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If the set is a sample from the whole population, then the unbiased sample variance can be calculated as 1017.538 that is the sum of the squared deviations about the mean of the sample, divided by 11 instead of 12. A function VAR.S in Microsoft Excel gives the unbiased sample variance while VAR.P is for population variance.
which is an unbiased estimator of the variance of the mean in terms of the observed sample variance and known quantities. If the autocorrelations are identically zero, this expression reduces to the well-known result for the variance of the mean for independent data. The effect of the expectation operator in these expressions is that the ...
Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.
An unbiased estimator for the variance is given by applying Bessel's correction, using N − 1 instead of N to yield the unbiased sample variance, denoted s 2: = = (¯). This estimator is unbiased if the variance exists and the sample values are drawn independently with replacement.
In estimating the population variance from a sample when the population mean is unknown, the uncorrected sample variance is the mean of the squares of deviations of sample values from the sample mean (i.e., using a multiplicative factor 1/n). In this case, the sample variance is a biased estimator of the population variance. Multiplying the ...
In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic.For an arbitrarily large number of samples where each sample, involving multiple observations (data points), is separately used to compute one value of a statistic (for example, the sample mean or sample variance) per sample, the sampling distribution is ...
Given an r-sample statistic, one can create an n-sample statistic by something similar to bootstrapping (taking the average of the statistic over all subsamples of size r). This procedure is known to have certain good properties and the result is a U-statistic. The sample mean and sample variance are of this form, for r = 1 and r = 2.
As regards weighting, one can either weight all of the measured ages equally, or weight them by the proportion of the sample that they represent. For example, if two thirds of the sample was used for the first measurement and one third for the second and final measurement, then one might weight the first measurement twice that of the second.