Statistics · Statistical distributions
Chapter 1 · 4
The idea
The normal distribution
The normal model N(μ, σ²) for continuous data — its symmetric bell shape, mean = median = mode = μ, spread set by σ, and standardising any normal variable to the standard normal Z = (X − μ)/σ.
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Statistics · Statistical distributions
The normal distribution
The normal model N(μ, σ²) for continuous data — its symmetric bell shape, mean = median = mode = μ, spread set by σ, and standardising any normal variable to the standard normal Z = (X − μ)/σ.
Why it works
The bell that nature keeps drawing
Heights, masses, exam marks, measurement errors — vast amounts of continuous, natural data pile up in the same shape: a symmetric bell curve. The normal distribution is the model for it, fixed by just two numbers: the mean (where the peak sits) and the standard deviation (how spread out it is).The key features
- Symmetric about , so the mean, median and mode are all . Exactly half the area lies on each side: .
- The total area under the curve is (it's a probability density), and a probability is an area under the curve between two values.
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