1. Bet you’ve never seen a graph like this one before. . .
Dot Plots
16 April 2017
16 April 2017
The Dot Plot
What is it? How to Draw it
Bet you’ve never seen a graph like this one before. . .
10 Dot Plots.ppt 1

2. What is a Dot Plot?
Dot Plots
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16 April 2017
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
Categorical or Qualitative
Quantitative or Numerical
10 Dot Plots.ppt 2

3. 2 Variables on a dot plot:
Dot Plots
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16 April 2017
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
Categorical or Qualitative
Quantitative or Numerical
10 Dot Plots.ppt 3

4. 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?”

5. Making a Dot Plot from Live Data
Dot Plots
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16 April 2017
Making a Dot Plot from Live Data
10 Dot Plots.ppt 5

6. Dot Plot Example Dot Plots 16 April 2017 16 April 2017
10 Dot Plots.ppt 6

7. Freq Table Example 4 Classes Combined
Dot Plots
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16 April 2017
Freq Table Example 4 Classes Combined
Mean = 2.52 pets
Median = 2 pets
Mode = 0 pets (37x)
Range = 30 pets
Spread = pets
n = 134 students
10 Dot Plots.ppt 7

8. Dot Plot Example 4 Classes Combined
Dot Plots
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16 April 2017
Dot Plot Example 4 Classes Combined 8
10 Dot Plots.ppt 8

9. Dot Plot: Statistical Vocabulary Background
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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
Categorical or Qualitative
Quantitative or Numerical
10 Dot Plots.ppt 9

10. Dot Plot: Statistical Vocabulary Background
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16 April 2017
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.
Categorical or Qualitative
Quantitative or Numerical
10 Dot Plots.ppt 10

11. Dot Plot: How to Describe It
Dot Plots
Dot Plot: How to Describe It
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16 April 2017
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
Categorical or Qualitative
Quantitative or Numerical
10 Dot Plots.ppt 11

12. Student Scores in Anderson’s Cr Writing

13. Student Scores in Anderson’s Cr Writing

14. % of Population Over 65

15. Population over 65 Data Sorted by %

16. Make Dot Plot of State Population Data

17. Dot Plot: How to Describe It
Dot Plots
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16 April 2017
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.
Categorical or Qualitative
Quantitative or Numerical
10 Dot Plots.ppt 17

18. Dot Plot: What it Looks Like
Dot Plots
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16 April 2017
Dot Plot: What it Looks Like
Shape: Symmetry
Symmetric
Categorical or Qualitative
Quantitative or Numerical
10 Dot Plots.ppt 18

19. Dot Plot: What it Looks Like
Dot Plots
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16 April 2017
Dot Plot: What it Looks Like
More on Shape: Non Symmetric
Skewed Left (negatively skewed)
Skewed Right (positively skewed)
tail
Categorical or Qualitative
Quantitative or Numerical
tail
10 Dot Plots.ppt 19

20. Goals by US Women’s Soccer

21. Goals by US Women’s Soccer Ordered Ascending

22. Dot Plot of Goals by US Women’s Soccer

23. Living in Poverty East of the Mississippi

24. Living in Poverty East of the Mississippi Ordered Ascending

25. Living in Poverty East of the Mississippi

26. Dot Plot: Mean & Median Essentials
Dot Plots
Dot Plot: Mean & Median Essentials
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16 April 2017
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
Categorical or Qualitative
Quantitative or Numerical
mean
tail
10 Dot Plots.ppt 26

27. Dot Plot: Mean & Median Essentials
Dot Plots
Dot Plot: Mean & Median Essentials
16 April 2017
16 April 2017
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
Categorical or Qualitative
Quantitative or Numerical
tail
10 Dot Plots.ppt 27

28. Dot Plot: Describing Peaks
Dot Plots
Dot Plot: Describing Peaks
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16 April 2017
Peaks
Unimodal
Bimodal
Categorical or Qualitative
Quantitative or Numerical
Multimodal (3 or more peaks)
10 Dot Plots.ppt 28

29. How to Sort Data in Ascending Order
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.

30. Dot Plot: TI Essentials
Dot Plots
Dot Plot: TI Essentials
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16 April 2017
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
Categorical or Qualitative
Quantitative or Numerical
10 Dot Plots.ppt 30

31. Glucose Blood Levels Dot Plots 16 April 2017 16 April 2017
Categorical or Qualitative
Quantitative or Numerical
10 Dot Plots.ppt 31

32. Glucose Blood Levels Dot Plots 16 April 2017 16 April 2017
Categorical or Qualitative
Quantitative or Numerical
10 Dot Plots.ppt 32

33. WBNA EAST Free Throws—Data in Ascending Order

34. WBNA Free Throws—Dot Plot

35. Dot Plot: How to Describe It
Dot Plots
Dot Plot: How to Describe It
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16 April 2017
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.
Categorical or Qualitative
Quantitative or Numerical
10 Dot Plots.ppt 35

36. Fuel Consumption—Data

37. Fuel Consumption—Dot Plot