The min/max values in qpc statistics are generated when we perform hourly rollups. Data is kept at a 5-minute resolution for 24 hours. Anything older than that is rolled up into a 1-hour interval, at which point min and max are calculated.
We do not collect per-query min/max times, but such information could be calculated using the query log with slow logging set to a low value (eg 1000) to log more instances of the query.
mysql> set global session_log_slow_threshold_ms = 1000;