Find average of collection of TimeSpans
Solution 1:
You can use the Average overload that takes a collection of long in parameter:
double doubleAverageTicks = sourceList.Average(timeSpan => timeSpan.Ticks);
long longAverageTicks = Convert.ToInt64(doubleAverageTicks);
return new TimeSpan(longAverageTicks);
Solution 2:
var average = new TimeSpan(sourceList.Select(ts => ts.Ticks).Average());
Note, your method returns a Nullable, but doesn't need to, unless you want to return null if the source list is empty, in which case just do a separate check first.
Solution 3:
In Addition to the above answer, I would suggest you take an average on the Seconds or MilliSeconds level (depending on what you require)
sourceList.Average(timeSpan => timeSpan.ToTalMilliseconds)
Now using this value you could arrive at the new TimeSpan using
TimeSpan avg = TimeSpan.FromMilliseconds(double value here)