StandardDeviation
StandardDeviation[list]
gives the sample standard deviation of the elements in list.
StandardDeviation[dist]
gives the standard deviation of the distribution dist.
Details

- StandardDeviation is also known as volatility.
- StandardDeviation measures dispersion of data or distributions.
- StandardDeviation[…] is equivalent to Sqrt[Variance[…]].
- StandardDeviation handles both numerical and symbolic data.
- StandardDeviation[{{x1,y1,…},{x2,y2,…},…}] gives {StandardDeviation[{x1,x2,…}],StandardDeviation[{y1,y2,…}]}.
Examples
open allclose allBasic Examples (3)
Scope (14)
Data (11)
Exact input yields exact output:
Approximate input yields approximate output:
StandardDeviation for a matrix gives columnwise standard deviations:
StandardDeviation for a tensor gives columnwise standard deviations at the first level:
SparseArray data can be used just like dense arrays:
Find the standard deviation of WeightedData:
Find the standard deviation of EventData:
Find the standard deviation of TemporalData:
Find the standard deviation of a TimeSeries:
The standard deviation depends only on the values:
Applications (7)
StandardDeviation is a measure of dispersion:
Transform data to have mean 0 and unit variance:
Identify periods of high volatility in the S&P 500 using a five-year moving standard deviation:
Find the mean and standard deviation for the number of cycles to failure of deep-groove ball-bearings:
Probability that the values lie within two standard deviations of the mean:
Investigate weak stationarity of the process data by analyzing standard deviations of slices:
Use a larger plot range to see how relatively small the variations are:
Compute standard deviation for slices of a collection of paths of a random process:
Compute standard deviations and means:
Create a standard deviation band around the mean:
Plot standard deviations around the mean over these paths:
Find the standard deviation of the heights for the children in a class:
Properties & Relations (9)
The square of StandardDeviation is Variance:
StandardDeviation is a scaled Norm of deviations from the Mean:
StandardDeviation is the square root of a scaled CentralMoment:
StandardDeviation is a scaled RootMeanSquare of the deviations:
StandardDeviation is the square root of a scaled Mean of squared deviations:
StandardDeviation as a scaled EuclideanDistance from the Mean:
StandardDeviation squared is less than MeanDeviation if all absolute deviations are less than 1:
StandardDeviation squared is greater than MeanDeviation if all absolute deviations are greater than 1:
StandardDeviation of a random variable as the square root of Variance:
Neat Examples (1)
The distribution of StandardDeviation estimates for 20, 100, and 300 samples:
Text
Wolfram Research (2003), StandardDeviation, Wolfram Language function, https://reference.wolfram.com/language/ref/StandardDeviation.html (updated 2007).
CMS
Wolfram Language. 2003. "StandardDeviation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/StandardDeviation.html.
APA
Wolfram Language. (2003). StandardDeviation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/StandardDeviation.html