If all the values of the data are not equally important, a weighted arithmetic mean is calculated after assigning appropriate weights to the values of the data. The basic difference between arithmetic mean and weighted arithmetic mean is the assignment of weights to each value in a collection according to its importance. If all the weights are equal to each other, the weighted mean equals the arithmetic mean. The concept of weighted arithmetic mean can be explained with the help of following problems.
Problem A: Given that A = 4, B+ = 3.5, B = 3, C+ = 2.5, C = 2, F = 0, determine the grade point average carried by a student in particular semester, based on the following grades.
The formula of weighted arithmetic mean is given as:
After taking information from problem A we get x (credit hours) and w (weights assigned to grades). By multiplying w with x we get wx and by adding all the values of wx we get ?wx. similarly ?w is obtained by adding all the values of w.
Weighted Arithmetic Mean= 49.5/16=3.094
Therefore the grade average point of the student is 3.094 which falls in B grade.
Problem B: Suppose there are 20 men and 10 women in an office. The average age of 20 men is 30 years while that of the 10 women is 25 years. Find the mean age of the employees working in the office.
By putting the values from above problem into the table we get:
Weighted Arithmetic Mean= 850/30=28.33
Therefore the average age of employees working in the office is 28.33 years.