Write SQL query to solve given problem: State the average median SAT value for institutes in the state with the most male graduate cohort in 2013.. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT AVG(T1.med_sat_value) FROM institution_details AS T1 INNER JOIN state_sector_grads AS T2 ON T1.state = T2.state WHERE T2.year = 2013 AND T2.gender = 'M' GROUP BY T2.grad_cohort ORDER BY COUNT(T2.grad_cohort) DESC LIMIT 1