weighted mean is getting the weighted average of students. normally, it is always use in computing the general average of the students to determine the ranking of the whole class.
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=stdev(...) will return the N-1 weighted sample standard deviation. =stdevp(...) will return the N weighted population standard deviation.
The weighted mean is simply the arithmetic mean; however, certain value that occur several times are taken into account. See an example http://financial-dictionary.thefreedictionary.com/weighted+average
Geometric mean
With a good sample, the sample mean gets closer to the population mean.
Arithmatic Mean