Grouping a Set of Numbers based on Difference between Groups

I have a series of number like:
185.5
184.6
176.7
176.6
176.0
173.5
172.0
170.4
170.4
159.0
150.0

I want an algorithm that will create a set of cut off values that groups the numbers where the difference between cut values is 2 to 4 with a maximum of 6 cut off values.

So the above numbers would be grouped like:

Group 1 - Numbers greater than 181
185.5
184.6

Group 2 - Numbers greater than 177, since difference between cut values is 4 and next grouping is at 176.7
No numbers

Group 3 - Numbers greater than 174
176.7
176.6
176.0

Group 4 - Numbers greater than 169, make 169 instead of 170 because no number in range 166 to 170
173.5
172.0
170.4
170.4

Group 5 - Numbers greater than 164, make 164 instead of 170 because no number in range 165 to 169
No numbers

Group 6 - All other Numbers less than 159
158.0
150.0

These numbers are speed numbers for a group of horses, so I am trying to group them based on the fact a difference of 2 to 4 points is significant.

If anyone knows the Mathematical name for this problem that would help to.

Thanks for any help.
Greg