Practice: Summarizing Categorical Data

1) Affiliation Party and Human-Droid Status

Consider the following contingency table with the counts for the affiliation party and human-droid status of some individuals.

Empire Rebellion Unaffiliated
Human 100 350 50
Droid 300 150 50


  1. What proportion of individuals are affiliated with the Empire? What kind of proportion is this?

  2. What proportion of individuals are affiliated with the Rebellion? What kind of proportion is this?

  3. What proportion of individuals are droids affiliated with the empire? What kind of proportion is this?

  4. What proportion of individuals are Human? What kind of proportion is this?

  5. Of the Unaffiliated individuals, what proportion are humans? What kind of proportion is this?

  6. What proportion of individuals are not Human? What kind of proportion is this?

  7. What proportion of the droid individuals are part of the Rebellion? What kind of proportion is this?

  8. What proportion of humans are not in the Rebellion?

  9. Of the Rebellion individuals, what proportion are humans?

  10. What are the dimensions of the raw data from which this table was constructed?

  11. True or False. You can derive a marginal proportion—from the contingency table—that has a numerator of 500.

  12. True or False. You can derive a joint proportion—from the contingency table—that has a numerator of 500.

  13. True or False. You can derive a conditional proportion—from the contingency table—that has a denominator of 500.

  14. Sketch a stacked bar chart of Affiliation party, color coding by human-droid status. To be more precise: use x-axis for affiliation, y-axis for counts, and color code bars by human-droid status.

  15. True or False. From the sketched bar chart, one can see that there is no association between affiliation party and human-droid status.

  1. 400 / 1000 (marginal prop)
  2. 500 / 1000 (marginal prop)
  3. 300 / 1000 (joint prop)
  4. 500 / 1000 (marginal prop)
  5. 50 / 100 (conditional prop)
  6. 500 / 1000 (marginal prop)
  7. 150 / 500 (conditional prop)
  8. 150 / 500
  9. 350 / 500
  10. rows: 1000 (one per individual); variables: 2
    • human-droid status
    • affiliation party
  11. True
  12. False
  13. True
  14. Graphic
Figure 1: Stacked bar chart
  1. False. There is clearly a large proportion of droids in the empire, as well as a large proportion of humans in the rebellion.