Average values can be interpreted geometrically. One method uses trapezoids.  In a trapezoid, each different average value is equal to the length of a line segment drawn parallel to and between, the bases, that satisfies the stated conditions.  H and h are perpendicular to the bases.  

Arithmetic average value

Geometric average value

Another method uses a circle with segments constructed as shown.  In each case, you are finding the average of a and b.

         

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Once you have read through this lesson on average values, you will be surprised at how much you know about finding different averages. In math (and in real life) there are many times when it is necessary to know how to find the average of something in more ways than one.