using sumifs/countifs to calculate average days between two columns of dates

I need to calculate the average days from two columns of dates based on a fixed date range.

I’ve been advised that a combination of countifs and sumifs to calculate the average is the way to go but can’t quite get to grips with this.
My data:

G5: start of date range: 01/04/2015 (>=)
G6: end of date range: 01/07/2015 (<)
R: The first columns of dates I need to use to calculate the average for the quarter
X: The second column of dates for the average calculation

Any help with this would be greatly appreciated.