What is the average climb gradient of an aircraft during the takeoff and early phase of a departure procedure? On chart plates it is written the minimum climb gradient with which an aircraft should climb for obstacle clearance or after ATC request (for traffic flow management etc.).

However, since this is the minimum required climb gradient, I am curious about what practically happens during real flights. For example, if a chart plate instructs an initial climb with a minimum climb gradient of i.e. 320 feet per nautical mile, will the aircraft try to maintain this minimum climb gradient until the termination altitude? Will it climb with the maximum climb gradient that its performance characteristics allow?

In other words, given an assigned climb gradient from a chart plate (i.e. from DEEZ5: "Standard with minimum climb of 250' per NM to 300), what would the average climb gradient of an aircraft during the initial climb phase be, provided that this value is taken into consideration not only for a lower but also for the calculation of an (hypothetical) upper limit?
The upper limit is a function of the airplane's performance at rated climb power at the normal speed used, modified somewhat by the wind (the gradient is based on ground speed).  What actually happens on a departure is simply whatever numbers that airplane's performance produces using the standard speed and power setting for that airplane. 

In a jet you are generally going somewhere around 200 kt once the flaps are up, then accelerate to 230-250 kt once past 3000 ft up to 10000 ft.

From the table below, assuming no wind, an airliner climbing at 3000 FPM at 200 kt will have a gradient of roughly 1000 ft/nm between the initial acceleration altitude (say 1000 ft) and 3000 ft: