The context of average speed provides us with an opportunity to develop a profound understanding of average in a continuous context. The nature of averaging as leveling the values to be averaged is embedded in the understanding of speed. This nature of speed surfaces when we find average speed through dynamic geometric representations of leveling. The idea of average speed as the speed leveled out connects average speed with the slope of a line through  the origin. This progressive perspective of average speed from leveling to slope guides us to see a fundamental structure underlying in  average speed. The structure helps us specialize and generalize our understanding of average speed so we can clarify the connection between average speed and arithmetic mean as well as the difference between average speed and average of speeds.

arithmetic mean, average speed, leveling interpretation of mean, geometric representation.