1. Univariate Visualization
CMSC 120: Visualizing Information
2/21/08

2. Types of Data
Qualitative: pertaining to fundamental or distinctive characteristics
Nominal: unordered (e.g., names, types)
Ordinal: ordered (e.g., cold, warm, hot)
Quantitative: pertaining to an amount of anything
Discrete: isolated intervals
Continuous: unbroken, immediate connection

3. Univariate Data
A single attribute

4. Weather Conditions: 2/17/08

5. Univariate Data A single attribute Characterize Observations
Temperature: quantitative
Condition: qualitative
Characterize Observations
Number
Type
Similarity

6. The Raw Data: A Dot Plot n ≤ 20 Distance between individual points
Emphasize clusters, gaps, outliers
Reveal frequency of each observation

7. Frequency Table Groups observations by class
Quantitative: an interval or part of the range of the sample
Qualitative: a potential value
Frequency: number of observations that fall into a class
Relative Frequency: frequency / sample size

8. Frequency Table Clear 5 17 % Mostly Cloudy 1 3 % Partly Cloudy 3 10 %
Condition
Frequency
Relative Frequency
Clear 5
17 %
Mostly Cloudy 1
3 %
Partly Cloudy 3
10 %
Overcast 16
55 %
Light Rain 4
14 %

9. Frequency Table 25-30 7 24% 30-35 1 3% 35-40 3 10% 40-45 45-50 13 45%
Temperature
Frequency
Relative Frequency
25-30 7
24%
30-35 1 3%
35-40 3
10%
40-45
45-50 13
45%
50-55
0 %
55-60
3 %
60-65

10. Stem and Leaf Plots Stem Leaf 2 5566789 3 1567 4 02555566677788999 5 8
Temperature 25 26 27 31 36 40 42
Stem
Leaf 2 5
Stem
Leaf 2 3
1567 4 5 8 6
Stem
Leaf 2
5567
Separate each number into a stem (class) and a leaf
Group numbers with the same stems

11. Pie Charts
Useful for qualitative data
Must sum to 100%

12. Histograms Pictorial representation of a Frequency Table
Set of boxes whose area represents relative frequency of observations per class
Total Area of all boxes = 100%
Shape of histogram determined by box
Number = number of classes
Width = class interval
Height

13. Histogram

14. Histogram

15. Patterns Outliers: observations well away from main body of data
Number of peaks (modes): most popular values
Abrupt Changes

16. Shape Central Values: where data appear to be centered
Mode
Mean
Central Values: where data appear to be centered
Spread: how spread out the points are
Symmetry (Skew)

17. How to Lie: Aggregation
Process of putting data into groups
Allows user to compare among groups
Hides differences between groups
Too little: noise of individual data overwhelms overall pattern
Too much: important patterns are hidden within groups

18. Interval Size = 7 Degrees

19. Interval Size = 14 Degrees

20. Shape of Shell Aperture

21. Shape of Shell Aperture

22. Shape of Shell Aperture

23. Shape of Shell Aperture

24. Shape of Shell Aperture

26. The 5 Number Summary Continuous, Quantitative Data
Order data from lowest value to highest
Minimum: lowest value
Lower Quartile: cuts off ¼ of the data
Median: middle value
Upper Quartile: cuts off ¾ of the data
Maximum: highest value

27. Minimum = 25 Lower Quartile = 30.9 Median = 45 Upper Quartile = 46.9
26.1 27 28
28.9
30.9
35.6 37
39.9
42.1
44.6 45 46
46.4
46.9 48
48.2
48.9
57.9
60.1
Minimum = 25
Lower Quartile = 30.9
Median = 45
Upper Quartile = 46.9
Maximum = 60.1

28. Box and Whisker Plot Maximum = 60.1 Outlier Largest Non-Outlier
Upper Quartile = 46.9
Median = 45
50% of Data
Lower Quartile = 30.9
Smallest Non-Outlier
Minimum = 25

29. Shell Shape