Introduction to Normal Distributions

Prerequisites
Distributions, Central Tendency, Variability

Learning Objectives

  1. Describe of shape of normal distribution
  2. State 7 features of normal distributions

The normal distribution is the most important and widely used distribution in statistics. It is sometimes called the "bell curve" although the tonal qualities of such a bell would be less than pleasing. It is also called the "Gaussian curve" after the mathematician Karl-Friedrich Gauss. As you will see in the section on the history of the normal distribution, although Gauss played an important role in its history, de Movire first discovered the normal distribution.

Strictly speaking, it is not correct to talk about "the normal distribution" since there are many normal distributions. Normal distributions can differ in their means and in their standard deviations.

Six features of normal distributions are listed below. These features are illustrated in more detail in the remaining sections of this chapter.

  1. Normal distributions are symmetric around their mean.
  2. The mean, median, and mode of a normal distribution are equal.
  3. The area under the normal curve is equal to 1.0.
  4. Normal distributions are denser in the center and less dense in the tails.
  5. Normal distributions are defined by two parameters, the mean (μ) and the standard deviation (σ).
  6. 68% of the area of a normal distribution is within one standard deviation of the mean.
  7. Approximately 95% of the area of a normal distribution is within two standard deviations of the mean.