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Household Income Boxplot Explorer

Run the Household Income Boxplot Explorer MicroSim Fullscreen

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<iframe src="https://dmccreary.github.io/statistics-course/sims/household-income-boxplot/main.html" height="620px" scrolling="no"></iframe>

About This MicroSim

Sylvia says: "I love a boxplot because it tells the whole story without making me count every acorn. The long whisker here is a big clue that a few households earn way more than most."

This MicroSim simulates household incomes in a city (in thousands of dollars). The distribution is intentionally right-skewed, so the median sits closer to Q1 than Q3, and the mean typically sits above the median. Toggle the high-income outlier to see how a long upper whisker highlights inequality.

Key features:

  • Right-skewed income data generated each time you click “New city sample”
  • Five-number summary shown beneath the plot
  • Mean marker to compare mean vs median
  • Outlier toggle to emphasize long upper whiskers
  • Individual points overlay to reveal household-level variation

Lesson Plan

Learning Objective

Students will interpret a right-skewed boxplot by identifying the five-number summary and comparing mean and median.

Bloom's Taxonomy Level: Analyze (L4)

Bloom's Verb: Interpret

Prerequisites

  • Understanding of quartiles and median
  • Familiarity with boxplots

Suggested Duration

10-15 minutes for guided exploration

Classroom Activities

Activity 1: Spot the Skew (5 minutes)

  1. Load the default view and ask students: "Which whisker is longer?"
  2. Have them explain what the long upper whisker implies about very high incomes.
  3. Ask: "Where is the median compared to Q1 and Q3?"

Activity 2: Mean vs Median (5 minutes)

  1. Keep the mean marker visible.
  2. Ask: "Is the mean above or below the median? Why?"
  3. Increase the inequality slider and observe how the mean moves.

Activity 3: Inequality Without Raw Data (3 minutes)

  1. Hide the individual points.
  2. Ask: "What can we say about inequality just from the boxplot?"
  3. Toggle the outlier and discuss the change in the maximum.

Discussion Questions

  1. Why does the median stay closer to Q1 in a right-skewed distribution?
  2. How does a single high-income outlier affect the maximum and whisker length?
  3. What does the distance between Q1 and Q3 tell you about typical households?

Assessment Opportunities

  • Quick write: "Describe the distribution using center and spread."
  • Compare two boxplots (before/after higher inequality) and interpret the change.

Common Misconceptions to Address

  • The mean equals the median: Show how skew pushes the mean upward.
  • Whiskers are averages: Clarify they show data ranges, not means.
  • Small box means low values: Emphasize that box size shows spread, not level.

Technical Notes

  • Built with Plotly.js
  • Responsive layout for iframe embedding
  • Incomes generated from a log-normal model and clamped to realistic bounds

Reminder: Create a screenshot named household-income-boxplot.png for social media previews.