Number of students who like table tennis = 13
Estimate 13 as 10.
Number of students who like basketball = 15
Estimate 15 as 20.
Number of students who like cricket = 17
Estimate 17 as 20.
Number of students who like badminton = 11
Estimate 11 as 10.
Total number of students = 10 + 20 + 20 + 10 = 60
So, approximately 60 students were surveyed.