I am stuck between A and B.

I guess I will choose B. Not sure why though.

Well I am not sure whats wrong with my calc. None of the answers actually give an SD the same as the original
The original SD is sqrt(8)
Because it is sqrt(((4 - 0)^2 + (4 - 2)^2 + (4 - 4)^2 + (4 - 6)^2 + (4 - 8)^2))/5)
which is sqrt(40/5) = sqrt(8)
Now the denominator for the sd within the sqrt for every option has to be 7 because you are adding two more numbers in the set
And for SD to remain the same the numerator has to be 7*8 i.e 56. Now which of the options yields a numerator of 56??. None
So I am not sure whats going on

IMO B.

5 nos are 0 2 4 6 8.

So we can see that every value is 2 units apart.

And the median is 4.

And if we will add 4 and 4.the SD will not change.

0 2 4 4 4 6 8. In this median remain the same(4).
and equal value on both the sides to the median.