How to retrieve the definition behind statistics added to tables
Between sys.stats and DBCC SHOW_STATISTICS you have all the info needed to see the statistics of your statistics. Eg.:

set nocount on;
declare @object nvarchar(256), @stat sysname;
declare crs cursor forward_only read_only static for
select quotename(object_schema_name(object_id)) + 
    '.' +quotename(object_name(object_id)), 
    name 
    from sys.stats;

open crs;
fetch next from crs into @object, @stat;
while 0 = @@FETCH_STATUS
begin
    dbcc show_statistics(@object, @stat) with NO_INFOMSGS, STAT_HEADER
    fetch next from crs into @object, @stat;
end

close crs;
deallocate crs;


That being said, anybody who understands when the stats need to be updated already knows how to look them up, so I would venture a guess you should not be updating your stats manually.