Find average of collection of TimeSpans

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);

var average = new TimeSpan(sourceList.Select(ts => ts.Ticks).Average());

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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.