Can we represent a population by its mean? Can we represent a population by its mean?
Is the answer simply "yes, unless there are outliers or the data is skewed"?

If I tell you that the average height of my friends is 173 centimeters, does it tell you anything about my friends? It tells you what the average height is, but doesn't tell you almost anything about the distribution of their heights, etc. You cannot make any reasonable guesses about the heights of my friends. The number "represents" the population only if you want to limit the representation to a single number with all the limitations of such representation.
As for outliers, it's not that simple. In fact, the sensitivity of the mean is a feature, not a bug, as you can learn from the If mean is so sensitive, why use it in the first place? thread. So the choice of the point estimate for the central tendency would be more complicated than deciding if there are outliers.
