average number of exoplanets in a system

Best answer is that we don't know. The techniques that are used for finding exoplanets are incomplete - that is they are capable of finding planets around stars in some circumstances but not in others.

For example, finding stars using the transit detection technique is more sensitive to planets that are (i) big, (ii) close to their parent star and (iii) orbiting their star with an edge-on orientation from our point of view. The doppler techniques are sensitive to (i) massive exoplanets, (ii) those that are close-in to their parent star, (iii) favour detection when the line of sight lies close to the orbital plane.

Each detection method (and each observing strategy and telescope/satellite) has their own particular selection bias, but overall the picture is that the census of exoplanets is more complete for close-in massive planets, and very incomplete for planets that are either small or orbiting with periods much longer than 10 years. Then at very large separations and very long orbital periods (think 100s of years), direct imaging surveys are again capable of spotting massive exoplanets. Microlensing observations are also capable of detecting even small planets at large distances from their star.

The result of all this is that any figure for the observed fraction of stars with exoplanets or the number of exoplanets per star is a lower limit.
The exception is where researchers try to account for the various selection effects and give a figure for the fraction of stars with certain types of planet in certain types of orbit around certain types of star.

At the moment it looks like the modal number of exoplanets per star is at least 1. In other words it seems increasingly likely that most stars have exoplanets of one sort or another.

Some facts and figures. From Kepler transit data, Petigura et al. (2013) say that 22% of Sun-like stars have "Earth-sized" planets orbiting in their habitable zone (my italics), but their plots show that the overall results for planets with orbital periods in the range 5-100 days (where Kepler is most sensitive), are that nearly 60% of stars have planets from Earth- to Jupiter- sized in this range. Cassan et al. (2012) use microlensing survey data to claim that 17% of stars have "Jupiters" at 0.5-10 au from their parent star, and that Neptune-sized or "super-Earth" sized objects orbit a further (approximately) 50% and 60% respectively. The combination of these figures also suggests multiple planets are not rare and indeed the title of their paper is "One or more bound planets per Milky Way star from microlensing observations".

The frequency of multiple planet systems is also hard to assess. All the techniques are capable of detecting certain types of multiple system, but equally all are capable of missing multiple planets even when they are there.
Kepler did detect many multiple transiting systems, so they are not rare. A study by Tremain & Dong (2012) estimated a minimum fraction of 20-30% of stars that have one transiting planet will also have others. This is on top of the 15% of Kepler planetary systems where multiple planets can be directly observed (i.e where the orbital planes are very close together).