1. Presentation of Data

2. Presentation Topics Tabulating and Graphing Numerical Data:
Frequency Distributions: Tables, Histograms, Polygons
Cumulative Distributions: Tables, the Ogive

3. Presentation Topics (continued)
Tabulating and Graphing Univariate Data:
The Summary Table
Bar and Pie Charts
Tabulating and Graphing Bivariate Data:
Side by Side Bar charts
Graphical Excellence and Common Errors in Presenting Data

4. Tabulating and Graphing Numerical Data
41, 24, 32, 26, 27, 27, 30, 24, 38, 21
Frequency Distributions
Cumulative Distributions
Ordered Array
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
4 1
Ogive
Histograms
Stem and Leaf
Display
Tables
Polygons

5. Tabulating Numerical Data: Frequency Distributions
(continued)
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Relative
Frequency
Percentage
Class Frequency
10 but under
20 but under
30 but under
40 but under
50 but under
Total

6. Graphing Numerical Data: The Histogram
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
No Gaps Between Bars
Class Midpoints

7. Graphing Numerical Data:
The Frequency Polygon
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Class Midpoints

8. Tabulating Numerical Data:
Cumulative Frequency
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58
Cumulative Cumulative
Class Frequency % Frequency
10 but under
20 but under
30 but under
40 but under
50 but under

9. Graphing Numerical Data: The Ogive (Cumulative % Polygon)
Data in ordered array:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

10. Graphing Categorical Data: Univariate Data
Graphing Data
Tabulating Data
The Summary Table
Pie Charts
Pareto Diagram
Bar Charts

11. (University Revenues)
Summary Table
(University Revenues)
Revenue Category Amount Percentage
(in thousands $)
Patient Services
Tuition/fees
Appropriations
Grants/Contracts
Total
Variables are Categorical.

12. Bar Chart
Enrollment Summary

13. Students by Classification
Pie Chart
(for a factbook)
Students by Classification
Seniors 15%
Freshmen 42%
Sophomores 14%
Percentages are rounded to the nearest percent.
Juniors 29%

14. Tabulating and Graphing Bivariate Categorical Data
Side by Side Charts

15. Graphing Categorical Data: Bivariate Data
Side by Side
Chart

16. Importance of Graphical Excellence
It is easy to understand.
We can make comparisons between different samples.
This technique can be used universally.
It saves time and energy.
Data can be easily remembered
Data can be condensed with the help of diagrams.
This gives us much more information as compared to tabulation.
This technique can be used for numerical type of statistical analysis.
Diagrams have impressive value also.

17. Errors in Presenting Data
Using ‘chart junk’
No relative basis
In comparing data
Batches
Compressing the
Vertical axis
No zero point on the

18. ‘Chart Junk’  Bad Presentation Good Presentation $ Minimum Wage
1960: $1.00 4
1970: $1.60 2
1980: $3.10
1990: $3.80
1960
1970
1980
1990

19. A’s received by students. A’s received by students.
No Relative Basis 
Bad Presentation
Good Presentation
A’s received by students.
A’s received by students.
Freq. %
300
30%
200


10%  FR SO JR SR FR SO JR SR
FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior

20. Compressing Vertical Axis
Bad Presentation
Good Presentation
Quarterly Income
Quarterly Income $ $
200 50
100 25
The number of information-carrying (variable) dimensions depicted should not exceed the number of dimensions in the data. Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4

21. No Zero Point on Vertical Axis
Bad Presentation
Good Presentation
Monthly Expenses
Monthly Expenses $ $ 45 45 42 42 39 39 36 36 J F M A M J J F M A M J
Graphing the first six months of sales.

22. No Zero Point on Vertical Axis
Bad Presentation
Good Presentation
Monthly Expenses
Monthly Expenses $ $ 45 60 42 40 39 20
Always show zero on your chart, then indicate the level of beginning measurement. 36 J F M A M J J F M A M J
Graphing the first six months of sales.