I have data for several individuals that takes the following form over time. Many individuals are flat over the course of a year, meaning their measurements stay roughly the same. Others have a peak or two and are then flat. And others have many peaks. For each individual I must find an average (representative) value that is not influenced by the peaks. For example, the overall average will not be a good measure because if an individual has several peaks, this will increase the average. Overall, I need an estimate of the baseline for each individual that is not influenced by the number of peaks an individual has.
Probably the first step would be thinking about how to define what one of your peaks is mathematically. E.g., maybe a peak in your case contains values greater than X% of the other values for each individual. At that point it would be easy to calculate the Xth percentile for the value for each individual using any statistical software.
If you are looking for a "representative" outcome that is robust to occasional large deviations, an obvious candidate would be the mode of the distribution. If your time-series data takes on discrete values and there is substantial repitition then it would be possible to estimate these values empirically; if the time-series data is continuous then you could form an appropriate kernel density estimator and estimate the mode as the value that maximises the estimated density.