Normal Distributions

… a core concept used in Quantitative Methods and Atlas104

Click for OnlineStatBook page

Concept description

Wikipedia (reference below) describes the normal (or Gaussian) distribution as “a very common continuous probability distribution … often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.”

OnlineStatBook (link on right) notes that:

“The normal distribution is the most important and most widely used distribution in statistics. It is sometimes called the “bell curve” [and it] is also called the “Gaussian curve” after the mathematician Karl Friedrich Gauss. …

“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. [The image above] shows three normal distributions. The green (left-most) distribution has a mean of -3 and a standard deviation of 0.5, the distribution in red (the middle distribution) has a mean of 0 and a standard deviation of 1, and the distribution in black (right-most) has a mean of 2 and a standard deviation of 3. These as well as all other normal distributions are symmetric with relatively more values at the center of the distribution and relatively few in the tails.”

OnlineStatBook lists seven features of normal distributions:

  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.
Atlas topic, subject, and course

Normal Distributions and Advanced Graphs (core topic) in Quantitative Methods and Atlas104 Quantitative Methods.


Wikipedia, Normal distribution, at, accessed 11 June 2017.

David Lane, OnlineStatBook, at, accessed 11 June 2017.

Page created by: Ian Clark, last modified 11 June 2017.

Image: OnlineStatBook, at, accessed 11 June 2017.