When you subtract two DATE datatype values, result is number of days. For example (based on Scott's schema):
SQL> alter session set nls_date_format = 'dd.mm.yyyy';
Session altered.
SQL> select deptno,
2 hiredate,
3 lag(hiredate) over (partition by deptno order by hiredate) lag_hiredate,
4 --
5 hiredate - lag(hiredate) over
6 (partition by deptno order by hiredate) diff
7 from emp
8 order by deptno, hiredate;
DEPTNO HIREDATE LAG_HIREDA DIFF
---------- ---------- ---------- ----------
10 09.06.1981
10 17.11.1981 09.06.1981 161
10 23.01.1982 17.11.1981 67
20 17.12.1980
20 02.04.1981 17.12.1980 106
20 03.12.1981 02.04.1981 245
30 20.02.1981
30 22.02.1981 20.02.1981 2
30 01.05.1981 22.02.1981 68
30 08.09.1981 01.05.1981 130
30 28.09.1981 08.09.1981 20
30 03.12.1981 28.09.1981 66
12 rows selected.
SQL>
If you want to select average difference, you'll have to use an inline view or CTE as AVG and analytic function can't be used at the same time, i.e. avg(lag(...)).
Finally, as you need number of minutes, multiply the result (days, right?) by 24 (as there are 24 hours in a day) and 60 (as there are 60 minutes in an hour):
SQL> with inter as
2 (select deptno,
3 hiredate - lag(hiredate) over
4 (partition by deptno order by hiredate) diff
5 from emp
6 )
7 select deptno,
8 avg(diff) avg_diff_days,
9 --
10 avg(diff) * (24 * 60) minutes
11 from inter
12 group by deptno;
DEPTNO AVG_DIFF_DAYS MINUTES
---------- ------------- ----------
10 114 164160
20 175,5 252720
30 57,2 82368
SQL>
[EDIT: added timestamp example]
SQL> create table test (datum timestamp);
Table created.
SQL> select * From test;
DATUM
---------------------------------------------------------------------------
04.06.18 08:57:34,000000
04.06.18 09:34:34,000000
04.06.18 09:34:34,000000
SQL>
SQL> select datum - lag(datum) over (order by datum) diff
2 from test;
DIFF
---------------------------------------------------------------------------
+000000000 00:37:00.000000
+000000000 00:00:00.000000
SQL> -- cast timestamps to dates first, then subtract them; for the final result,
SQL> -- multiply number of days by 24 hours (in a day) and 60 minutes (in an hour)
SQL> select avg(diff) * 24 * 60 avg_minutes
2 from (select cast(datum as date) - cast(lag(datum) over (order by datum) as date) diff
3 from test
4 );
AVG_MINUTES
-----------
18,5
SQL>