Are these class and constructor signatures provided in this way? If so, I don't see any purpose to adding these private methods to BarWithAverage either. Since they can't be called outside of the class, nor is the BarWithAverage provided with any information regarding the averages of other items or a file in which it can read, it has no practical use within the BarWithAverage itself. That really makes more sense to use on the BarChartWithAverage given what you have here for the two classes and their construction. Now if you have other setters such as taking the average or giving it the data array, then sure that would be alright in the BarWithAverage.
What I'm trying to figure out looking at this is if the BarWithAverage is to paint itself, or simply return data. Since drawBars isn't provided, we cannot tell if it intends to paint itself or simply describe itself to the BarChartWithAverge.
So the only way I can see the BarWithAverage actually making use of these private methods is if you provide it with a graphics to paint on, the entire dataset available (or a file or whatever to get them from), and then you can paint with the class. To me, these still seem like they should be on the BarChartWithAverage class (non-static of course; the drawBars you have is static). This way it can iterate an array of BarWithAverage objects and paint accordingly.
I think you'll need to get more clarification on what these classes are responsible for doing.