why do the outer planets have a lower density than the inner planets?

Answer: When the solar system formed most of the mass near the sun was drawn into it as it formed or driven away by the solar “wind”. All that was left was a few rocky lumps and a bit of gas that had gotten close enough to the rocky lumps that their gravitational attraction had overcome the pressure of the solar wind. But out past the asteroid belt the pressure from the solar wind was weaker and so was the solar gravity. The water wasn’t warm enough to be vapour. It was ice. So the rocky lumps out there acquired thick coatings of ice, creating a much bigger core with higher gravity that attracted much more gas. So much that the planets were more gas than solid. And that gas and ice is what makes the planets out there much lower density.

The planet's density is related to its composition. The four inner terrestrial planets are dense compared to the four outer planets. The inner planets are made up mainly of dense, solid rock. The outer planets are composed primarily of gas, so their overall density is lower.