1. Organizing, Displaying and Interpreting Data
Chapter 3:Hawkes
STAT 3090

2. Statistics: The science of data
Data: information about individuals
Variables: characteristics of individuals
The information
Exploratory Data Analysis
How to extract information from data?
First step => “Plot the data”
“A picture is worth 1000 words.”

3. What can we learn from a picture?
Distribution of the variable(s)
Value and Frequency
Shape
Center
Spread
Variability
Extreme values

4. Two Basic Types of Data Categorical Quantitative Qualitative
male/female, colors, phone numbers, race
Places individual into one or several “categories”
Have no “value”
can’t perform math functions
Quantitative
Numerical values – temperature, money, time
Can perform mathematical functions
Can be discrete (finite) – number of children in famly.
Or continuous – age, time, distance

5. Displaying Data Quantitative Categorical (Qualitative)
Numerical values
Continuous or discrete
Frequency plots
Maintain original values
Histograms
Create ‘groups’ ‘bins’
Bars touch (continuous data)
Stemplots
Dot plots
Time Series
Categorical
(Qualitative)
Counts, Discrete Data
Pie Charts
Bar Graphs (bars do not touch)
Frequency Tables
Spreadsheets
Relative Frequency Tables

6. Qualitative Data: The Common Displays

7. Frequency distribution
Summarizes data into classes and provides in tabular form a list of classes along with the number of observations in each class Must have a frequency distribution before any type of graph can be constructed Use Excel “count if” function

8. Frequency Table 60 15 5 20 65 35 Cell Phone
No Cell Phone
Accidents 60 15
No Accidents 5 20
Column
Total 65 35

9. Relative Frequency Distribution
The proportion (or percent) of observations within a category
Found using the formula:
___frequency
relative frequency = sum of all frequencies
Relative Frequency Distribution lists each category of data with the relative frequency?
What is the advantage of using a relative frequency distribution over simple counts?

10. Relative Frequency Table
Cell Phone %
Accidents 60
92%
No Accidents 5 7%
Column
Total 65
100

11. Bar graph (or chart)
A simple graphical display in which each bar corresponds to the number of observations in a category
Label each category of data on either horizontal or vertical axis
Rectangles of equal width for each category
Height of each rectangle represents category’ frequency OR relative frequency
Bars don’t touch
Bars should always start at zero
Used for qualitative or discrete quantitative data

12. Example of Bar Graph with Time (side-by-side)

13. Pareto Chart
A Pareto chart is a bar graph where the bars are drawn in decreasing order of frequency or relative frequency

14. Pie Charts
A circle divided into sectors. Each sector represents a category of data. The area of each sector is proportional to the frequency of the data.
Proportions (percents)MUST add to 1 (100%)
Angle of the “wedges” :
(frequency)/(total # observations) = proportion
(proportion)(360) = Angle

15. Pie Chart (What’s Missing?)

16. QuantITative Data: The Common Displays

17. Frequency Distribution for Quantitative Data
Not appropriate to have a bar for each value so develop classes
Number of classes generally more than 4 but less than 20
Class Width = (Largest Value – Smallest Value)/Number of Classes
Should be rounded to whole numbers for ease of understanding
Class boundaries: Subtract 0.5 from lower limit and add 0.5 to upper limit.
(See page 93)

18. Other Frequency Distribution for Quantitative Data
Relative Frequency Distribution
Same process as for Qualitative Data
Cumulative Frequency Distribution
Add frequencies in each successive class
Total must equal total number of observations

19. Histogram
A bar graph of a frequency or relative frequency distribution in which the heights of each bar corresponds to the frequency or relative frequency of each class.
Edges touching
Covers entire range of values of a variable
May need to create “bins”

20. Guidelines for “Bins” Cover complete range of data
Group or bin size is basically arbitrary
Can have open or closed bins
Less than 5,5 to 10, 11 to 15, over 15 (for example)
Bins are mutually exclusive
Bins can be of equal or unequal size
Reflects the clumping of the observations
General formula for interval size
I = H – L k
Where H = value of highest observation, L = value of lowest, and k = number of classes (bins, groups)

21. Interpreting Histograms
Patterns of the data
Shape, center, spread
Shape
Symmetrical
Skewed right (tail stretches to the right)
Skewed left (tail stretches to the left)

22. Stem – and – Leaf Display
Separate each observation into stem
All but final digit
And leaf
Final digit
Stems have as many digits as needed; each leaf is only one digit

23. Stemplot
Data: 32, 37, 39, 40, 41, 41, 41, 42, 42, 43, 44, 45, 45, 45, 46, 47, 47, 49, 50, 51
3 | 2 7 9
4 |
5 | 0 1

24. Plots each observation against the time at which it was measured
Timeplots
Plots each observation against the time at which it was measured
Time on x-axis (horizontal)
Variable on y-axis (vertical)

25. Scatterplot showing Sales by Region over Time