My answer: d) 2 and 6
For this one I knew there was a rule involved, because there is no way they want you to work it all out. However, I don't know the rule so I grabbed my ti-83 and worked out the numbers to try and see the rule.
The mean of the numbers is 4. Each pair is an equal distance from the mean. After running the numbers I got the answer to be 2 and 6. Those numbers immediately stood out to be the medians of the lower half and upper half of the number set.
So I ran the same test using the numbers 0,2,4,6,8,10,12. I then added two more numbers 2 and 10 which are the median numbers of the lower half and upper half. This left me with the number set 0,2,2,4,6,8,10,10,12. For both number sets the standard deviation was 4.
I assume the rule is that when you have a number set and then the same number set plus two more numbers, then the median number of each half will give you the closest new standard deviation to the original.
Could somebody who knows chime in?