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  2. Weighted arithmetic mean - Wikipedia

    en.wikipedia.org/wiki/Weighted_arithmetic_mean

    Typically when a mean is calculated it is important to know the variance and standard deviation about that mean. When a weighted mean is used, the variance of the weighted sample is different from the variance of the unweighted sample. The biased weighted sample variance ^ is defined similarly to the normal biased sample variance ^:

  3. Reduced chi-squared statistic - Wikipedia

    en.wikipedia.org/wiki/Reduced_chi-squared_statistic

    The unbiased weighted estimator of the sample variance can be computed as follows: = = (=) = = (¯). Again, the corresponding standard deviation is the square root of the variance.

  4. Algorithms for calculating variance - Wikipedia

    en.wikipedia.org/wiki/Algorithms_for_calculating...

    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 be much less than the inherent precision of the floating-point arithmetic used to perform the computation.

  5. Pooled variance - Wikipedia

    en.wikipedia.org/wiki/Pooled_variance

    In statistics, pooled variance (also known as combined variance, composite variance, or overall variance, and written ) is a method for estimating variance of several different populations when the mean of each population may be different, but one may assume that the variance of each population is the same.

  6. Three-point estimation - Wikipedia

    en.wikipedia.org/wiki/Three-point_estimation

    These values are used to calculate an E value for the estimate and a standard deviation (SD) as L-estimators, where: E = (a + 4m + b) / 6 SD = (b − a) / 6. E is a weighted average which takes into account both the most optimistic and most pessimistic estimates provided. SD measures the variability or uncertainty in the estimate.

  7. Standard deviation - Wikipedia

    en.wikipedia.org/wiki/Standard_deviation

    When only a sample of data from a population is available, the term standard deviation of the sample or sample standard deviation can refer to either the above-mentioned quantity as applied to those data, or to a modified quantity that is an unbiased estimate of the population standard deviation (the standard deviation of the entire population).

  8. Inverse-variance weighting - Wikipedia

    en.wikipedia.org/wiki/Inverse-variance_weighting

    For normally distributed random variables inverse-variance weighted averages can also be derived as the maximum likelihood estimate for the true value. Furthermore, from a Bayesian perspective the posterior distribution for the true value given normally distributed observations and a flat prior is a normal distribution with the inverse-variance weighted average as a mean and variance ().

  9. PERT distribution - Wikipedia

    en.wikipedia.org/wiki/PERT_distribution

    The mathematics of the distribution resulted from the authors' desire to make the standard deviation equal to about 1/6 of the range. [ 2 ] [ 3 ] The PERT distribution is widely used in risk analysis [ 4 ] to represent the uncertainty of the value of some quantity where one is relying on subjective estimates, because the three parameters ...