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Symmetric Distribution Identifier

Run the Symmetric Distribution Identifier Fullscreen

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You can include this MicroSim on your website using the following iframe:

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<iframe src="https://dmccreary.github.io/statistics-course/sims/symmetric-distribution/main.html" height="402px" width="100%" scrolling="no"></iframe>

Description

This interactive MicroSim helps students develop the ability to recognize symmetric distributions by visual comparison of histogram shapes. The simulation generates random distributions that are either symmetric (where the left and right sides mirror each other around a center line) or asymmetric (skewed or unbalanced).

How to Use:

  1. Observe the Histogram: Each histogram shows 10-15 bars representing data distribution. A vertical dashed red line marks the center.

  2. Make Your Classification: Click "Symmetric" if you think the left and right sides are mirror images, or "Not Symmetric" if they differ.

  3. Use the Fold Feature: Click "Show Fold" to see the right side of the histogram fold over onto the left side. If the distribution is truly symmetric, the folded bars will align with the original bars.

  4. Track Your Progress: Your score updates after each answer. After 10 questions, you will see your final results.

  5. Adjust Difficulty:

  6. Easy: Clear differences between symmetric and asymmetric distributions
  7. Medium: Subtle differences with some noise
  8. Hard: Very subtle asymmetries that require careful observation

Distribution Types You Will See:

  • Normal (bell-shaped): Symmetric, peaks in the middle
  • Uniform: Roughly equal bar heights across the distribution
  • Bimodal: Two peaks that may be symmetric or asymmetric
  • Skewed: Tail extends longer on one side (asymmetric)

Lesson Plan

Learning Objectives

By completing this MicroSim activity, students will be able to:

  1. Recognize symmetric distributions by visually comparing left and right sides of histograms (Bloom Level 1: Remember)
  2. Identify the center of a distribution and use it as a reference for symmetry assessment
  3. Distinguish between different distribution shapes (normal, uniform, bimodal, skewed)

Target Audience

  • AP Statistics students (Chapter 3: Displaying Quantitative Data)
  • High school students in introductory statistics courses
  • College students in Statistics 101

Prerequisites

  • Understanding of histograms and how they represent data
  • Familiarity with the concept of frequency distributions

Classroom Activities

Activity 1: Introduction (5 minutes)

  • Introduce the concept of symmetry in distributions
  • Explain that symmetric distributions have matching shapes on both sides of the center
  • Demonstrate the fold animation concept: if you fold a symmetric distribution at its center, both sides match

Activity 2: Guided Practice (10 minutes)

  • Project the MicroSim for the class
  • Work through 3-4 examples together on Easy mode
  • Discuss what features make a distribution symmetric or asymmetric
  • Use the "Show Fold" button to verify answers visually

Activity 3: Independent Practice (10 minutes)

  • Students complete the 10-question quiz on their own devices
  • Start on Easy, then progress to Medium as confidence builds
  • Record final scores for self-assessment

Activity 4: Discussion (5 minutes)

  • Ask students to share strategies for identifying symmetry
  • Discuss common mistakes and how to avoid them
  • Connect to real-world examples of symmetric data (heights, IQ scores) vs. skewed data (income, home prices)

Assessment Suggestions

  • Formative: Use quiz scores to gauge understanding (aim for 70%+ on Medium difficulty)
  • Summative: Include histogram symmetry identification questions on unit tests
  • Extension: Have students create their own examples of symmetric and asymmetric datasets

Differentiation

  • Struggling students: Focus on Easy mode, use fold animation frequently
  • Advanced students: Challenge them to achieve 90%+ on Hard mode without using the fold feature

References

  1. AP Statistics Course Framework - College Board - Official curriculum guidelines for symmetry and distribution shape
  2. OpenIntro Statistics - Chapter on Examining Numerical Data - Free textbook with distribution shape concepts
  3. Khan Academy: Describing Distributions - Video lessons on distribution shapes and symmetry