Calculating representative value for data

#1
Assume there are ten data with values a_1, a_2, ..., a_10 each with different non-symmetric errors. The problem confronting me in brief is, to combine the 10 results a_i and their associated non-symmetric errors according to some acceptable precept so as to determine the value of a and its errors which best represents the aggregate of observations.

I would appreciate any insight into this problem.