To add to the arguments already presented, it's not like you never encounter practical scenarios where a mean does not exist. A good example would be earthquak

To add to the arguments already presented, it's not like you never encounter practical scenarios where a mean does not exist. A good example would be earthquakes. The commonly used Richter law [1] suggests that the number of earthquakes decreases exponentially with the magnitude, while the intensity increases exponentially with the magnitude. In seismically active regions the frequency and intensity even appear to be inversely proportional. This results in a model where there is no average intensity. Sure this model is bound to break down eventually, but until the first earthquake that quite literally breaks the mould we likely won't know what the upper bound may be. [1]:https://en.wikipedia.org/wiki/Gutenberg%E2%80%93Richter_law https://en.wikipedia.org/wiki/Gutenberg%E2%80%93Richter_law