Glossary term
Normal Distribution
The symmetric bell-shaped distribution where values crowd around the mean and become rare evenly on both sides.
Visual intuition
mean
Standard deviation is the looseness around the mean
Two numbers pin down a normal distribution: where the mean sits and how loose the scatter around it is (the standard deviation) — the bell shape follows from just those two.
Example
If adult women's heights about 165 cm with a near 7 cm (illustrative round numbers), roughly 95% fall between about 151 and 179 cm.
How It Works
Measure enough adult heights and the forms a bell: most people near the middle, symmetric thinning on both sides. Two numbers pin the whole shape — the sets the center, the the width — and about 68% of values fall within one standard deviation of the mean, about 95% within two. Averages of many small independent effects tend toward this shape, which is why it appears so often; but incomes, house prices, and many other everyday quantities are not normal.
Concepts
Central Limit Theorem
The central limit theorem says that averages of many independent, similar-sized random influences tend to form a bell-shaped sampling distribution, even when the original data are not bell-shaped. It explains why averages are often more predictable than individual observations.
Standard Deviation
Standard deviation describes how spread out individual observations are around their mean. It is about variation in the data itself. Standard error is different: it describes how much an estimate such as the sample mean would vary across repeated samples.
