Weighted mean divided by weighted standard deviation

WEIGHTED MEAN DIVIDED BY WEIGHTED STANDARD DEVIATION SERIES

The unbiased weighted estimator of the sample variance can be computed as follows:ДЄgain the corresponding standard deviation is the square root of the variance. The biased weighted estimator of variance can be shown to be: When individual determinations of an age are not of equal significance it is better to use a weighted mean to obtain an 'average' age, as follows: The standard deviation is the square root of the variance. When each measured value can be assumed to have the same weighting, or significance, the biased and unbiased (or 'population' and ' sample', respectively) estimators of the variance are computed as follows: The arithmetic mean of the age determinations is:Д«ut this value can be misleading unless each determination of the age is of equal significance. 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.

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.

WEIGHTED MEAN DIVIDED BY WEIGHTED STANDARD DEVIATION SERIES

Often the geochronologist will determine a series of age measurements on a single sample, with the measured value having a weighting and an associated error for each age determination. Mean square weighted deviation is used extensively in geochronology, the science of obtaining information about the time of formation of, for example, rocks, minerals, bones, corals, or charcoal, or the time at which particular processes took place in a rock mass, for example recrystallization and grain growth, or alteration associated with the emplacement of metalliferous ore deposits.

Weighted mean divided by weighted standard deviation