Write a SQL query to create a comprehensive summary by account type.
| account_type | num_accounts | total_balance | avg_balance | max_balance | |--------------|--------------|---------------|-------------|-------------| | Savings | 6 | 534502.0 | 89083.67 | 180000.0 | | Current | 2 | 1250000.0 | 625000.0 | 750000.0 | | ... | ... | ... | ... | ... |