Weighted Arithmetic Average
Weight in relation to the statistical data means the relative importance of the data. As a matter of fact, all the items of a series are not equally important for the purpose of a study. For example, 60% marks in English is not equal to 60 % marks in Statistics for that it is not as easy to secure 60% marks in English as it is in statistics. Further, a rise in the price level of wheat is not as important for a rice eater as it is in case of a rise in the price level of rice. Thus, different weights are given to the different items in accordance with the nature and purpose of the study. For a comparative study, it is always advisable to find out the weighted averages and to comment accordingly.
However, in the computation of the weighted average, the same procedure as it is followed in case of a frequency series is followed except that the factor F (i.e. frequency) only is substituted by the W (i.e. weight). Thus, the respective formula are modified slightly as under:
In case of continuous series X will be replaced by m.
Annotations
Where, X(w) = Weighted arithmetic average
∑wx = Sum of the products of the values and their corresponding weights
∑w =Sum of the Weights
A = Assumed Average
∑wd= Sum of the products of deviations from the assumed average and their corresponding weights
C = Common Factor
X = Last Value
I = Interval of the Values in Common
W1 = average of the cumulative weights i.e. ∑cw/∑w
