1. Statistics-MAT 150 Chapter 2 Descriptive Statistics
Prof. Felix Apfaltrer
Office:N518
Phone: 7421
Office Hours: Tue/Thu 1:30-3:00pm

2. Characteristics of data
Center middle or average value
Variation measures the amount data values vary
Distribution nature or shape of distribution of data
Outliers values that are very far out
Time changing characteristics of data in time
Mnemonic: CVDOT - computer viruses destroy or terminate
Observe data set and give intuitive examples of these characteristics!

3. Organizing Qualitative Data
Qualitative data values can be organized by a frequency distribution
A frequency distribution lists
Each of the categories
The frequency for each category
Good practices in constructing bar graphs
The horizontal scale
The categories should be spaced equally apart
The rectangles should have the same widths
The vertical scale
Should begin with 0
Should be incremented in reasonable steps
Should go somewhat, but not significantly, beyond the largest frequency or relative frequency

4. blue, blue, green, red, red, blue, red, blue
A simple data set is
blue, blue, green, red, red, blue, red, blue
A frequency table for this qualitative data is
The most commonly occurring color is blue
Color
Frequency
Blue 4
Green 1
Red 3
The relative frequencies are the proportions
(or percents) of the observations out of the total
Color
Relative Frequency
Blue
.500
Green
.125
Red
.375

5. Bar graphs for our simple data (using Excel) 1) Frequency bar graph
2) Relative frequency bar graph
Good practices in constructing bar graphs
The horizontal scale
The categories should be spaced equally apart
The rectangles should have the same widths
The vertical scale
Should begin with 0
Should be incremented in reasonable steps
Should go somewhat, but not significantly, beyond the largest frequency or relative frequency

6. An example side-by-side bar graph comparing
educational attainment in 1990 versus 2003

7. A pie chart is a circle divided into sections, one for each category
The area (angle) of each sector is proportional to the frequency of that category
Pie charts are useful to show the relative proportions of each category, compared to the whole

8. Data

9. Organizing Quantitative Data: The Popular Displays
Learning objectives
Organize discrete data in tables
Construct histograms of discrete data
Organize continuous data in tables
Construct histograms of continuous data
Draw stem-and-leaf plots
Draw dot plots
Identify the shape of a distribution

10. Frequency distributions
Lower class limits: 0,100,…
Upper class limits: 99,…
Class boundaries: numbers used to separate classes without gaps; 99.5, 199.5,…
Class midpoints: center of class; 49.5, 149.5, …
Class width: diference between two consecutive lower (or upper) class limits: 100

11. Constructing frequency distribution
Decide on number of classes n : 5-20
Class width =(highest value-lowest value)/n
Starting point: lowest data value of convenient lowest value (smaller)
List lower class limits
List upper class limits
Tally data: count the data values falling in each class
Q. How do you go from one to the other?

12. Cummulative Frequency distribution

13. Visualizing data Histogram
A histogram is a bar graph in which the horizontal scale represents classes of data values and the vertical scale represents frequencies

14. (Relative) frequency histograms, polygons and ojives

15. Other ways of representing data
Dot plot: find out what this is!
Stem-and-leaf plot
keep track of all your data
only works in certain specific cases
condensed stem-and-leaf plot

16. …and more ways of representing data
Which of the following are represented in the data sheet given in class?
Pareto charts
Pie charts
Time charts
Napoleon’s chart
Scatter plot

17. Napoleon’s campaign chart 1812

18. Class sheet page 1

19. Organizing and Summarizing Data Summary
Summaries of qualitative data
Frequency tables
Bar graphs
Summaries of quantitative data
Histograms
Pie graphs, time-series graphs, etc.
Cumulative frequencies, ogives, etc.