standard deviation

noun

Statistics.

1. a measure of dispersion in a frequency distribution, equal to the square root of the mean of the squares of the deviations from the arithmetic mean of the distribution.

standard deviation

noun

1. statistics a measure of dispersion obtained by extracting the square root of the mean of the squared deviations of the observed values from their mean in a frequency distribution

standard deviation

1. A statistic used as a measure of the dispersion or variation in a distribution, equal to the square root of the arithmetic mean of the squares of the deviations from the arithmetic mean.

standard deviation

1. In statistics, a measure of how much the data in a certain collection are scattered around the mean. A low standard deviation means that the data are tightly clustered; a high standard deviation means that they are widely scattered.

About sixty-eight percent of the data are within one standard deviation of the mean.

Word History and Origins

Origin of standard deviation¹

First recorded in 1920–25

Example Sentences

Even accounting for a step-change in inflation-adjusted stock market trends following the Great Depression in the 1930s, real U.S. equity prices are still elevated and more than 1 standard deviation above trend, Colmar notes.

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For one, the cyclically adjusted price-to-earnings ratio, also known as the Shiller P/E ratio — a widely watched long-term valuation measure — rose above two standard deviations from its historical average in the summer of 2024.

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This is appropriate, since this portfolio has a similar risk profile, with a standard deviation of annual returns over the past two decades that is similar to the average endowment.

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That says the amount of a risky asset you want in your portfolio is equal to its expected excess return, divided by the square of the standard deviation of returns.

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The magnitudes of the changes were calculated in terms of standard deviations, which are used in statistics to convey how tightly a group of data points is clustered together.

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