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The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.
Unbiased estimation of standard deviation. In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a population of values, in such a way that the expected value of the ...
A common source of confusion occurs when failing to distinguish clearly between: the standard deviation of the population ( σ {\displaystyle \sigma } ), the standard deviation of the sample ( σ x {\displaystyle \sigma _ {x}} ), the standard deviation of the mean itself ( σ x ¯ {\displaystyle \sigma _ {\bar {x}}} , which is the standard error), and the estimator of the standard deviation of ...
Sample size determination or estimation is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined ...
For example, consider a normal population with mean and variance . Assume we repeatedly take samples of a given size from this population and calculate the arithmetic mean for each sample – this statistic is called the sample mean. The distribution of these means, or averages, is called the "sampling distribution of the sample mean".
Coefficient of variation In probability theory and statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation to the mean (or its absolute value ...
Two-pass algorithm An alternative approach, using a different formula for the variance, first computes the sample mean, and then computes the sum of the squares of the differences from the mean, where s is the standard deviation. This is given by the following code:
For example, to calculate the 95% prediction interval for a normal distribution with a mean (μ) of 5 and a standard deviation (σ) of 1, then z is approximately 2.