F.2 MATH

Let the median height be 155cm
=> (The sum of 3rd and 4th data)/2=155cm
=> The sum of 3rd and 4th data=310cm...(1)

The median height is 3 cm more than the mode of the heights
=> the mode=152cm...(2)

The mean height is 2 cm more than the median height
=> the mean=157cm
=> the sum of 6 players=157*6=942cm...(3)

Let the 1st, 2nd, 3rd and 4th data be 152, 152, 154 and 156 so that this set of data satisfies (1) and (2) with different 5th and 6th data.

From (3),
The sum of 5th and 6th data=942-(152+152+154+156)=328

Set the 5th and 6th data to be 158cm and 170cm

Hence, the possible set of the heights is 152, 152, 154, 156, 158 and 170cm.