1. Organizing and Presenting Data
GTECH 201
Session 11

2. Terminology Classes Frequency Frequency Distribution
Categories for grouping data
Frequency
Number of observations that fall in a class (frequency is a count)
Frequency Distribution
A listing of all classes along with their frequencies
Relative Frequency
The ratio of the frequency of a class to the total number of observations
Relative Frequency Distribution
A listing of all classes along with their relative frequencies
Width/Class Interval
The difference between the upper and lower cut points (breaks) of a class

3. Organizing Data Classification Rules
Aim is to create categories or classes
First step is to compute range
Range = Largest Value – Smallest Value
Interval or Ratio Scale data only
Class Intervals
Width of Class Interval
Equal based on range
Unequal based on range
Quantile (Quartile or Quintile)
Natural

4. Classification Methods
Natural breaks
Equal interval
Quantile
Manual

5. How to Decide (on a classification scheme)
Rule of thumb: classes
Classification histogram (see later today)

6. Classification method How many classes to have
How to Decide, part II
Classification method
When to use
How many classes to have
Natural breaks
When attributes are distributed unevenly across the overall range of values
Look for natural groups
Equal interval
When you want all classes to have the same range
Easily understood interval, such as 2, 50, 1000, etc.
Quantile
When attributes are distributed in a linear fashion
Determined by purpose of the map
Manual
When you want classes to break at specific values

7. Graphs
Line graph
Bar graph
Scatterplots

8. Creating a Line Graph
The growth of the population of students at a Midwestern university is as follows

9. Line Graph

10. Bar Graphs
Here are data on the percent of females among people earning doctoral degrees in 1990, in several different fields of study

11. Bar Graph

12. Scatter Plots
Graph bi-variate data when both variables are measured in an interval/ratio or ordinal scale
Units for one variable are marked on the horizontal axis
Independent variable should always go on the horizontal, x axis

13. Scatterplots
Survey of 3368 people asking them to estimate number of calories in common foods.

14. Example
A city planner collected data on the number of school age children in each of 30 families.
Construct a grouped data table using classes based on a single value

15. Computing Frequency There are three ways you can create classes
a < but not equal to b
b < but not equal to c
a – b, c – d, e - f
single value grouping

16. Distributions Histograms Difference between histograms and bar graphs
Bars in a histogram are always vertical
Base scale is marked off in equal units; there is no base scale in a bar graph
Width of bars in a histogram have meaning
Bars in a histogram touch each other

17. Constructing a Histogram
Histogram – height of bar equal to frequency of class represented
Bar extends from lowest value to highest value of the class

18. Histogram Chart

19. Frequency Polygons Similar to a histogram
Midpoint of the class is indicated
Points connected by straight lines
Cumulative frequency polygon, ogive