Consequently, if all the observations have equal variance, , the weighted sample mean will have variance where . The variance attains its maximum value, , when all weights except one are zero. Its minimum value is found when all weights are equal (i.e., unweighted mean), in which case we have , i.e., it degenerates into the standard error of the mean, squared.
Consequently, if all the observations have equal variance, , the weighted sample mean will have variance where . The variance attains its maximum value, , when all weights except one are zero. Its minimum value is found when all weights are equal (i.e., unweighted mean), in which case we have  i.e., it degenerates into the standard error of the mean, squared.