It is all said in the other answers. But I think it might be useful to restate
things formally for a different point of view, possibly new to a physicist
readership, thus requiring a more detailed explanation (apologies), and this is why I decided to make it an answer rather than a
comment as I originally intended.
This is really a question of linguistics, not physics.
You have two entities/quantities of interest in your physics discourse, the average of the speed over time, and the magnitude of the average velocity, and
you need to name them both. The way language works, at least in many systems
of language analysis, and particularly in programming languages, which are on
a level of formality that is similar to physics, is as follow (this is a gross
oversimplification, at least for natural language):
You have elementary concepts that are expressed by various names or symbols,
which form a vocabulary (with different categories: name, verb, scalar,
function,...). Then you have syntactics rules (grammar) that you use to to
build larger structures from elementary ones, such as expressions or
sentences. Functional meaning is associated to syntactic rules.
Then getting the meaning of an expression or sentence is done more or less by
considering that this meaning is a homomorphic image from the syntactic domain
of sentence to the abstract domain of meanings. The homomorphism is defined by
the correspondence between the elements of the vocabulary with elementary
entities, and between the syntactic rules and their functional meaning.
This has been actually used in a very formal mathematical way to define
This homomorphic approach, based on getting the meaning of the whole by
composing (according to grammatical syntax) the meanings of the parts, is the
essence, on a very trivial example, of the answer given by user541686
Now, people do not always respect syntax (just listen radio or TV). They can
also take expressions and arbitrarily decide (when they have power to do so)
that this meaning is other than what the homomorphism would derive. This may
even happen through evolution in the case of natural language. But it just
makes understanding things more complicated, possibly more prone to errors and
Thus, you do not get to decide what "average speed" is. The meaning of this
expression must be derived in a standard way from the functionnal meaning of
average, applied to the meaning of speed, in the same way that you would for
average pressure or average weight (well there is much that is implicit, and
language is seldom simple).