Average power would usually be much less than typical or surge, and is not usually a factor in choosing an inverter. If you run a pump for 20 minutes and a small TV for 20 minutes during a one hour period, the average might be only 300 watts, even though the pump requires 2000. Average power is only useful in estimating battery capacity needed. Inverters come in size ratings all the way from 50 watts up to 50,000 watts, although units larger than 11,000 watts are very seldom used in household or other PV systems. The first thing you have to know about your inverter is what will be the maximum surge, and for how long.
All inverters have a continuous rating and a surge rating.
The surge rating is usually specified at so many watts for so many seconds. This means that the inverter will handle an overload of that many watts for a short period of time. This surge capacity will vary considerably between inverters, and different types of inverters, and even within the same brand. The highest surge ratings are the transformer based low-frequency switchers. While high frequency switching allows a much smaller and lighter unit, due to the much smaller transformers used it also reduces the surge or peak capacity.