normal distribution


Definition of normal distribution

: a probability density function that approximates the distribution of many random variables (such as the proportion of outcomes of a particular kind in a large number of independent repetitions of an experiment in which the probabilities remain constant from trial to trial) and that has the form {latex}f(x) = \frac{1}{\sqrt{2\pi\sigma^{2}}}e^{-\frac{(x - \mu)^{2}}{2\sigma^{2}}}{/latex} where μ is the mean and σ is the standard deviation — compare normal curve

Examples of normal distribution in a Sentence

Recent Examples on the Web Buying up the supplies and bestowing a vaccine monopoly on state governments blocked the normal distribution channels that connect producers with vaccinators. Star Tribune, 6 Jan. 2021 On a graph, a normal distribution of the likely rise in temperature would look like a hump: a low tail at the left (unlikely), leading to a high hump in the middle (most likely), and a low tail on the right (unlikely). Gilbert E. Metcalf, Scientific American, 19 May 2020 As Scott and his colleagues noted in their paper, if a pathogen grows exponentially and a population receives a statistically normal distribution of exposures to it, then a lognormal distribution of incubation times should result. Quanta Magazine, 1 Mar. 2018 There are many naturally arising normal distributions, like the birth weight of babies and the amount of milk that cows produce. Eugenia Cheng, WSJ, 19 June 2019 The most famous statistical pattern of all is the normal distribution, which takes the shape of a bell curve and describes the statistical distribution of a wide range of uncorrelated events (like heights in a population or scores on the SAT). Quanta Magazine, 6 May 2019

These example sentences are selected automatically from various online news sources to reflect current usage of the word 'normal distribution.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

See More

First Known Use of normal distribution

1897, in the meaning defined above

Keep scrolling for more

Learn More About normal distribution

Time Traveler for normal distribution

Time Traveler

The first known use of normal distribution was in 1897

See more words from the same year

Statistics for normal distribution

Cite this Entry

“Normal distribution.” Dictionary, Merriam-Webster, Accessed 19 Jun. 2021.

Style: MLA
MLACheck Mark Icon ChicagoCheck Mark Icon APACheck Mark Icon Merriam-WebsterCheck Mark Icon

More from Merriam-Webster on normal distribution Encyclopedia article about normal distribution


Test Your Vocabulary

Return of Name that Color!

  • a light greenish blue color
  • Name that color:
Name That Thing

Test your visual vocabulary with our 10-question challenge!

 AlphaBear 2

Spell words. Make bears.

Love words? Need even more definitions?

Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!