SQL take average number of rows per minute over a period of time

Question

I'm trying to run an SQL query on my database table. I need to calculate the average number of rows over the space of a minute based on my created_at column dating back for about 5 minutes. Meaning, if There are 10 entries in 1 minute, 20 entries in another minute then the average per minute would be 15 per minute.

When I attempt to run my query using the AVE function, I just get the following error:

Syntax error or access violation: 1305 FUNCTION database.AVE does not exist

If I remove my AVE function and simply use a COUNT then it'll give me the total number of rows for that minute, which seems like I'm very close!

SELECT
    DATE_FORMAT(created_at, '%Y-%m-%d %H:%i:00') AS date,
    COUNT(*) as count,
    AVE(count) as average
FROM tlp_queue_manager_stats
    WHERE created_at >= DATE_SUB(NOW(), INTERVAL 5 MINUTE)
GROUP BY DATE_FORMAT(created_at, '%Y-%m-%d %H:%i:00')
ORDER BY created_at DESC

will error.

Then this is the one that gives me a count, minus an average:

SELECT
    DATE_FORMAT(created_at, '%Y-%m-%d %H:%i:00') AS date,
    COUNT(*) as count
FROM tlp_queue_manager_stats
    WHERE created_at >= DATE_SUB(NOW(), INTERVAL 5 MINUTE)
GROUP BY DATE_FORMAT(created_at, '%Y-%m-%d %H:%i:00')
ORDER BY created_at DESC

the data

array(5) {
  [0]=>
  array(1) {
    [0]=>
    array(2) {
      ["date"]=>
      string(19) "2022-04-08 14:46:00"
      ["count"]=>
      string(2) "32"
    }
  }
  [1]=>
  array(1) {
    [0]=>
    array(2) {
      ["date"]=>
      string(19) "2022-04-08 14:45:00"
      ["count"]=>
      string(2) "32"
    }
  }
  [2]=>
  array(1) {
    [0]=>
    array(2) {
      ["date"]=>
      string(19) "2022-04-08 14:44:00"
      ["count"]=>
      string(2) "32"
    }
  }
  [3]=>
  array(1) {
    [0]=>
    array(2) {
      ["date"]=>
      string(19) "2022-04-08 14:43:00"
      ["count"]=>
      string(2) "32"
    }
  }
  [4]=>
  array(1) {
    [0]=>
    array(2) {
      ["date"]=>
      string(19) "2022-04-08 14:42:00"
      ["count"]=>
      string(2) "32"
    }
  }
}