This gets each day, and the number of questions:
select q.myTimestamp, count(*)
from questionsTable q
where q.myTimeStamp >= '6/1/2010'
and q.ResponseID IS NULL
group by myTimestamp
To get the average you need both the count of days, and sum of number of questions... I would probably do this with 2 queries to MySQL and calculate in PHP.
$query1 = "select count(*) as totalCount from questionsTable where myTimestamp >= '6/1/2010' and ResponseID IS NULL";
$query2 = "select count(*) as totalDays from (select distinct myTimestamp from questionsTable where myTimestamp >= '6/1/2010' and ResponseID IS NULL) a";
$res1 = mysql_query($query1);
$res2 = mysql_query($query2);
$row1 = mysql_fetch_array($res1);
$row2 = mysql_fetch_array($res2);
$avgPostCount = ($row1['totalCount'] / $row2['totalDays']);
not optimal, but should work..
I made an assumption, that you wouldn't want to count days where there were no questions.. otherwise it could be simplified to one query using a mysql function to get the number of days since 6/1/2010.