standard deviation

noun

1
: a measure of the dispersion of a frequency distribution that is the square root of the arithmetic mean of the squares of the deviation of each of the class frequencies from the arithmetic mean of the frequency distribution
also : a similar quantity found by dividing by one less than the number of squares in the sum of squares instead of taking the arithmetic mean
2
: a parameter that indicates the way in which a probability function or a probability density function is centered around its mean and that is equal to the square root of the moment in which the deviation from the mean is squared

Examples of standard deviation in a Sentence

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Bond market volatility, as measured by the MOVE Index, surged more than 3 standard deviations above its recent average, reaching the highest level since the pandemic shock in March 2020. George Calhoun, Forbes.com, 25 May 2025 Individual investors bought a net $4.1 billion worth of stocks on Monday from the open through 12:30 p.m. ET, the largest level ever for the time of day and a more than 11 standard deviation move, according to data from JPMorgan’s trading desk. Yun Li, CNBC, 20 May 2025 An Urban Institute study last year similarly found that improving math scores by 0.5 standard deviations for students up to age 12 was associated with larger increases in earnings by age 30 than other factors in the study. Bruce Rauner, The Orlando Sentinel, 22 Apr. 2025 Students exposed to it from kindergarten to the third grade gained a 0.25 standard deviation improvement in reading scores. Harry Anthony Patrinos, The Conversation, 26 Mar. 2025 See All Example Sentences for standard deviation

Word History

First Known Use

1895, in the meaning defined at sense 1

Time Traveler
The first known use of standard deviation was in 1895

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Cite this Entry

“Standard deviation.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/standard%20deviation. Accessed 29 May. 2025.

Kids Definition

standard deviation

noun
: the square root of the arithmetic mean of the squares of differences between the arithmetic mean of a frequency distribution and the values of the variable

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