Thinking about income

  • What income distribution is "fair"?
  • Sketch a histogram that represents what you believe to be the income distribution in the United States
  • Include your guesses for the mean and median income

Fair Income

  • Sketch a second histogram representing what you think should be the income distribution in the United States
  • Include the mean and median income, and describe the shape, center, and spread of this histogram
  • Give justification for what you think income distribution should look like


  • What data would help us understand the situation?
  • What limitations might we have in obtaining this information?

Let's look at the data!

  • How might we want to represent this data?








  • Notice that the bin corresponding to the greatest incomes does not have an upper limit.
  • What might we choose as an upper limit? How could we justify this?

Analyzing the data

  • Estimate the mean and median incomes. How do they compare, and why?
  • What assumptions did you need to make to estimate the mean and median?
  • Are these reasonable assumptions?


  • What do these histograms tell us about income inequality in the U. S.?
  • What surprises you about income inequality in the U. S.?
  • How do we deal with the uppermost income bin being unbounded?
  • How does using the lower, midpoint, or upper points of each bin interval affect the mean and median incomes?
  • How does data presented in bins affect our calculating the mean and median of the data?
    • Does it make histograms easier/ harder to create?
    • What, if anything, do we gain (and what do we lose) from the presentation of data in this form versus the raw data?
    • Who gets to choose the bin sizes?


  • Median U. S. household income is $51324, and mean U. S. household income is $70909.
    • Why might these be higher than the AGI data that we have?
    • What might we hypothesize about the income distribution of households? (more skewed, less skewed, and why)