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

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There are many naturally arising normal distributions, like the birth weight of babies and the amount of milk that cows produce. Eugenia Cheng, WSJ, "Averages Aren’t Always What They Seem," 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, "Universal Pattern Explains Why Materials Conduct," 6 May 2019 Philadelphia’s income distribution is remarkably similar to that of small Pennsylvania towns, which if anything are closer to a statistically normal distribution. Elizabeth Currid-halkett, WSJ, "The False Stereotype of Two Americas," 26 Dec. 2018 Pick something like a normal distribution for step sizes and see if this same stuff works. Adam Rogers, WIRED, "What Random Walks in Multiple Dimensions Teach You About Life," 10 Apr. 2018

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.

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First Known Use of normal distribution

1897, in the meaning defined above

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Last Updated

10 Jul 2019

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The first known use of normal distribution was in 1897

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