It is wide question. First this doesn't have to be necessary spatial task. You can look at it as sets of values for different trails and count average/mean/min/max for values in every trail (whatever the position of points in trail is)...
If you have points, you must somehow specify which points belongs to which trails:
a) separate file for every trail
b) in the table have column as "trail_identificator"
Technically all you need is software able to work with table data like Open Office Calc.
You can create table with columns like:
point_id, x, y, trail_identificator, observed_value, mean_value_for_trail, sum_for_trail etc.
GIS software (like QGIS) allows you ta save/export or load/import table data so after your calculations you can spatially visualize the information as colored points. Or you can have/create trails as lines and add this final values to table connected to these lines and color/scale line symbol based on your calculated value.
I am not going to explain how to automatically convert points to lines or how to visualize variable probability value along the line because that is way more complicated and I guess it is not needed in this case.