Average of Accumulative Physical Quantity

Weighted Average

Similar to the making use a density function to obtain the mean or average value of an accumulative physical quantity in a probability distribution, a weighted average of accumulative physical quantity can also be determined by integration when the physical quantity can be expressed as a weighted quantity and quantified in the form of  an infinitesimal element. imply

And the total weighting is

The average weighted physical quantity can then be determined as an average value of accumulative physical quantity . Imply

Weighted Average of a sample

For example the mean of continuous random variable x with physical distribution g(x) over [0,10] can be determined by integration.

The total accumulative weighted quantity is

And the total of the weighting is

Then the weighted of accumulative physical quantity can then be determined as an average value of accumulative physical quantity . Imply