Hypothetical question, so I don't have actual data or visualization to share, but this is a problem I might face in the future.

Let's say I have a map of a region, divided by counties. I take samples from the population of these counties. I want to represent the proportion of people aged < 15 in each of these counties. As this is a sample, there's an uncertainty associated with the observed proportions, that we can formalize with confidence intervals.

How to correctly represent this uncertainty on a map, without it becoming bloated or unreadable?

A solution that came to my mind is to simply display the confidence intervals numbers on each county (e.g. under the form [0.21, 0.35]), but I guess it could become quickly unreadable if the map includes many counties or some other text (names of the counties, major cities, etc.).

Another solution would be to give up the idea of representing the uncertainty on the map, and presenting the confidence intervals on a separate table. The risk I see here is that a table might be overlooked by readers when it is a crucial piece of information. In addition, it might be that there's some sort of relation between the uncertainty and the location (e.g. perhaps the uncertainty is greater in northern counties), and that would be a phenomenon more difficult to see with a table.

The other solution I see is to represent the uncertainty on two separate maps (corresponding to the lower and upper CIs), but I fear they might be a bit overlooked too. In addition, this solution may require an effort to link an observed value to its uncertainty, compared to representing all the info on a single map.

What would be some good alternatives, if any? Thanks.