In physical science for example, the reported standard deviation of a group of repeated measurements should give the precision of those measurements. Standard deviation may serve as a measure of uncertainty. It has a mean of 1007 meters, and a standard deviation of 5 meters.
: egin may represent the distances traveled by four athletes, measured in meters. The standard deviation σ of a real-valued random variable "X" is defined as: The standard deviation of a (univariate.) probability distribution is the same as that of a random variable having that distribution. Tandard deviation of a probability distribution or random variable When only a sample of data from a population is available, the population standard deviation can be estimated by a modified standard deviation of the sample, explained below. A useful property of standard deviation is that, unlike variance, it is expressed in the same units as the data. If all data values are equal, then the standard deviation is zero. If many data points are close to the mean, then the standard deviation is small if many data points are far from the mean, then the standard deviation is large. It is defined as the root-mean-square (RMS) deviation of the values from their mean, or as the square root of the variance.Formulated by Galton in the late 1860s, ] the standard deviation remains the most common measure of statistical dispersion, measuring how widely spread the values in a data set are. The standard deviation is usually denoted with the letter "&sigma " (lowercase sigma). It can apply to a probability distribution, a random variable, a population or a data set.
In probability and statistics, the standard deviation is a measure of the dispersion of a collection of values.
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