Given that 1% of a population has atleast $x$ amount of wealth, can you work out the average wealth of the entire population, or would you need more information.
I tried working it myself but don't know where to start, so I'm thinking more information would be required, such as what percentage $x$ wealth is, out of the total wealth that the population holds.
No, you can't. One distribution that fits your data is $99\%$ having nothing and $1\%$ having $x$, for an average of $\frac x{100}$. Another is the same except one of the $1\%$ has $10^{12}x$ for a much higher average. There are many other distributions that will fit your data. The average could be anything above $\frac x{100}$