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What is so normal about the normal distribution?
  1. Steven Reid
  1. Correspondence to Steven Reid, Department of Liaison Psychiatry, St Mary's Hospital, London W2 1PF, UK steve.reid{at}nhs.net

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There are few equations of more significance in statistics than this one. It is fundamental to medical research yet for the most part passes unrecognised, and given its complexity perhaps unsurprisingly so. The equation describes the normal distribution, also referred to as the bell curve or Gaussian distribution. The familiar, symmetrical bell-shaped curve represents a probability distribution: a description of all of the outcome values that a variable can take and the individual probabilities of those values.

The distribution is defined by two parameters, the mean and the variance (spread of data around the mean). Although the concept is integral to an understanding of statistical analysis for many, it remains a source of confusion. In particular, what's so normal about it? The term normal should not be taken literally to mean that this distribution is common or typical; it originates from the Latin word normalis (meaning perpendicular), which was used in Gauss's mathematical proof.

Although the normal distribution is traditionally associated with the German mathematician Carl Friedrich Gauss (hence the name), it was introduced by an earlier statistician and professional gambler, Abraham de …

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