Editing Weighted arithmetic mean (section)

====Frequency weights====
If the weights are ''frequency weights'', the ''unbiased'' weighted estimate of the covariance matrix <math>\textstyle \mathbf{C}</math>, with Bessel's correction, is given by:<ref name="PRICE-1972"/>

:<math>\mathbf{C} = \frac {\sum_{i=1}^N w_i \left(\mathbf{x}_i - \mu^*\right)^T \left(\mathbf{x}_i - \mu^*\right)} {V_1 - 1}.</math>

This estimator can be unbiased only if the weights are not [[Standard score|standardized]] nor [[Normalization (statistics)|normalized]], these processes changing the data's mean and variance and thus leading to a [[Base rate fallacy|loss of the base rate]] (the population count, which is a requirement for Bessel's correction).