1. Organizing Information Pictorially Using Charts and Graphs
Topic 1
Organizing Information Pictorially Using Charts and Graphs

2. Characteristics of the individuals under study are called variables
Some variables have values that are attributes or characteristics … those are called qualitative or categorical variables
Some variables have values that are numeric measurements … those are called quantitative variables
The suggested approaches to analyzing problems vary by the type of variable

3. Examples of categorical variables
Gender
Zip code
Blood type
States in the United States
Brands of televisions
Categorical variables have category values … those values cannot be added, subtracted, etc.

4. Examples of quantitative variables
Temperature
Height and weight
Sales of a product
Number of children in a family
Points achieved playing a video game
Quantitative variables have numeric values … those values can be added, subtracted, etc.

5. 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

6. A relative frequency distribution lists
The relative frequencies are the proportions (or percents) of the observations out of the total
A relative frequency distribution lists
Each of the categories
The relative frequency for each category

7. A relative frequency table for this qualitative data is
A relative frequency table can also be constructed with percents (50%, 12.5%, and 37.5% for the above table)
Color
Relative Frequency
Blue
.500
Green
.125
Red
.375

8. Bar graphs for categorical data
Bar graphs for our simple data (using Excel)
Frequency bar graph
Relative frequency bar graph

9. Comparative Bar Graph
An example side-by-side bar graph comparing educational attainment in 1990 versus 2003

10. Pie Chart
An example of a pie chart

11. Histogram for quantitative data
Quantitative data sometimes cannot be put directly into frequency tables since they do not have any obvious categories
Categories are created using classes, or intervals of numbers
The data is then put into the classes

12. For ages of adults, a possible set of classes is
20 – 29
30 – 39
40 – 49
50 – 59
60 and older
For the class 30 – 39
30 is the lower class limit
39 is the upper class limit
The class width is the difference between the upper class limit and the lower class limit
For the class 30 – 39, the class width is
40 – 30 = 10

13. All the classes have the same widths, except for the last class
The class “60 and above” is an open-ended class because it has no upper limit
Classes with no lower limits are also called open-ended classes

14. In this table, there are 1147 subjects between 30 and 39 years old
The classes and the number of values in each can be put into a frequency table
In this table, there are 1147 subjects between 30 and 39 years old
Age
Number
(frequency)
20 – 29
533
30 – 39
1147
40 – 49
1090
50 – 59
493
60 and older
110

15. Good practices for constructing tables for continuous variables
The classes should not overlap
The classes should not have any gaps between them
The classes should have the same width (except for possible open-ended classes at the extreme low or extreme high ends)
The class boundaries should be “reasonable” numbers
The class width should be a “reasonable” number

16. Just as for discrete data, a histogram can be created from the frequency table
Instead of individual data values, the categories are the classes – the intervals of data

17. Stemplots
A stemplot is a different way to represent data that is similar to a histogram
To draw a stem-and-leaf plot, each data value must be broken up into two components
The stem consists of all the digits except for the right most one
The leaf consists of the right most digit
For the number 173, for example, the stem would be “17” and the leaf would be “3”

18. Stemplots In the stem-and-leaf plot below The smallest value is 56
The largest value is 180
The second largest value is 178

19. Stemplots To draw a stemplot
Write all the values in ascending order
Find the stems and write them vertically in ascending order
For each data value, write its leaf in the row next to its stem
The resulting leaves will also be in ascending order
The list of stems with their corresponding leaves is the stem-and-leaf plot

20. Comparative Stemplots
If we wanted to compare two sets of data, we could draw two stem-and-leaf plots using the same stem, with leaves going left (for one set of data) and right (for the other set)

21. Some common distribution shapes are
A useful way to describe a variable is by the shape of its distribution
Some common distribution shapes are
Uniform
Bell-shaped (or normal)
Skewed right
Skewed left

22. A variable has a uniform distribution when
Each of the values tends to occur with the same frequency
The histogram looks flat

23. A variable has a bell-shaped distribution when
Most of the values fall in the middle
The frequencies tail off to the left and to the right
It is symmetric

24. A variable has a skewed right distribution when
The distribution is not symmetric
The tail to the right is longer than the tail to the left
The arrow from the middle to the long tail points right
Right

25. A variable has a skewed left distribution when
The distribution is not symmetric
The tail to the left is longer than the tail to the right
The arrow from the middle to the long tail points left
Left

26. The two graphs show the same data … the difference seems larger for the graph on the left
The vertical scale is truncated on the left

27. However, it is much more than twice as large as the one on the left
The gazebo on the right is twice as large in each dimension as the one on the left
However, it is much more than twice as large as the one on the left
Original
“Twice” as large