10
31 N Mexico
11
7 Connecticut
14
32 N York
13
8 Delaware
13
33 N Carolina
13
9 Florida
19
34 N Dakota
15
10 Georgia
10
35 Ohio
13
11 Hawaii
13
36 Oklahoma
14
12 Idaho
11
37 Oregon
14
13 Illinois
13
38 Penn
16
14 Indiana
13
39 R Island
16
15 Iowa
15
40 S Carolina
12
16 Kansas
14
41 S Dakota
14
17 Kentucky
13
42 Tennessee
13
18 Louisiana
11
43 Texas
10
19 Maine
14
44 Utah
9
20 Maryland
11
45 Vermont
12
21 Mass
14
46 Virginia
11
22 Michigan
12
47 Washington
12
23 Minnesota
12
48 W Virginia
15
24 Mississippi
12
49 Wisconsin
13
25 Missouri
14
50 Wyoming
11
14
Population over 65 Data Sorted by %
1 Alaska
5
26 Indiana
13
2 Utah
9
27 Kentucky
13
3 Colorado
10
28 Alabama
13
4 Georgia
10
29 Montana
13
5 Texas
10
30 Arizona
13
6 N Mexico
11
31 Wisconsin
13
7 California
11
32 N York
13
8 Virginia
11
33 Ohio
13
9 Wyoming
11
34 Oklahoma
14
10 Maryland
11
35 Oregon
14
11 Idaho
11
36 Kansas
14
12 Louisiana
11
37 N Jersey
14
13 Nevada
11
38 Maine
14
14 Washington
12
39 Missouri
14
15 N Hampshire
12
40 Nebraska
14
16 S Carolina
12
41 Mass
14
17 Vermont
12
42 Connecticut
14
18 Mississippi
12
43 S Dakota
14
19 Michigan
12
44 Arkansas
15
20 Minnesota
12
45 N Dakota
15
21 Illinois
13
46 Iowa
15
22 N Carolina
13
47 W Virginia
15
23 Tennessee
13
48 R Island
16
24 Delaware
13
49 Penn
16
25 Hawaii
13
50 Florida
19
15
Make Dot Plot of State Population Data
Percent of Population over 65 years of Age
in the 50 States
.
:
: :
.
.
:
. : :
:
: : :
.
:
: : :
:
:
:
: : :
: :
.
|
|
|
|
|
|
|
|
|
4
6
8
10
12
14
16
18
20
Source: Statistical Abstract of the US
x-axis: Number in % to nearest integer
16
Dot Plot: How to Describe It
More on Shape
Symmetric
When the left & right sides of a distribution are mirror
images of one another
Fairly Symmetric
When the left and right sides of a distribution are
almost mirror images of one another, but there are
small exceptions.
Skewed Left (negatively skewed)
If a distribution extends much farther out to the left.
The direction of skewness is on the side of the longer
tail, in this case LEFT.
Skewed Right (positively skewed)
If a distribution extends much farther out to the right.
The direction of skewness is on the side of the longer
tail, in this case RIGHT.
17
Dot Plot: What it Looks Like
Shape: Symmetry
Symmetric
18
Dot Plot: What it Looks Like
More on Shape: Non Symmetric
Skewed Left (negatively skewed)
Left Skew
tail
Skewed Right (positively skewed)
Right Skew
tail
19
Goals by US Women’s Soccer
Number of Goals Scored by US Women's
Soccer Team in 34 games in 2004
3
5
3
6
3
0
2
7
8
2
1
1
4
5
3
3
2
1
2
2
6
1
5
5
1
3 Source: US Soccer Assn.
4
1
2
1
4
1
4
4
20
Goals by US
Women’s Soccer
Ordered Ascending
0
1
3
3
6
6
1
1
1
1
1
1
1
2
2
2
2
2
2
3
3
3
3
4
4
4
4
4
5
5
5
5
7
8
21
Dot Plot of Goals by US Women’s Soccer
Goals per Game by US Women's Soccer Team in 2004
:
:
:
:
.
:
:
:
:
:
.
:
:
:
:
:
:
.
.
|
|
|
|
|
|
|
|
|
|
|
0
1
2
3
4
5
6
7
8
9
10
Source: US Women's Soccer Assn
x-axis: # of goals per game
22
Living in Poverty East of the Mississippi
Percent of State Residents Living in Poverty
East of Mississippi River, 1999 Source: Stat Abs of US
Alabama
Connecticut
Delaware
Florida
Georgia
Illinois
Indiana
Kentucky
Maine
13
6
7
9
10
8
7
13
8
Maryland
6 Penn
Mass
7 Rhode Is
Michigan
7 S Caroliina
Mississippi 16 Tennessee
New Hamp
4 Vermont
New Jersey 6 Virginia
NY
12 W Virginia
N Carolina
9 Wisconsin
Ohio
8
8
9
11
10
6
7
14
6
23
Living in Poverty
East of the
Mississippi
Ordered
Ascending
New Hamp
Wisconsin
Maryland
Connecticut
New Jersey
Vermont
Delaware
Indiana
Mass
Virginia
Michigan
Illinois
Maine
4
6
6
6
6
6
7
7
7
7
7
8
8
Ohio
Penn
Rhode Is
Florida
N Carolina
Georgia
Tennessee
S Caroliina
NY
Alabama
Kentucky
W Virginia
Mississippi
8
8
9
9
9
10
10
11
12
13
13
14
24
16
Living in Poverty East of the Mississippi
.
|
|
4
5
% of State Residents Living in Poverty East of
the Mississippi River in 1999
.
.
:
:
:
.
:
:
:
:
:
.
.
:
.
|
|
|
|
|
|
|
|
|
6
7
8
9
10 11 12
Source: Statistical Abstract of the US
x-axis: Values to the nearest %
13
14
|
.
|
15
16
25
Dot Plot: Mean & Median Essentials
Skew on a dot plot in relation to mean and
median
You’ve drawn the line that connects the dot plot
points on the top of the distribution. The line
clearly shows right or left skew.
If you have right skew, the mean will be to the
right of (greater than) the median, as the mean
follows the tail of the distribution.
median
mean
Right Skew
tail
26
Dot Plot: Mean & Median Essentials
Skew on a dot plot in relation to mean and
median
If you have left skew, the mean will be to the left
of (less than) the median, as the mean follows
the tail of the distribution.
median
mean
tail
Left Skew
27
Dot Plot: Describing Peaks
Peaks
Unimodal
Unimodal
Bimodal
Bimodal
Multimodal (3 or more peaks)
Trimodal
or Multimodal
28
TI83 and Sort Ascending
• How to Sort Data in Ascending Order
Enter all values in a list at STAT EDIT
Exit to Home Screen using 2nd MODE
Hit STAT key. Go to #2 SORT A(. Hit ENTER
Type 2nd 1 (if the data is in List 1). Hit Enter
Done appears
Check your data in List 1. It should be sorted.
Use your eyes to find the range & spread
from the sorted list.
29
Dot Plot: TI Essentials
Finding Mean and Median
Enter your data as a list in STAT EDIT
Exit to home screen 2nd Mode
Go to 2nd STAT.
Right Arrow to MATH
#3 is Mean; hit Enter; type 2nd and list #;
Enter
#4 is Median; hit Enter; type 2nd and list #;
Enter
Calculator does not give Mode. You need
your eyes for that
30
Glucose Blood Levels
Glucose Blood Levels for Adult Women
55 66 83 71 76 64 59 59
76 82 80 81 85 77 82 90
87 72 79 69 84 71 87 69
81 76 74 83 67 91 74 94
89 94 73 74 93 85 83 80
31
Glucose Blood Levels
GLUCOSE BLOOD LEVELS in mg/ml
for 40 Women at Sutter Health in March 2009
:
:
:
.
. .
:
: . . : . : .
. : : : : . :
:
. . .
. .
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94
Source: Sutter Health Clinic
x-axis: glucose level in mg/ml
32
WBNA EAST Free Throws—Data in
Ascending Order
Women's National Basketball Assn Free
Throw Percentages for 1998 from WNBA
46 47 48 50 50 50 52 53
55 57 57 58 60 61 61 62
63 63 63 63 63 63 63 64
64 67 67 67 69 71 72 72
72 72 73 75 75 75 75 75
76 77 78 79 79 80 81 81
82 83 83 85 89 91 92 100
33
WBNA Free Throws—Dot Plot
WNBA
EASTERN CONFERENCE FREE THROW
PERCENTAGES 1998
.
. .
.
:
|
|
|
|
|
46
48
50
52
54
.
.
: .
.
: .
.
:
:
: :
|
|
|
|
|
|
|
|
|
56
58
60
62
64
66
68
70
72
.
.
:
:
. :
.
.
:
: .
. .
: .
: .
|
|
|
|
|
|
|
|
|
|
|
|
|
|
74
76
78
80
82
84
86
88
90
92
94
96
98
100
.
Source: WNBA
:
.
.
. .
.
x-axis: %age of converted free throws
per game
34
Dot Plot: How to Describe It
Unusual Features.
Possibilities include-Potential Outliers: any data value that falls out of the
pattern of the rest of the distribution. A potential
outlier will lie at either extreme of the data when it is
written in order. (We will learn how to calculate actual
outliers later. For now, we will call these points
potential outliers)
Clusters: isolated groups of values. Clusters begin
when frequency >1 and end before frequency returns to
1 or zero.
Gaps: large spaces between values. Write gap values
from beginning empty space to end empty space. A gap
of one number is NOT a gap.
35
Fuel Consumption—Data
Fuel Consumption for 2009 Passenger Fords
30 27 22 25 24 25 24 15
35 35 33 49 49 10 27 18
20 23 24 25 30 24 24 24
18 20 25 27 24 32 29 27
24 27 26 25 24 28 33 30
36
Fuel Consumption—Dot Plot
Fuel Consumption for 2009 Passenger Fords
.
:
:
:
.
.
:
:
. . :
|
|
|
|
|
|
|
|
10 12 14 16 18 20 22 24
Source: Consumer Reports
.
:
: .
|
26
.
:
.
: . . :
. :
:
:
|
|
|
|
|
|
|
|
|
|
|
|
28 30 32 34 36 38 40 42 44 46 48 50
x-axis: miles per gallon
37