Transcript LSP 120: Quantitative Reasoning and Technological Literacy

LSP 120: Quantitative Reasoning
and Technological Literacy
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Making and Interpreting Graphs
There are 3 types of graphs we use in Quantitative Reasoning class:
1. Pie Charts
2. Bar charts
3. XY graphs (or line graphs)
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Pie charts
• We can only use pie charts when we have a quantitative
variable associated with a list of categories, where both the
categories and the quantities each add up to a whole.
• The categories must also be disjoint. (not overlapping)
• Consequently, pie charts are very limited in their
applicability.
• The most common student errors with pie charts are to use a
pie chart on a set of categories that do not make a whole and
to use a pie chart when the categories overlap.
• On class website: click on EnergyConsumption.xls
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Pie charts
• Reminder!
• Select both the categories and the values (either the
absolute numbers or percentages).
• Do not to include the category that lists the total value in
your pie chart and make sure you add percentage data
labels.
• Make sure that the graph needs a descriptive title
• Be aware that the percentages in the pie chart might need
to be "increased" to show one or two decimal places. We will
do this in class but also see the detailed tutorial on how to
create charts on Excel (2007).
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Bar charts (in Excel: Column charts)
•
Bar charts can be used whenever there is a quantitative value associated with the a
categorical variable:
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Example: percentage of different home heating sources in years 1950 and 1997. In this case,
percentages are the quantitative values associated with the categorical variable of different
home heating sources. Years 1950 and 1997 are two separate series that have data on this
categorical variable.
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Bar charts even be used with a quantitative x-axis.
•
They are great when you have a limited amount of data, or when you want to compare more
than one series.
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Advantages and Disadvantages of Multiple Bar Charts
– The main advantage of bar charts is their succinctness and the ability they afford to make comparisons
within categories and across categories; they are best used in printed works so that a viewer can study
them carefully.
– Their disadvantage is that they sometimes present far to much information to view and as part of
presentations; it is hard to make a single, clear point with them, and presenters tend not to leave them up
long enough to absorb the information fully.
•
On class website: click on HomeHeating.xls
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Important tips, reminders about Bar Charts
• Important! If you do use a bar chart and have years along the x-axis, be sure
the years are in equal intervals. Otherwise, you can be guilty of creating a
misleading graph.
• One item to address is that Excel, by default, puts a legend on every bar
graph and xy graph. Remove the legend (click on it and press delete) when
there is only one data series. On the other hand, a legend is absolutely
required in a multiple bar graph where multiple series are involved. We will
learn how to re-label legends in class. Also, see Creating Graphs using Excel
2007 for instructions on how to label each series in a multiple bar graph.
• A very common problem with multiple bar charts is that, very frequently
people make bar charts with quantitative data on the x-axis (i.e. years), but
they are not careful about the fact that a bar chart treats the x-axis
categorically. On excel you need to right click on the chart and click on add
data to edit the series involved to correct this.
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XY graphs
• xy graphs should be used when you have "a lot" of data points and the categories
along the x-axis are numerical.
• In Excel, the students will choose the xy scatter type and then choose a graph
option with connected data points (usually Layout 9 under chart design tools on
Excel 2007, but you can also play with other xy scatter chart layouts).
• Important!!!: What Excel calls a "line graph" is very confusing and should
essentially never be used. (Excel "line graph" always treats the x-axis categorically,
which is a seemingly endless source of mistakes.)
•
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The goal is for students to be able to make xy graphs and to write paragraphs
which carefully describe what the graph is saying about the context, generally going
from left to right as a trend, telling the "story" of the graph. In order to do this you
can use some very useful vocabulary such as: increasing, decreasing, absolute
maximum and minimum, relative maximums and minimums, increasing at an
increasing/decreasing rate, decreasing at an increase/decreasing rate, periodic.
On class website: click on LakeMichiganLevels1988-2006.xls
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You need to create an effective graph.
• To create an effective graph, you need to address each of the following
items each time you make a graph:
•
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What is the purpose of making a graph from this data?
What type of graph should you make?
– Pie, bar, xy?
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Decide on a title and consider the the W's (who, what, where and when)
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Legend:
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Descriptive x-axis label (if applicable)
yes
no
• Descriptive y-axis label (if applicable)
• Scale (if applicable)
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Source
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Tutorial on How to Describe Graphs
• Describing Graphs
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How to describe the graphs
• A graph should be able to stand alone without any
words to tell the reader what they are looking at.
• If the reader doesn't understand the graph without
a caption (or story) then the graph isn't very good.
• In the paragraph describing the graph, you should
first tell your audience briefly what the graph is
about, and also point out what you want the
reader to know about the graph.
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Misleading Graphs
• Difference between a bad graph and a
misleading graph
• Bad graph: a graph with incorrect information,
incorrectly designed. Etc…
• Misleading graph: data is "correctly" displayed
on the graph and yet gives different messages
depending on how it is formatted.
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