Quiz: Understanding Income Distributions — 4 questions

1. What does an income histogram display on its axes for European incomes in the standard version?

A. Income on the horizontal axis and frequency on the vertical axis

B. Income density on the horizontal axis and frequency on the vertical axis

C. Log income on the horizontal axis and income density on the vertical axis

D. Frequency on the horizontal axis and income on the vertical axis

Answer: (A)

Explanation

An income histogram groups income values into intervals and shows how often each interval occurs, so income is plotted on the x-axis and frequency on the y-axis. The density and log-income options describe different plot types or transformations.

2. How does a log-income histogram differ from a standard income histogram?

A. It replaces frequency with income density on the vertical axis while keeping income on the horizontal axis

B. It replaces income with log income on the horizontal axis while keeping frequency on the vertical axis

C. It replaces income with cumulative proportion on the horizontal axis while keeping frequency on the vertical axis

D. It replaces grouped bars with a smooth curve while keeping income on the horizontal axis

Answer: (B)

Explanation

A log-income histogram uses the logarithm of income on the x-axis but still uses frequency on the y-axis. The smooth curve description refers to a density plot, not a histogram.

3. What does a density plot of income show?

A. A step function giving the cumulative share of observations at or below each income level

B. A bar chart counting how many observations fall in each income interval

C. A scatter plot showing individual incomes against country labels

D. A smooth curve estimating the income density across the income axis

Answer: (D)

Explanation

A density plot replaces histogram bars with a smooth curve that estimates the distribution of income values. The bar chart and step function describe a histogram and an ECDF, respectively.

4. Which axis labels are used in the income density plots for Europe and the UK?

A. Log income on the horizontal axis and income density on the vertical axis

B. Income on the horizontal axis and frequency on the vertical axis

C. Income density on the horizontal axis and frequency on the vertical axis

D. Income on the horizontal axis and income density on the vertical axis

Answer: (D)

Explanation

The density plots place Income on the x-axis and Income Density on the y-axis. Frequency is used for histograms, not density plots.