Calculating Averages Over a Time Range

I have two tables - one where the first column is days and the second column is a list of pressure readings from those days. The second table's first column represents the beginning of a list of time ranges and the second column represents the end of those time ranges. I need to find the average of the pressure data over the range indicated by those columns. I have WAY too much data to do this manually - I need a function that pulls the start and end date from my spreadsheet and does all the calculation and referencing for me.

Below is an example spreadsheet.

The pressure data is on a table that looks like this.

Day	Pressure
1	8000
2	9000
3	8500
4	9500

And the second table looks like this. The AVERAGE() functions in the third column are what it would be if I just input what I wanted manually - the spreadsheet needs to figure out what range to average on its own. What would I want to input to get these averages?

Start Day	End Day	Average Pressure
1	3	AVERAGE(B2:B4)
1	2	AVERAGE(B2:B3)
2	4	AVERAGE(B3:B5)
3	4	AVERAGE(B4:B5)
1	4	AVERAGE(B2:B5)

Any help with this would be appreciated. I have tried using combinations of the AVERAGE() and IF() functions as well as AVERAGE() with INDEX() but have had no success yet.

Thanks in advance for the help!