How to fetch the first and last record of a grouped record in a MySQL query with aggregate functions?

You want to use GROUP_CONCAT and SUBSTRING_INDEX:

SUBSTRING_INDEX( GROUP_CONCAT(CAST(open AS CHAR) ORDER BY datetime), ',', 1 ) AS open
SUBSTRING_INDEX( GROUP_CONCAT(CAST(close AS CHAR) ORDER BY datetime DESC), ',', 1 ) AS close 

This avoids expensive sub queries and I find it generally more efficient for this particular problem.

Check out the manual pages for both functions to understand their arguments, or visit this article which includes an example of how to do timeframe conversion in MySQL for more explanations.

Try This to start with... :

Select YearWeek, Date, Min(Low_Price), Max(High_Price)
From
   (Select YEARWEEK(date) YearWeek, Date, LowPrice, High_Price
    From Symbols S
    Where Date BETWEEN(.. ..)
    GROUP BY YEARWEEK(date)) Z
Group By YearWeek, Date