I make a certain measurement and I would like to arrive at a single descriptive number that would give me an idea of both the average value of the measurement, as well as the deviation from the mean. In fact, the deviation (general extent - how far do the values go?) interests me more than the mean, but I am aware that interpreting the standard deviation value without the mean will lead me astray. I am considering adding mean and standard deviation together (mean + stdiv = new measure) - how horridly wrong will that be from the statistical point of view?
As requested, here are the details: my goal is to measure the extent of saturation in the hidden layer outputs of a neural network. Hidden layer consists of hidden units, where every unit receives weighted real-valued inputs and produces a real-valued output within a certain range (typically [0,1]). An individual output is produced for every pattern in a dataset.
In other words, I have a data set (outputs of the hidden units for all patterns in the data set, recorded n times, where n is the number of algorithm iterations), and I would like to see how the average activation value (hidden unit output) changes from iteration to iteration, as well as how much it fluctuates.