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Population and Sample Visualization

Run the Population and Sample Visualization Fullscreen

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/population-sample-visual/main.html" height="452px" scrolling="no"></iframe>

Description

Let's crack this nut! This MicroSim helps you understand one of the most fundamental concepts in statistics: the relationship between a population and a sample.

Imagine you want to know the average height of all students at Lincoln High School. You could measure every single student, but that would take forever. Instead, statisticians select a smaller group, a sample, to represent the whole population. This MicroSim lets you experience that process firsthand.

What You See

  • Population Area (left): All 90 students at Lincoln High School are shown as small person icons. Notice they have different heights and shirt colors, just like real people.
  • Sample Panel (right): This shows the individuals you have selected for your sample.
  • Statistics Display: Shows the population size, your sample size, and what percentage of the population your sample represents.

How to Use It

  1. Click on individuals in the population area to add or remove them from your sample. Selected individuals turn bright orange with a glow effect.
  2. Random Sample button: Click this to randomly select individuals. This simulates how statisticians often choose samples to avoid bias.
  3. Clear Sample button: Removes all selections so you can start fresh.
  4. Sample Size slider: Adjust how many individuals the Random Sample button will select (from 5 to 25).

Key Concepts to Notice

  • A sample is always smaller than the population.
  • The sample percentage shows what fraction of the population you are studying.
  • Random sampling helps ensure your sample represents the whole population fairly.

Acorn for your thoughts? Try clicking individuals one by one. Do you notice yourself picking certain types of people? That is called selection bias, and it is exactly why random sampling is so important.

Lesson Plan

Learning Objectives

By the end of this activity, students will be able to:

  1. Explain the difference between a population and a sample
  2. Demonstrate how to select a random sample from a population
  3. Calculate and interpret sample percentage
  4. Recognize the importance of random sampling to avoid bias

Target Audience

  • High school students (grades 9-12)
  • College introductory statistics students
  • AP Statistics students

Prerequisites

  • Basic understanding of percentages
  • Familiarity with the concept of data collection

Duration

15-20 minutes

Activities

Activity 1: Explore the Visualization (5 minutes)

  1. Ask students to click on several individuals to add them to their sample.
  2. Have them observe how the statistics update in real-time.
  3. Discussion question: "What happens to the percentage as you add more people?"

Activity 2: Manual vs Random Selection (5 minutes)

  1. Have students manually select 10 individuals they think best represent the school.
  2. Click "Clear Sample" and then click "Random Sample" with the slider set to 10.
  3. Discussion question: "Which method do you think gives a more fair representation? Why?"

Activity 3: Sample Size Exploration (5 minutes)

  1. Use the slider to try different sample sizes (5, 10, 15, 20, 25).
  2. Click "Random Sample" several times at each size.
  3. Discussion question: "How does sample size affect how well the sample might represent the population?"

Assessment Questions

  1. If the population is 90 and your sample is 15, what percentage of the population did you sample?
  2. Why might a researcher choose random sampling instead of picking individuals they think are representative?
  3. What are some limitations of using a sample instead of measuring the entire population?

Common Misconceptions

  • "A bigger sample is always better." While larger samples are often more representative, they also require more resources. The key is finding a balance.
  • "My hand-picked sample is just as good as a random sample." Personal selection often introduces unconscious biases.

References

  1. Population vs Sample - Khan Academy - Educational video explaining the difference between populations and samples.

  2. Simple Random Sampling - Stat Trek - Comprehensive overview of random sampling methods and their importance.

  3. AP Statistics Course Description - College Board - Official AP Statistics curriculum framework covering sampling methods.