Summarizing Categorical Data

STAT 20: Introduction to Probability and Statistics

Concept Questions

CQ 1

• The next four subquestions are based on the same table.

The table below displays data from a survey on a class of students.

What proportion of the class was in the marching band?

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An example of a marginal proportion.

What proportion of those in the marching band where juniors?

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An example of a conditional proportion.

What proportion were sophomores not in the marching band?

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An example of a joint proportion.

What were the dimensions of the raw data from which this table was constructed?

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How would you characterize the association between these two variables?

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CQ 2

Political affiliation and college degree status of 500 survey participants.

Which group is the largest?

The General Social Survey is a widely used sources of data on the attitudes, behaviors, and attributes of Americans. This plot shows the relationship between the political affiliation and college degree status of 500 participants.

Cannot tell which group is the largest since this plot as been normalized so that the proportions within each party sum to 1. The unnormalized plot on the following slide is one that allows us to answer this questions.

The unnormalized bar chart of counts preserves original counts and thus is good at comparing joint proportions. The normalized bar count shows condition proportions and thus is good for showing associations between variables.

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CQ 3

What does this plot show?

Important note: it looks like a leading “1” was cropped from the numbers along the y axis.

This is a confusing stacked bar chart! (unfortunately I wasn’t able to track down the source.)

The height of each total bar appears to be the energy supply from renewables worldwide in each of these years. The proportion on top, however, appears to be that number divided by the global total energy supply, which changes every year. The fact that those proportions are decreasing left to right as the bar heights are increasing suggests that renewables are increasing every year (the numerator) but the total energy supply (the denominator) is increasing at a faster rate.

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Worksheet: Summarizing Categorical Data

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Break

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Lab Part 1: Class Survey

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