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Bell Curve (Normal Curve): Definition

Probability and Statistics Index > Statistics Definitions > Bell Curve / Normal Curve

What is a Bell Curve or Normal Curve?

A bell curve is another name for a normal distribution curve (sometimes just shortened to “normal curve”) or Gaussian distribution. The name comes from the fact it looks bell-shaped.
bell curve
The term “bell curve” is usually used in the social sciences; in statistics, it’s called a normal distribution and in physics, it’s called a Gaussian distribution. However, they all refer to exactly the same thing: a probability distribution that has certain characteristics, including the fact it’s shaped like a bell.

Characteristics of Bell Curves, Normal Curves

  1. The mean (average) is always in the center of a bell curve or normal curve.
  2. A bell curve / normal curve has only one mode, or peak. Mode here means “peak”; a curve with one peak is unimodal; two peaks is bimodal, and so on.
  3. A bell curve / normal curve has predictable standard deviations that follow the 68 95 99.7 rule (see below).
  4. A bell curve / normal curve is symmetric. Exactly half of data points are to the left of the mean and exactly half are to the right of the mean.

Some other distributions are bell-shaped as well, including the T Distribution and the Cauchy distribution, but they have different characteristics (including different measures for standard deviations).

Many phenomena have probability distributions that are bell curves, including:

  • Heights
  • Weights
  • IQ scores
  • Growth rates
  • Exam scores
  • Temperatures connected to Global warming

Bell Curve Standard Deviations

empirical rule

Bell curve showing standard deviations. Image credit: University of Virginia.


A standard deviation is a unit of measurement that can help you with figuring out where data items are likely to fall. For example, 68% of all measurements fall within one standard deviation either side of the mean. In other words, the bulk of your data will fall between -1 and +1 standard deviations from the mean. If you go out to two standard deviations, that percentage rises to 95; almost all (99.7%) of your data will fall within three standard deviations.

Bell Curve (Normal Curve): Definition was last modified: January 30th, 2016 by Andale

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