Constructing Charts from Categorical Data

 Your Writing Prompts. Constructing Charts from Categorical Data 

Here is a spreadsheet showing data about our class that I collected from the Introduction survey:  

::Class Data Spreadsheet::

Your job for this part of the assignment is to create displays that collect and organize this data, as described below.

You can make choices about how to group and organize the data into categories.  This is more or less straightforward for some categories, but more complicated for others.  There is no best way to do this but depends on what kind of story you’re trying to tell with the data.  As a rule of thumb, too many different categories usually gives information overload whereas too few categories doesn’t tell an interesting enough story.  Finding the middle ground depends on the tastes and preferences of the graph-maker (that’s you!).

a. Simple Bar Graph

Choose one of the variables “Where are you from?”, “What is your favorite subject in school?”, or “What is your favorite music?”

Create a bar chart to summarize this class data for the variable you chose.  Along the way, you will need to organize the responses into your own categories.  When you do this, explain your organizational choices and why you made them to your reader.

(note: Google Sheets and Excel do have ways of making bar charts automatically, but that is not my intention for this assignment.  Rather than just pressing a button to create the chart, I want you to construct it yourself.)

b. Contingency Table and Compound Bar Graph

Now choose any of the other two categorical variables from the whole data set that you think are most interesting.  Construct a contingency table showing the relationship between those variables.

Again, if you need to make organizational choices, explain them and your motivation for making them to your reader.

After you’ve made a contingency table, use it to create either a stacked bar chart or a multi-column bar chart (see ::this page:: for more details) to show this information.  Explain to your reader why you chose the format that you did.

2. Visualizing Quantitative Rent Data

Here is a link to a data set showing the ::average monthly rent price of a 2-bedroom apartment:: in various similarly-sized cities across America (Seattle, Denver, Columbus, Detroit, Austin).  You will choose three cities to compare in the analysis below.

::This worksheet:: provides a guide to help you use Google Sheets to do this analysis.  

(You’re welcome to use Excel instead of Google Sheets, but some of the details may vary.)

1. Box Plots, medians, and quartiles

For each city, use a spreadsheet to compute the min, Q1, median, Q3, and max. 

Describe what this information tells you about these cities.  Be specific.

For each city, use a spreadsheet to compute the interquartile range, fence length, upper and lower fences.

Use this information to draw adjacent boxplots of the rent prices in these cities.  Draw these boxplots along the same scale so that we can directly compare them.

Use your box plots and computations to write a comparison between the data sets.

Rank the cities in order of their “center.” (How is center measured here? How do the box plots show this?)

Rank the cities in order of their “spread.” (How is spread measured here? How do the box plots show this?)

Which city has outliers?  How can you tell from the box plot?

What other observations can you make from these computations and pictures?

2. Histograms, means, standard deviations

For each city, use a spreadsheet to compute the mean and standard deviation.

Describe what this information tells you about these cities.  Be specific.

For each city, use the spreadsheet to draw a histogram of the rent distribution.  

Use the same lower and upper limit on your x-axis .

Use the same bin size for all 5 graphs so that you can directly compare them.

Use your histograms and computations to write a comparison between data sets.

Rank the cities in order of their “center.” (How is the center measured here? How can we see this visually on a histogram?)

Rank the cities in order of their “spread.” (How is spread measured here? How can we see this visually on a histogram?)

Which city has outliers? How can you tell from the histogram?

What other observations can you make from these computations and pictures? 

3. Summary

Compare the two measures of center.  Are they similar or different for each city?

Compare the two measures of spread.  Are they similar or different for each city?

What information and conclusions do you think are easier to see using the boxplots?

What information and conclusions do you think are easier to see using the histograms?

Write 5-6 sentences speculating about why the rent prices are like this in these cities.  What could cause rent prices to be high or low? What could cause rent prices to be spread apart or concentrated in a city?

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