LSP 120: Quantitative Reasoning and Technological Literacy

Özlem Elgün

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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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• Detailed tutorial on how to create charts • on Excel (2007)• On Excel (2003)

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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 Prepared by Ozlem Elgun 4

• Reminder!– When selecting the cells on Excel to make the pie chart you

should select both the categories and the values (either the absolute numbers or percentages).

– Do not to include the total value/category in your pie chart and make sure you add percentage data labels.

– Make sure that the graph has a descriptive title.

– The percentages in the pie chart should show two decimals.

• See the detailed tutorial on how to create charts on Excel (2007).

Pie charts

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• Bar charts can be used whenever there is a quantitative value associated with the a categorical variable:

• 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.

• Bar charts can 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.

• 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

Bar charts (in Excel: Collumn charts)

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• 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 accordingly to correct this.

Important tips, reminders about Bar Charts

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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.)

• 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, maximum and minimum values, 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:

• What is the purpose of making a graph from this data?

• What type of graph should you make?– Pie, bar, xy?

• Decide on a title and consider the the W's (who, what, where and when)

• Legend: yes no

• Descriptive x-axis label (if applicable)

• Descriptive y-axis label (if applicable)

• Scale (if applicable)

• Source

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• Guides: – How to create charts on Excel 2007– Describing Graphs– Graphing Checklist

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Tutorials on How to Describe Graphs

How to describe the graphs

• Your 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 displayed.

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