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A large standard deviation indicates that the data points can spread far from the mean and a small standard deviation indicates that they are clustered closely around the mean. For example, each of the three populations {0, 0, 14, 14}, {0, 6, 8, 14} and {6, 6, 8, 8} has a mean of 7. Their standard deviations are 7, 5, and 1, respectively.
Bias in standard deviation for autocorrelated data. The figure shows the ratio of the estimated standard deviation to its known value (which can be calculated analytically for this digital filter), for several settings of α as a function of sample size n. Changing α alters the variance reduction ratio of the filter, which is known to be
Standard deviation is a widely used measure of the spread or dispersion of a dataset. It quantifies the average amount of variation or deviation of individual data points from the mean of the dataset. It uses squared deviations, and has desirable properties. Standard deviation is sensitive to extreme values, making it not robust. [7]
The Yamartino method, introduced by Robert J. Yamartino in 1984, solves both problems [2] A further discussion of the Yamartino method, along with other methods of estimating the standard deviation of wind direction can be found in Farrugia & Micallef. It is possible to calculate the exact standard deviation in one pass.
The geometric standard deviation is used as a measure of log-normal dispersion analogously to the geometric mean. [3] As the log-transform of a log-normal distribution results in a normal distribution, we see that the geometric standard deviation is the exponentiated value of the standard deviation of the log-transformed values, i.e. = ( ()).
In probability and statistics, the 97.5th percentile point of the standard normal distribution is a number commonly used for statistical calculations. The approximate value of this number is 1.96, meaning that 95% of the area under a normal curve lies within approximately 1.96 standard deviations of the mean.
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The standard deviations will then be the square roots of the respective variances. Since the square root introduces bias, the terminology "uncorrected" and "corrected" is preferred for the standard deviation estimators: s n is the uncorrected sample standard deviation (i.e., without Bessel's correction)