Standard deviation

Standard deviation measures how dispersed values are around their mean. It is the square root of variance and is expressed in the same units as the data.

Arithmetic mean: The sum of a set of values divided by the number of values. Standard deviation measures dispersion around this central value.
Population standard deviation: The square root of the mean squared deviation from the population mean. It uses every value in the population and divides squared deviations by the population size.
Normal distribution: A continuous, symmetric probability distribution shaped like a bell curve and determined by its mean and variance. Its standard deviation sets the horizontal scale of the bell curve.
Mean absolute deviation: The average absolute distance of observations from a chosen center, often the mean or median. Unlike standard deviation, it does not square deviations, so extreme values have less influence.
Deviation (statistics): The difference between an observed value and a reference value, commonly the mean. Each value’s distance from the mean contributes to the spread being measured.
Sample standard deviation: An estimate of population spread computed from sample data, usually using the sample mean and a denominator of n − 1. Its denominator corrects the tendency of a sample’s squared deviations to underestimate population variance.
Standard error: The standard deviation of a statistic’s sampling distribution. It distinguishes uncertainty in an estimated mean from spread among individual observations.
Interquartile range: The difference between the third and first quartiles, spanning the middle half of a dataset. It describes central spread while resisting outliers that can inflate standard deviation.
Variance: The average squared deviation of values from their mean, using a specified population or sample convention. Standard deviation is the square root of this measure.
Bessel's correction: The use of n − 1 rather than n when estimating a population variance from a sample of size n. It underlies the usual sample standard deviation formula.

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