Normal distributions as models for data

The family of normal distributions consists of symmetric bell-shaped distributions that are defined by two parameters, µ and σ. The mean and standard deviation of a normal distribution are equal to µ and σ, respectively.

Data sets are sometimes assumed to be random samples from populations that have normal distributions.

Grass intake by cows

Data with skew distributions can often be transformed into a fairly symmetrical form. A normal distribution may be a reasonable model for the transformed data.

Summary statistics

A more important reason for the importance of the normal distribution in statistics is that many summary statistics have normal distributions (at least approximately).