Using ArrayFormula on Query with Multiple and Bounded Criteria - google-sheets

Question

This question is concerning summarizing a database in Google spreadsheet using a predetermined criteria.
I have a data table like so in range A1:B8
A B
-------------
310 890.00
210 875.00
100 849.00
80 845.00
70 842.00
61 842.00
60 841.00
53 825.50
I also have a criteria table which specifies the boundaries for the ranges to be used in the merged table. The criteria table looks like this.
START END
------------
210 310
95 200
69 90
53 65
The criteria table is derived independently from the data table and as you can see, not all the values in the criteria table are present in the data table.
How can I use ArrayFormula such that the final table will have the following data.
START END MAX MIN START VALUE END VALUE
210 310 890 875 875 890
95 200 849 849 849 849
69 90 845 842 842 845
53 65 842 825.5 825.5 842
Here are the starting formulas used to calculate the MAX, MIN, START VALUE, and END VALUE
MAX FORMULA
INDEX(
query(
{ ARRAYFORMULA(VALUE(table1!$A$1:$A$8)),
ARRAYFORMULA(VALUE(table1!$B$1:$B$8)) },
" select max(Col2)
where Col1>="& VALUE(table2!A2) &" and Col1<=" & VALUE(table2!B2) &
" label max(Col2) ''"
),
1,
1
)
MIN FORMULA
INDEX(
query(
{ ARRAYFORMULA(VALUE(table1!$A$1:$A$8)),
ARRAYFORMULA(VALUE(table1!$B$1:$B$8)) },
" select min(Col2)
where Col1>="& VALUE(table2!A2) &" and Col1<=" & VALUE(table2!B2) &
" label min(Col2) ''"
),
1,
1
)
START VALUE FORMULA
INDEX(
query(
{ ARRAYFORMULA(VALUE(table1!$A$1:$A$8)),
ARRAYFORMULA(VALUE(table1!$B$1:$B$8)) },
" select Col2
where Col1>="& VALUE(table2!A2) &" and Col1<=" & VALUE(table2!B2) &
" order by Col1 asc"
),
1,
1
)
END VALUE FORMULA
INDEX(
query(
{ ARRAYFORMULA(VALUE(table1!$A$1:$A$8)),
ARRAYFORMULA(VALUE(table1!$B$1:$B$8)) },
" select Col2
where Col1>="& VALUE(table2!A2) &" and Col1<=" & VALUE(table2!B2) &
" order by Col1 desc"
),
1,
1
)
Here is the link to the publicly editable google sheet with the sample data on it.
How can I use ARRAYFORMULA in Google Sheets such that the details will be autopopulated for a very large dataset.
I have looked at FILTER and VLOOKUP. But since not all the values in the criteria table are actually in the data table, I am having trouble utilizing their ability to work well with ARRAYFORMULA. Please enlighten me. Thanks.

Answer 1

Not exactly what you want but very much easier:
E1 to F9 is named ArStart and used for ColumnC in:
=ArrayFormula(vlookup(A2:A,ArStart,2))
Output is by pivot table.