To find the standard deviation we need: the mean, the set of numbers in the list.

1) The mean in the list = the mean of M. Since the list is equally spaced, we can calculate the mean by \(\frac{first\ number\ +\ last\ number}{2}\) = \(\frac{4+\ 22}{2}\) = 13

Since the given list has 10 elements, the sum will be 13 * 10 = 130
Since list M has 8 elements, the sum will be 13 * 8 = 104
The difference inbetween the lists is equal to the sum of the two missing numbers in list M. The difference is 26.
-> This is insufficient information as there are several ways of finding a difference of 26 (e.g 10+16 or 18+8)


2) We are told list M does not contain the number 22.
We do not know the mean of list M with this information, as we do not know what other number list M does not contain.
-> insufficient

C) With 1) and 2) combined we know that the second number not contained in the list will be 22 + x = 26. x = 4.

We know have all the information required to find the standard deviation
C) is the correct answer