It depends really.

**I'm going to say the below in an electronic perspective and it may have nothing to do with maths.**

For example, quantum computers are based off qubits. Now, qubits are constantly on 1 and 0. So qubits are defined as being both at 1 and 0 at the same time. So this leads rise to how this is even possible. Now to prevent confusion in a situation where something can be both, the average is taken as this is only a definition, not something tangible.

Its like having the complex plane over the real plane. The complex plane can not be found in everyday life, unless it is necessary in a few strands of engineering and science. However, we use the real plane all the time. For example, we never pay $2i dollars for milk at the local shop. Instead we pay $2.

So its kinda like a definition rather than something you can get.

When programming softwares for such things, they will either spew out no answer, 1/2 or both 0 and 1 at the same time (or simultaneously). They will not spew out just a 0 or just a 1 as this leads to an indefinite argument. Logic gates would preferably spew out a 0 and 1 at the same time. This mixed signal would be averaged in the electronic circuit and you would get half of the full amount of a 1.

For example, let the signal for 1 be a voltage of 5V, and the 0 have a voltage of -5V.

In the end, the output signal would be 0V, which is thus the average of the two values.

However, this case only works for two values which are negative of each other (conjugates) or else the result would be a little different and would not exactly be the average (its some complex stuff to do with electronics).

I don't know whether what I just said above has anything to do with it mathematically, but I know that the above would be the case in electronics.