Weighted Arithmetic Mean
Another aspect to be considered is the importance we assign to each observation. The arithmetic mean as we calculated it so far gives equal importance to every observation. Hence, it is called Simple Arithmetic Mean. However, it may be necessary to give different weightages or importance to different observations.
Weighted Arithmetic Mean may be defined as the average whose component items are being multiplied by certain values known as 'weights' and the aggregate of the multiplied results are being divided by the total sum of their 'weights' instead of the sum of the items.
The term 'weight' stands for the relative importance of the differing items. The formula for computing weighted arithmetic mean is
Where represents the weighted arithmetic mean; X represents the variable values, i.e. X1, X2...Xn