A cursory search doesn't reveal a where-to-be-born [1] or human development [2] index for the lower half or quartile of a given nation's population. It would indeed be an interesting thing to view. I suspect that there's something to be said about the mean score vs the spread of values across the various quartiles of the populations of the countries.

[1]: https://en.wikipedia.org/wiki/Where-to-be-born_Index [2]: https://en.wikipedia.org/wiki/Human_Development_Index