The Dot Plot

What is it? How to Draw it

Bet you’ve never seen a graph like this one before. . .

2

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 plotA dot plot only has an x-axis. The y-axis is never drawn

Advantage of a dot plotModerate amounts of quantitative data can be quickly visualized

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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

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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?”

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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

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Dot Plot ExampleNumber of Pets Per Household

for Ms. H's Intro Stat Classes

2009

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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

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Freq Table

Example 4 Classes Combined

Mean = 2.52 pets

Median = 2 pets

Mode = 0 pets (37x)

Range = 30 pets

Spread = 0 - 30 pets

n = 134 students

Fre- Relative

Class quency Freq

0 pets 37 27.6%1 pet 31 23.1%2 pets 27 20.1%3 pets 8 6.0%4 pets 10 7.5%5 pets 7 5.2%6 pets 2 1.5%7 pets 3 2.2%8 pets 2 1.5%9 pets 1 0.7%

10 pets 1 0.7%11 pets 3 2.2%12 pets 0 0.0%13 pets 1 0.7%14 pets 0 0.0%15 pets 0 0.0%16 pets 0 0.0%17 pets 0 0.0%18 pets 0 0.0%

19 pets 0 0.0%

20 pets 0 0.0%

21 pets 0 0.0%

22 pets 0 0.0%

23 pets 0 0.0%

24 pets 0 0.0%

25 pets 0 0.0%

26 pets 0 0.0%

27 0 0.0%

28 0 0.0%

29 0 0.0%

30 1 0.7%

Totals 31 classes 134 100%

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Dot Plot Example 4 Classes Combined.

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: Number of Pets Per Household

: . for Ms. H's Intro Stat Classes

: : Oct 6, 2010

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0 1 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

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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

Units are important

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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.

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Dot Plot: How to Describe ItShape

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

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Student Scores in Anderson’s Cr WritingName Gender 3rd Per Grade ID Test #10

Teacher No %1 Benson, Paul M Kling 11 0754447 952 Bishop, Sally F Smith 12 2310476 573 Chan, Alex M Yale 11 4512683 924 Chaney, Brenda F Fernando 11 1268130 755 Darosa, Rick M Iijima 11 7481322 836 Dovsten, Stan M Browne 10 9181322 867 Dring, Pamela F Nikola 11 5381421 688 Gomez, Tom M Lunceford 12 4681967 669 Hart, Ron M Tyler 10 2588132 75

10 Ho, DJ M Cedric 11 4678194 8211 Hughes, Kim F Dorman 12 5524911 9212 Kennedy, Fred M Ho 11 6582044 8713 Khangura, Sam M Horvath 11 9562648 6014 Lace, Bob M Kwok 11 3219403 7515 Lamar, Candy F Falck 11 6651060 8116 Lunda, Alice F Edwards 12 8650602 6817 Nester, Lucy F Ho 10 9651060 5818 Pomodor, Gorden M Horvath 10 9631068 8819 Prado, Cindy F Kang 11 7510253 8220 Rice, Dale M Duerr 12 3651054 82

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Student Scores in Anderson’s Cr Writing

Anderson's English Class Test 101 Scores

. . . . . . : : . : . .. . : .

| | | | | | | | | | |50 55 60 65 70 75 80 85 90 95 100

Source: Teacher Records x-axis: Score in pts.

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% of Population Over 651 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

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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

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Make Dot Plot of State Population Data

Percent of Population over 65 years of Age

in the 50 States

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4 6 8 10 12 14 16 18 20

Source: Statistical Abstract of the US

x-axis: Number in % to nearest integer

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Dot Plot: How to Describe ItMore on Shape

SymmetricWhen the left & right sides of a distribution are mirror

images of one anotherFairly 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.

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Dot Plot: What it Looks LikeShape: Symmetry

Symmetric

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Dot Plot: What it Looks LikeMore on Shape: Non Symmetric

Skewed Left (negatively skewed)

Skewed Right (positively skewed)

Left Skew

Right Skew

tail

tail

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Goals by US Women’s Soccer

Number of Goals Scored by US Women's

Soccer Team in 34 games in 2004

3 0 2 7 8 2 4 4

5 1 1 4 5 3 1 1

3 3 2 1 2 2 2 4

6 6 1 5 5 1 1 4

3 3 Source: US Soccer Assn.

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Goals by US Women’s Soccer

Ordered Ascending

0 3 6

1 3 6

1 3 7

1 3 8

1 3

1 3

1 4

1 4

1 4

2 4

2 4

2 5

2 5

2 5

2 5

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Dot Plot of Goals by US Women’s Soccer

Goals per Game by US Women's Soccer Team in 2004

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0 1 2 3 4 5 6 7 8 9 10

Source: US Women's Soccer Assn

x-axis: # of goals per game

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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 13 Maryland 6 Penn 8

Connecticut 6 Mass 7 Rhode Is 9

Delaware 7 Michigan 7 S Caroliina 11

Florida 9 Mississippi 16 Tennessee 10

Georgia 10 New Hamp 4 Vermont 6

Illinois 8 New Jersey 6 Virginia 7

Indiana 7 NY 12 W Virginia 14

Kentucky 13 N Carolina 9 Wisconsin 6

Maine 8 Ohio 8

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Living in Poverty East of the Mississippi

Ordered Ascending

New Hamp 4 Ohio 8

Wisconsin 6 Penn 8

Maryland 6 Rhode Is 9

Connecticut 6 Florida 9

New Jersey 6 N Carolina 9

Vermont 6 Georgia 10

Delaware 7 Tennessee 10

Indiana 7 S Caroliina 11

Mass 7 NY 12

Virginia 7 Alabama 13

Michigan 7 Kentucky 13

Illinois 8 W Virginia 14

Maine 8 Mississippi 16

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Living in Poverty East of the Mississippi

% of State Residents Living in Poverty East of

the Mississippi River in 1999

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4 5 6 7 8 9 10 11 12 13 14 15 16

Source: Statistical Abstract of the US

x-axis: Values to the nearest %

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Dot Plot: Mean & Median EssentialsSkew 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.

Right Skew

meanmedian

tail

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Dot Plot: Mean & Median EssentialsSkew 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.

medianmean

Left Skewtail

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Dot Plot: Describing Peaks

Peaks

Unimodal

Bimodal

Unimodal

Bimodal

Multimodal (3 or more peaks)

Trimodalor Multimodal

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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.

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Dot Plot: TI EssentialsFinding 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

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Glucose Blood Levels

Glucose Blood Levels for Adult Women55 66 83 71 76 64 59 5976 82 80 81 85 77 82 9087 72 79 69 84 71 87 6981 76 74 83 67 91 74 9489 94 73 74 93 85 83 80

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Glucose Blood Levels

GLUCOSE BLOOD LEVELS in mg/mlfor 40 Women at Sutter Health in March 2009

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58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94Source: Sutter Health Clinic x-axis: glucose level in mg/ml

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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 5355 57 57 58 60 61 61 6263 63 63 63 63 63 63 6464 67 67 67 69 71 72 7272 72 73 75 75 75 75 7576 77 78 79 79 80 81 8182 83 83 85 89 91 92 100

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WBNA Free Throws—Dot Plot

WNBAEASTERN CONFERENCE FREE THROWPERCENTAGES 1998 .

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46 48 50 52 54 56 58 60 62 64 66 68 70 72.:

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74 76 78 80 82 84 86 88 90 92 94 96 98 100Source: WNBA x-axis: %age of converted free throws

per game

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Dot Plot: How to Describe ItUnusual 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.

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Fuel Consumption—Data

Fuel Consumption for 2009 Passenger Fords30 27 22 25 24 25 24 1535 35 33 49 49 10 27 1820 23 24 25 30 24 24 2418 20 25 27 24 32 29 2724 27 26 25 24 28 33 30

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Fuel Consumption—Dot Plot

Fuel Consumption for 2009 Passenger Fords

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10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Source: Consumer Reports x-axis: miles per gallon