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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Of the 92% S & P 500 companies that have reported, 60% have beaten consensus earnings per share forecasts by more than a standard deviation of analyst estimates, according to data from the firm. Sean Conlon, CNBC, 18 Aug. 2025 From 2021-24, his fly ball, line drive and ground ball exit speeds were over one-half standard deviation above average, except for grounders in 2023. Tony Blengino, Forbes.com, 12 Aug. 2025 According to Drollette, children showed an average 8-point gain on the KTEA-3 reading fluency scale—roughly half a standard deviation, or the difference between scoring in the 50th percentile and the 70th percentile. Daniella Gray, MSNBC Newsweek, 12 Aug. 2025 Owing to the salary-cap system in the United States, MLS comes out with the lowest standard deviation and the highest competitiveness statistically. Mark Carey, New York Times, 7 July 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 9 Sep. 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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