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The standard deviation of a random variable, sample, statistical population, data set, or probability distributionis the square rootof its variance. It is algebraicallysimpler, though in practice less robust, than the average absolute 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 calculation equals the true value.
The following expressions can be used to calculate the upper and lower ... whereas the standard deviation of the sample is the degree to which individuals within ...
Sum ← Sum + x. SumSq ← SumSq + x × x. Var = (SumSq − (Sum × Sum) / n) / (n − 1) This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to ...
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 ...
Standard score. In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.
Bessel's correction. In statistics, Bessel's correction is the use of n − 1 instead of n in the formula for the sample variance and sample standard deviation, [1] where n is the number of observations in a sample. This method corrects the bias in the estimation of the population variance. It also partially corrects the bias in the estimation ...
For a large sample from a normal distribution, 2.22Q n is approximately unbiased for the population standard deviation. For small or moderate samples, the expected value of Q n under a normal distribution depends markedly on the sample size, so finite-sample correction factors (obtained from a table or from simulations) are used to calibrate ...