The only fuel you can make from water is hydrogen. The RS-25 engines used on the SLS core stage and the Space Shuttle used liquid hydrogen, as did the J-2 engines on the second and third stage of the Saturn V (but not the first stage, which used RP-1 (kerosene) burning F-1 engine)
Starship’s Raptor engines use liquid methane however. There are a bunch of tradeoffs between the different fuels, but generally liquid hydrogen is more difficult and expensive to deal with. With low cost reusability being one of the primary objectives of Starship, liquid methane was chosen as the best option. The fact that it can also be manufactured on Mars was also considered, since CO2 is abundant in Martian atmosphere.
The word average is often used to mean mean, however it can be used less specifically - median is a type of average as well.
From Merriam-Webster definition of average:
1a) a single value (such as a mean, mode, or median) that summarizes or represents the general significance of a set of unequal values
Also, things like testosterone levels in a population usually follow a normal distribution, where both mean and median are the same, so the distinction is often meaningless for practical purposes