Normal Distribution
핵심 개념
The normal distribution is one of the most important concepts in introductory statistics. It appears constantly in nature and measurement, and it connects directly to the ideas you've already studied in Central Tendency and Spread. Lecture notes.md
Shape & Symmetry
The normal distribution produces a bell-shaped curve that is perfectly symmetric around its center. Because of this symmetry, all three measures of central tendency collapse to a single point: mean = median = mode. Lecture notes.md
The 68-95-99.7 Rule (Empirical Rule)
This rule tells you what percentage of data falls within a given number of standard deviations (σ) from the mean. Lecture notes.md
| Range | % of data covered | What it means |
|---|---|---|
| mean ± 1σ | 68% | About 2 in 3 values fall here |
| mean ± 2σ | 95% | Almost all "typical" values |
| mean ± 3σ | 99.7% | Nearly everything — extremes are rare |
Key implication: the chance of a value falling *outside* mean ± 2σ is only about 5%. Lecture notes.md
How σ Changes the Curve
- A larger σ stretches the bell wider and flatter — data is more spread out.
- A smaller σ squeezes the bell narrower and taller — data clusters tightly around the mean.
- When σ = 0, there is no spread at all; every value is identical. (See Spread for a full treatment of σ.) Lecture notes.md
Connection to Other Topics
| Topic | How it links to Normal Distribution |
|---|---|
| Central Tendency | |
| Spread | |
| Correlation vs Causation |
Lecture notes.md
큐 질문 (능동적 회상)
Test yourself — try to answer from memory before checking the notes above. All questions are also pooled on the Review & Spaced Repetition page.
- 1.What shape does the normal distribution have, and what does its symmetry imply about mean, median, and mode?
- 2.**State the 68-95-99.7 rule in your own words. What is the probability of a value falling *outside* mean ± 2σ?**
- 3.What happens to the bell curve visually when σ increases? What about when σ decreases?
- 4.If σ = 0, what does that tell you about the dataset?
- 5.Why is the normal distribution described as "common in nature and measurement"? Can you think of a real-world example?
요약
The normal distribution is a symmetric bell curve where mean = median = mode; the 68-95-99.7 rule shows that nearly all data sits within ±3σ of the center, and a larger σ simply makes that bell wider and flatter. Lecture notes.md