Skip to content

Random Digit Table Simulator

Run the Random Digit Table Simulator Fullscreen

Edit in the p5.js Editor

About This MicroSim

"Let's crack this nut!" Sylvia exclaims. "Random digit tables were the OG random number generators—and while we have fancy computers now, understanding how they work teaches you exactly what 'random selection' means!"

This interactive simulation lets students practice using a random digit table to select a simple random sample. The step-by-step approach shows exactly why certain numbers are accepted or rejected, building deep understanding of the sampling process.

What You'll Learn

  • How to read multi-digit numbers from a random digit table
  • When to skip numbers (out of range, already selected, or zero)
  • How the process ensures every population member has an equal chance of selection
  • Why starting position doesn't matter (as long as it's random)

How to Use

  1. Set your population size (1-999) by clicking the input box and typing
  2. Set your sample size (1-50) similarly
  3. Click "New Table" to generate a fresh random digit table
  4. Click "Step →" (or press spacebar) to read the next number
  5. Watch the log to see why each number was selected or skipped
  6. Continue until your sample is complete

Understanding the Display

Element Meaning
Yellow highlight Current digits being read
Gray digits Already processed
Green panel Selected sample members
Step log Explains each decision

Key Concepts

Reading Two-Digit Numbers (Population ≤ 99)

For a population of 50 students (numbered 01-50): - Read: 15 → Select student 15 - Read: 02 → Select student 02 - Read: 83 → Skip (greater than 50) - Read: 47 → Select student 47

Reading Three-Digit Numbers (Population ≤ 999)

For a population of 250 members (numbered 001-250): - Read: 150 → Select member 150 - Read: 028 → Select member 28 - Read: 392 → Skip (greater than 250)

"Acorn for your thoughts?" Sylvia asks. "Notice how we skip numbers that are out of range—but that doesn't bias our sample! Every valid number still has an equal chance of appearing."

Embedding This MicroSim

1
<iframe src="https://dmccreary.github.io/statistics-course/sims/random-digit-table/main.html" height="502px" width="100%" scrolling="no"></iframe>

Lesson Plan

Learning Objectives

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

  1. Use a random digit table to select a simple random sample
  2. Determine how many digits to read based on population size
  3. Apply the three skip rules: out of range, already selected, starts with zero
  4. Explain why this process produces an unbiased sample

Target Audience

  • AP Statistics students (high school)
  • Introductory statistics college students
  • Research methods courses

Prerequisites

  • Understanding of simple random sampling
  • Concept of population and sample
  • What it means for selection to be "random"

Classroom Activities

Activity 1: Manual Practice (15 minutes)

  1. Give students a printed random digit table
  2. Have them select a sample of 8 from a population of 75
  3. Compare results—each student should have different samples!
  4. Verify using the simulator

Activity 2: Efficiency Investigation (10 minutes)

  1. Set population to 30 and observe how often you skip
  2. Set population to 90 and compare skip frequency
  3. Set population to 10 and compare again
  4. Discuss: Why are some population sizes more "efficient"?

Activity 3: What If? Scenarios (10 minutes)

Discuss these questions: - "What if two students start at the same position?" (Same sample!) - "What if I always start at row 1, column 1?" (Predictable—not truly random) - "What if my population is 1000?" (Use 4 digits: 0001-1000)

Common Mistakes to Address

  1. Reusing numbers: Once selected, skip duplicates
  2. Inconsistent digit reading: Always read the same number of digits
  3. Starting at the same place: Starting position should vary randomly
  4. Including 00 or 000: Zero is typically not a valid member number

Assessment Questions

  1. You have a population of 200 students. How many digits should you read at a time from the random digit table?

  2. While selecting a sample from a population of 45, you read the digits 6-2-0-3-8. Which of these would you select: 62, 03, 38?

  3. Explain why skipping numbers greater than the population size doesn't introduce bias.

  4. A researcher always starts reading from row 1, column 1 of the same random digit table. Is this appropriate for multiple studies? Why or why not?

References

  • Chapter 11: Sampling and Bias - Concepts: Simple Random Sample, Random Digit Table, Random Number Generator
  • Random.org - True random number generation
  • NIST Random Number Tables - Historical context