# 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

Recent Examples on the Web Hours of exercise per week: Average: 7.5; standard deviation: 2.03 Hours of sleep per day: Average: 9; standard deviation: 3.32 Correlation between the two: 0.816 On average, the people in your sample exercise 7.5 hours per week and sleep nine hours per day. Jack Murtagh, Scientific American, 7 Sep. 2023 Big Sky has the lowest standard deviation of snowfall (most consistent snowfall) in the northern Rockies, which means that while other resorts may see significant peaks and valleys, Big Sky's snowfall tends to stay consistent year after year. Roger Sands, Forbes, 22 Jan. 2023 Leveraging Continuous Improvement For Growth Practicing continuous improvement involves tracking key performance indicator (KPI) averages and identifying phenomena that are more than three standard deviations away from the mean. Guy Yehiav, Forbes, 21 Feb. 2023 Digging into statistics a little, the global sea surface temperature anomaly on June 10 is 4.47 standard deviations above the mean. Scott Dance, Anchorage Daily News, 14 June 2023 His staff has worked to refine the data so that every district can log in and look up individual teacher performance, including those who are defined as high impact teachers because their students achieve at more than one standard deviation above the mean. Cynthia Howell, Arkansas Online, 24 May 2023 Alphabet stock is trading within one standard deviation of its 40-day moving average for the sixth time in the past three years. Schaeffer's Investment Research, Forbes, 3 May 2023 The seven All-Stars in the latest ranking scored at least one standard deviation above the mean in all five categories, meaning their scores were in the top 15% to 20% for more than 900 companies studied by Drucker. WSJ, 6 Feb. 2023 Sheikh advised that devices with standard deviation readings of less than one are considered consistent. Tori Zhou, Verywell Health, 10 Jan. 2023 See More

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'standard deviation.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

## 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

## Dictionary Entries Near standard deviation

standard deviation

## Cite this Entry

“Standard deviation.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/standard%20deviation. Accessed 5 Oct. 2023.

## 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

## More from Merriam-Webster on standard deviation

Last Updated: - Updated example sentences
Love words? Need even more definitions?

Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!