Note that we do not often use the mean to describe onset times.  The reason is that it is too much influenced by a few extreme values.

note that the intervals in the above chart would really be at least one-stage more precise than are shown here.   For example, "51-60" really means 51.00 to 60.99 (if we mean decimal hours) or 50:00 to 60:59 (if we mean hours and minutes)  

IF the outbreak is very sudden, with a steep initial onset curve,

and the exact exposure point is NOT known, it can be estimated.

You can try this but it gives only an approximate time of exposure.