A simple Postgres aggregate function for calculating a trimmed mean, excluding values outside N standard deviations from the mean: `tmean(v, standard_deviations)` (for example: `tmean(rating, 1.75)`).

example.sql

DROP TABLE IF EXISTS foo;
CREATE TEMPORARY TABLE foo (x FLOAT);
INSERT INTO foo VALUES (1);
INSERT INTO foo VALUES (2);
INSERT INTO foo VALUES (3);
INSERT INTO foo VALUES (4);
INSERT INTO foo VALUES (100);

SELECT avg(x), tmean(x, 2.0), tmean(x, 1.5) FROM foo;

--  avg | tmean | tmean 
-- -----+-------+-------
--   22 |    22 |   2.5

tmean.sql

DROP TYPE IF EXISTS tmean_stype CASCADE;

CREATE TYPE tmean_stype AS (
  deviations FLOAT,
	count INT,
	acc FLOAT,
	acc2 FLOAT,
	vals FLOAT[]
);

CREATE OR REPLACE FUNCTION tmean_sfunc(tmean_stype, float, float)
RETURNS tmean_stype AS $$
	SELECT $3, $1.count + 1, $1.acc + $2, $1.acc2 + ($2 * $2), array_append($1.vals, $2);
$$ LANGUAGE SQL;

CREATE OR REPLACE FUNCTION tmean_finalfunc(tmean_stype)
RETURNS float AS $$
DECLARE
	fcount INT;
	facc FLOAT;
	mean FLOAT;
	stddev FLOAT;
	lbound FLOAT;
	ubound FLOAT;
	val FLOAT;
BEGIN
	mean := $1.acc / $1.count;
	stddev := sqrt(($1.acc2 / $1.count) - (mean * mean));
	lbound := mean - stddev * $1.deviations;
	ubound := mean + stddev * $1.deviations;
	-- RAISE NOTICE 'mean: % stddev: % lbound: % ubound: %', mean, stddev, lbound, ubound;

	fcount := 0;
	facc := 0;
	FOR i IN array_lower($1.vals, 1) .. array_upper($1.vals, 1) LOOP
		val := $1.vals[i];
		IF val >= lbound AND val <= ubound THEN
			fcount := fcount + 1;
			facc := facc + val;
		END IF;	
	END LOOP;

	IF fcount = 0 THEN
		return NULL;
	END IF;
	RETURN facc / fcount;
END;
$$ LANGUAGE plpgsql;

CREATE AGGREGATE tmean(float, float)
(
	SFUNC = tmean_sfunc,
	STYPE = tmean_stype,
	FINALFUNC = tmean_finalfunc,
	INITCOND = '(-1, 0, 0, 0, {})'
);