Lesson 3: The Law of Large Numbers

About 30 minutes — Activity-based lesson

What You Will Learn

This lesson covers:

What the law of large numbers says: more trials = closer to theory
10 flips vs 100 flips vs 1000 flips: watching convergence
Why this matters: small samples are unreliable
Activity: flip a coin 10, 50, and 100 times — graph how the percentage changes

What the law of large numbers says: more trials = closer to theory

This section covers the key ideas about what the law of large numbers says: more trials = closer to theory. Discuss with your group or family and explore the concepts together.

10 flips vs 100 flips vs 1000 flips: watching convergence

This section covers the key ideas about 10 flips vs 100 flips vs 1000 flips: watching convergence. Discuss with your group or family and explore the concepts together.

Why this matters: small samples are unreliable

This section covers the key ideas about why this matters: small samples are unreliable. Discuss with your group or family and explore the concepts together.

Activity: flip a coin 10, 50, and 100 times — graph how the percentage changes

This section covers the key ideas about activity: flip a coin 10, 50, and 100 times — graph how the percentage changes. Discuss with your group or family and explore the concepts together.

Check Your Understanding

1. What is the law of large numbers?

Answer: As you repeat an experiment more and more times, the experimental probability gets closer and closer to the theoretical probability. More trials = more reliable results.

2. Why might 10 coin flips give 7 heads?

Answer: With only 10 trials, random variation is high. 7/10 heads is unusual but not impossible. With 1,000 flips, you would almost certainly be close to 50%.

3. How many trials is enough?

Answer: There is no magic number, but generally: more is better. For simple experiments, 50-100 trials gives reasonable results. For important decisions, thousands may be needed.

4. Why does this matter for data science?

Answer: Because it explains why small surveys and small experiments can give wrong impressions. The law of large numbers is why sample size matters so much.

Key Takeaways

What the law of large numbers says: more trials = closer to theory
10 flips vs 100 flips vs 1000 flips: watching convergence
Why this matters: small samples are unreliable
Activity: flip a coin 10, 50, and 100 times — graph how the percentage changes

Ready for More?

Next Lesson

Continue to Lesson 4: Why Small Samples Fool Us

Start Lesson 4

Session Home

Review all lessons and materials.

Back to Session Home