Data
Representing Data Using Graphs
MATH 112
Section 7.1: Representing and Interpreting Data
Prof. Jonathan Duncan
Walla Walla College
Fall Quarter, 2006
Conclusion
Data
Representing Data Using Graphs
Outline
1
Data
2
Representing Data Using Graphs
3
Conclusion
Conclusion
Data
Representing Data Using Graphs
Conclusion
Data
In chapter 7 we focus on investigating ideas of data and chance.
Two Questions about Data
When presented with a set of data, there are two questions which
you should ask:
1
Reliability
How accurate is the collected data? Would two people
collecting this data have garnered the same results?
2
Validity
Were the methods used and questions asked appropriate with
respect to the questions we want answered?
Example
In your hand-squeezing exercise, were the methods you chose to
use reliable? Where they valid?
Data
Representing Data Using Graphs
Tabular Data
In many instances, data will be presented as a table of values.
Consider the following example.
Example
The table below lists the number of U.S. households with VCR’s
during each year from 1978 to 1990.
Year
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
Households (000’s)
200
400
840
1440
2530
4580
8800
17,600
30,920
42,560
51,930
58,400
66,940
Observations:
Ownership has increased
Doubled each year to 1987
000’s represent thousands
Questions:
How accurate is the data?
How valid is the data?
Why start at 1978 and end at 1990?
Conclusion
Data
Representing Data Using Graphs
Questions about Tabular Data
As with any method of displaying data there are both good and
bad things about using tables.
Advantages of Tabular Data
What are some of the advantages of displaying data in a table?
Data is well organized
It is easy to detect larger trends
We can see actual values for each category
Disadvantages of Tabular Data
What are some of the disadvantages to displaying data in a table?
Raw data is not included
Hard to spot smaller trends
Not as visual as graphs, charts, etc.
Conclusion
Data
Representing Data Using Graphs
Two Types of Graphs
As we saw in the last slide, representing data in tables does have
some disadvantages. Graphs can help overcome some of these.
Example
The following graphs display the VCR data from the previous
example in two different ways.
Conclusion
Data
Representing Data Using Graphs
Conclusion
Line vs. Bar Graphs
Each type of graph has advantages and disadvantages.
Line Graphs
Easy to see the slope
Emphasizes changes over time
Can be misleading – not a straight line between years
Bar Graphs
Often easier to understand
Emphasizes change between adjacent years
accurately represents the data given
Example
To represent this data set, which type of graph would you choose
and why?
Data
Representing Data Using Graphs
Conclusion
Graphing Cautions
There are several cautions to keep in mind when creating graphs.
Graphing Cautions
Avoid each of the following when constructing graphs.
Scale – it is important that the scale of the graph be
consistent throughout the graph.
Horizontal Spacing – Maintain consistent horizontal spacing
between points on the graph.
Missing Data Points – If you are missing data points, do not
alter your horizontal scale, rather leave blanks.
Example
For each caution, construct a graph which violates the rule and
explain why it misrepresents the data being presented.
Data
Representing Data Using Graphs
Conclusion
Circle Graphs
When attempting to present a breakdown of a total into parts
represented by a percent or piece of the whole, a circle graph
(sometimes called a pie chart) is one of the best ways to do this.
Example
Construct a circle graph to represent the distribution of expenses in
the average American family.
Category
Food
Medical
Housing
Household
Transportation
Amount
907.4
1,032.3
855.9
646.5
647.4
Data
Representing Data Using Graphs
Conclusion
Choosing a Graph Type
We have seen several different graph times in this section. How do
you choose which type of graph is best suited for a given set of
data?
Bar Graphs
Bar graphs are best suited for displaying sets of data side by side or
displaying data which has “gaps” between the values.
Line Graphs
Line graphs are best suited for displaying a single data set over
time or emphasizing change in data values.
Circle Graphs
Circle graphs are best suited for displaying relationships between
parts of a whole.
Data
Representing Data Using Graphs
Conclusion
Graphing with a Spreadsheet
As we have seen, graphing can be relatively time consuming. This
is an area where the computer can help speed things up.
Example
Use Excel to construct each of the following graphs:
A Bar Graph
A Line Graph
A Circle Graph
Data
Representing Data Using Graphs
Important Concepts
Things to Remember from Section 7.1
1
Reliable vs. valid data
2
Methods for representing data
3
The advantages/disadvantages of various types of graphs
Conclusion