| user         | Mark       | Points   |
|--------------|------------|----------|
| John         |    0       |    2     |
| Paul         |    5       |    3     |
| John         |    4       |    4     |
| Paul         |    7       |    5     |

| user         | Avg(Mark)  | Sum(Points) |
|--------------|------------|-------------|
| John         |    4       |    6        |
| Paul         |    6       |    8        |

select user, avg(Mark>0), sum(Points) from Table group by user;

select user,
       avg(case when mark > 0 then mark end),
       sum(mark)
from   ...

select
    user, -- very bad choice for column name, but i assume it's just SO example, not real column
    sum( mark ) / count (nullif(mark, 0))
from
    table
group by
    user

SELECT
    "user",
    AVG(mark) FILTER (WHERE mark > 0),
    SUM(points)
FROM
    "table"
GROUP BY
    "user"