Question

Consider the following data: 3,4,6,7,9,9,11

Answer 1

The data is already sorted for us. The median of this set is the middle most value which is 7 (in slot 4; three values to the left and three values to the right). 

So the median is originally 7

If we add 5 to each data value we get
3+5 = 8
4+5 = 9
6+5 = 11
7+5 = 12
9+5 = 14
9+5 = 14
11+5 = 16

So the old data set
{3,4,6,7,9,9,11}
shifts to
{8,9,11,12,14,14,16}
after we add 5 to each value

The middle most value of the updated set is 12. It corresponds exactly to the old median of 7.

So we technically didn't even need to add 5 to all of the values to see what the new median would be. We simply need to add 5 to the old median to get the new median

I.e,
(new median) = (old median) + 5