This Quora answer (https://www.quora.com/What-is-the-average-number-of-planets-...) takes a dataset of 2560 stars and comes out with an average of 1.3 planets per star. As the author caveats, this is an extremely small sample and probably not accurate, but it's something to start from.
The way we detect planets only detect some of them.
The best method is to notice when a planet passes in front of its star, by how it gets slightly dimmer. That only works if its orbit happens to be directly between us and that star.
We can also detect them by a Doppler shift of the star, because the planet (if big enough) will move the star as it orbits. This works when the transit method fails, but provides fewer data on the planet itself.
Caveat++++: Factor in rogue planets that don't orbit any stars, or large asteroids drifting through nebulas etc...
I'm sure the number of solid bodies — potential habitats for life or artificial constructs — in our universe is magnitudes larger than the number of stars we've detected, and the latter is already a mind boggling quantity.
I would tend to agree. The effective gravitational influence of a star would be relative to its mass. We can pretty easily determine the (rough) mass of a star, and ours appears(?) to be somewhere in the middle, so it stands to reason that 8-ish decently sized planets is not an unreasonable number.
