Hi, there. I'm happy to help with this one.

Prompt: K is a list of integers, what is the standard deviation of the list of numbers?

In general, it's quite a rigmarole to find the standard deviation of a set. I won't explain the whole procedure now, but you need to know the numerical value of every single number in the set.

The only time there's a shortcut is when all the elements of a set are identical. When every single member of a set is the same, then the standard deviation is zero --- they don't deviation from each other at all!

Statement #1: The median of them is 1.

This is beyond useless. The standard deviation is calculated from the mean of the set, not the median. If we knew the mean, we still couldn't calculate the s.d. without knowing all the members of the list, but at least knowing the mean would be a step in the right direction. Knowing the median doesn't contribute bupkis to establishing what the s.d. is. Statement #1 is insufficient.

Statement #2: The range of them is 0.

The range = 0. This mean, all the elements are the same value, because there is zero difference between the highest and the lowest. That, in turn, means we can use the only s.d. shortcut: the standard deviation = 0, because all the elements of the set are identical. Statement #1 is sufficient.

Answer = B

Does all that make sense?

Here is another DS question concerning standard deviation.

https://gmat.magoosh.com/questions/347

When you submit an answer to that question, the next page will bring up a video that gives a full explanation of the question.

Please let me know if you have any further questions.

Mike