MySQL 5.6

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CREATE TABLE IF NOT EXISTS `transactions` (
  `transactions_ts` timestamp ,
  `user_id` int(6) unsigned NOT NULL,
  `transaction_id` bigint NOT NULL, 
  `item` varchar(200), PRIMARY KEY (`transaction_id`)
) DEFAULT CHARSET=utf8;
INSERT INTO `transactions` (`transactions_ts`, `user_id`, `transaction_id`,`item` ) VALUES
  ('2016-06-18 13:46:51.0', 13811335,1322361417, 'glove'),
  ('2016-06-18 17:29:25.0', 13811335,3729362318, 'hat'), 
  ('2016-06-18 23::07:12.0', 13811335,1322363995,'vase' ),
  ('2016-06-19 07:14:56.0',13811335,7482365143, 'cup'),
  ('2016-06-19 21:59:40.0',13811335,1322369619,'mirror' ),
  ('2016-06-17 12:39:46.0',3378024101,9322351612, 'dress'),
  ('2016-06-17 20:22:17.0',3378024101,9322353031,'vase' ),
  ('2016-06-20 11:29:02.0',3378024101,6928364072,'tie'),
  ('2016-06-20 18:59:48.0',13811335,1322375547, 'mirror');
select 

sum(dist_ts)/count(*) as avg_ts_per_user

from (

select 
count(distinct transaction_id) as dist_ts, 
us_id 
from 

(select 
user_id as us_id, 
min(transactions_ts) as first_trans, 
min(transactions_ts) + interval 12 hour as right_trans 

from transactions 
group by us_id ) 

as t1 

inner join 

(select * from transactions ) 
as t2 

on t1.us_id=t2.user_id

where transactions_ts >= first_trans
and transactions_ts <  right_trans
group by us_id
	
) as t3	
	


avg_ts_per_user


2.5000