SELECT MIN("Average") FROM table_34735 WHERE "Lowest" > '288' AND "Team" = 'east stirlingshire'
Lowest larger than 288, and a Team of east stirlingshire has what lowest average?
CREATE TABLE table_34735 (
    "Team" text,
    "Stadium" text,
    "Capacity" real,
    "Highest" real,
    "Lowest" real,
    "Average" real
)