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Mysql min and max values and corresponding “date” for each month

I have a table named "rates" and it has two fields "date" and "rate". I like to get MIN and MAX rate values and their dates on which they occurred for each month. But I could not manage.

SELECT date,
MIN(rate) AS minRate,
MAX(rate) AS maxRate,
MONTH(date) AS monthName,
YEAR(date) AS yearName
FROM rates
GROUP BY yearName ASC, monthName ASC

Clarification: I like to get something like this:

 Months  MIN    mindate     MAX      maxdate  
 Jan     1.234  2012-01-13   1.534  2012-01-24  
 Feb     1.165  2012-02-28   1.373  2012-02-11  

and so on

Try this query, the database name is test, you can use yours or remove it:

SELECT 
  MIN(rate) AS minRate,
  (select date from test.rates where rate = min(co.rate) and  
    month(date) = month(co.date) and year(date) = year(co.date) limit  
  )as min_date,
  MAX(rate) AS maxRate,
  (select date from test.rates where rate = max(co.rate) and  
    month(date) = month(co.date) and year(date) = year(co.date) limit 1) as 
  max_date
FROM test.rates co 
GROUP BY year(date) , month(date)

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