1. Welcome to Data Analysis and Interpretation
22-23 March 2011
Dick Schwanke

2. What will we be doing?
Examining different mathematical /statistical analysis techniques
Applying those techniques to our data.
Definition of Statistics: the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions

3. Who is Data?
What is data?
Fact or Proposition used to draw a conclusion or make a decision
Can be numerical
Can be non-numerical

4. Definitions Population: The group to be studied
Parameter is numerical summary of population
It is all Greek to me
Sample: The subset of the population
Statistic is a numerical summary of a sample
When in Rome, do as the Romans do

5. Definitions
Qualitative variable – classification of individuals based on some attribute or characteristic
Quantitative variable – provide numerical measures of individuals
Discrete Variable – has either countable or finite number of possible values
Continuous variable – has an infinite number of possible values

6. Some Administrative Details
Let us gather some data
Introductions
Name / Job Function / Excel Experience / 1 fact
Discuss these items with adjacent team member
Class roster completed
Schedule of these two days
Mix of lecture with problems
Computer lab with Microsoft Excel 2007

7. Organizing and Summarizing Quantitative Data
Step 1: Organize raw data into classes
Step 2: Create tables for the data:
frequency distribution
relative frequency distribution
cumulative frequency distribution
relative cumulative frequency distribution

8. Organizing and Summarizing Quantitative Data
Step 3: Create graphs
bar charts
pie charts
histograms
frequency polygons
ogives
stem-and-leaf plots
dot plots
Step 4: Be cautious of misleading graphs

9. Organizing and Summarizing Quantitative Data
Organize Data
Put into classes
Start with lowest value
Create Table
Frequency distribution
Relative frequency distribution,
Cumulative frequency distribution
Relative cum. frequency distrib.
Draw Graphic Displays
Histogram
Frequency polygon
Ogive
Stem & leaf plot
Steps:
Organize raw data into classes
Create table with frequency distribution, relative frequency distribution, cumulative frequency distribution, and relative cumulative frequency distribution
Create graphical displays with histogram, frequency polygon, ogive, stem & leaf plot
Page &p of 6

10. Ways of Displaying Data - Histogram
A graph using rectangles for each class of data, where the height of each rectangle is the frequency or relative frequency of the class
Note 1 : width of each rectangle is the same and rectangles touch each other
Note 2: methods for discrete and for continuous data

11. More Ways of Displaying Data – Cumulative Distributions
Cumulative frequency distribution: displays aggregate frequency of category i.e. total number of observations less than or equal to that category
Cumulative relative frequency distribution: displays the percentage (or proportion) of observations less than or equal to that category

12. More Ways of Displaying Data – Cumulative Distributions
Additional notes:
Works as a table or as a graph
For continuous data display the total number of observations less than or equal to the upper class limit of a class
Class midpoint – determined by adding consecutive lower class limits then divide the result by 2

13. More Ways of Displaying Data – Frequency Polygons
Construct with:
class on horizontal axis
frequency on vertical axis
Plot a point above each class midpoint
Draw straight lines between consecutive points
Page &p of 6

14. More Ways of Displaying Data – Ogives
Like a frequency polygon except represents cumulative frequency or cumulative relative frequency for the class
Construct with:
upper class limits on horizontal axis
cumulative frequency (or cumulative relative frequency) on vertical axis

15. More Ways of Displaying Data – Stem and Leaf Plot
Step 1: Select stem – the digit(s) to the left Leaf will be the rightmost digit
Step 2: Write the stems in a vertical column in increasing order. Draw vertical line to right of stems
Step 3: Write each leaf to right of its stem
Step 4: (re)Write leaves in ascending order

16. More Ways of Displaying Data – Stem and Leaf Plot
Other notes about stem and leaf plots:
Best used when data set is small
Can use “split stem” method if data seems too bunched
These sections give us many “tools” for our “toolbox”, so that we may use the best one (the best graphical display) for our audience’s understanding of our point

17. Shapes of Distributions
Uniform
Symmetric (bell shaped)
Skewed right (long tail to right)
Slewed left (long tail to left)

18. Graphic Suggestions Title both axis, label includes unit of measure
Include data source when appropriate.
Minimize white space in the graph, using available space to let the data stand out
Avoid clutter: pictures, excessive gridlines
Avoid distortion. Never lie about the data
Avoid three dimensional charts and graphs
Let the data speak for themselves.