1) GRUMP uses a proportional allocation algorithm to distribute population across a landscape based on land area that also takes into account whether a pixel is classified as urban or rural.
2) If an administrative unit has a large amount of land area, but a small population count, the result might be that certain pixels are coded with floating point values of less than 1 for population count. This is an artifact of the proportional allocation algorithm.
3) Due to this fact, the GRUMPv1 dataset (or any global dataset of a coarse resolution) is not appropriate for pixel level analysis. What is more appropriate is to examine the data in terms of locality (neighborhood). If you are doing a local study then it would be best to look for a higher spatial resolution local dataset.