An average that looks at the proportional relevance of each component, rather than treating each component equally is called a weighted average. A weighted average with all weights equal will turn into a simple average. A weighted average will still be between the largest and smallest values of the dataset irrespective of the weights attached to those data points.
For example, if the average height of group A is say 180 cm and average height of group B is say 170 cm, the average of the set comprising of both the groups might not be the simple average of these two values which is 175 cm. It will actually depend on the number of people in each of these groups which will act as a weight to the original average figures. Let us assume that there are 20 people in group A and 40 people in group B.
So, the weighted average = [ (20x180) + (40x170) ] / 60 = 173.33 which will be the actual average of the new group.