I've been using Mean Coordinates in QGIS to find weighted mean centers based on different attributes for the counties in a singular state of the US. However I have come across a problem in which the calculation is affected by the number of polygons within a shape.

For example in the attached image I have been trying to simply find the geographical mean center of the state of Maine (no weights). The center should be further north but because the islands towards the south act as attraction factors the star, which is the result, finds its way towards the south.

Is there anyway to fix/work-around this issue? Do I just have to delete all islands?