Find outliers to each band of records - sql

Question

The goal is to find extremely small or large records for each band based on a formula.
Input:
Distance Rate
10 5
25 200
50 300
1000 5
2000 2000
Bands are defined by my input. For example, I want to have two bands for this input (actually there are more, like 10 bands) for distance: 1-100, 101-10000.
For each band, we want to find all records that the rates are outliers by formula f (two standard deviations away from mean, if you are interested in the formula)
The formula f I want to use
(Rate- avg(Rate) over ()) / (stddev(Rate) over ()) > 2
Output:
Distance Rate
10 5
1000 5 (this number is for illustrative purpose only.)
The difficult part is I do not know how to do it for each band, and it makes applying formula more difficult.

Answer 1

Without knowing how you intend to apply your formula (my guess would be UDF), you can create your "bands" by grouping by a CASE expression:
GROUP BY CASE
WHEN Distance BETWEEN 1 AND 100 THEN 'Band1'
WHEN Distance BETWEEN 101 AND 10000 THEN 'Band2'
ETC
END
Similarly you use the same CASE expression in a RANK() OVER () function, if that works better for the rest of your query.
EDIT: based on your clarification, you need to handle this with a correlated sub-query in your WHERE clause. I would consider encapsulating it in a UDF to make the main query look cleaner. Something like:
WHERE (Rate- {Correlated query to select the AVG(rate) of all rows in this band (using the above CASE statement to determine "this band"} over ()) / (stddev(Rate) over ()) > 2