Hi Prem,

Kindly check the question before posting.

Here is the original question

4, 6, 8, 10, 12, 14, 16, 18, 20, 22

List M(not shown) consists of 8 different integers, each of which is in the list shown(above). What is the standard deviation of the numbers in list M?

(1) The average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list shown.
(2) List M does not contain 22.

Standard deviation of any set depends on two things:

1. deviation of all the elements from the mean
2. number of elements in the set

Statement 1 : The average of the given list is 13 ((4 + 22)/2) and the sum of all the elements is 130. So for set M to have an average 13, the sum of all the elements of list M which has 8 elements has to be 13 * 8 = 104. 104 is 26 less than 130, so we need to remove two elements from the given list which add up to 26 i.e. (4,22), (6, 20), (8, 18). (10, 16), (12, 14)

Possibility 1 : If we remove 4 and 22 then we need to find the SD of 6, 8, 10, 12, 14, 16, 18, 20

Possibility 2 : If we remove 20 and 6 then we need to find the SD of 4, 8, 10, 12, 14, 16, 18,  22.

Now in both these cases the number of elements are the same, but the mean and deviations from the mean are different. So we get multiple answers for the SD. Insufficient.

Statement 2 : Clearly insufficient, as we can select any 8 of the remaining 9 values which gives us different SD’s.

Combining 1 and 2 : The sum of the 8 elements need to be 104. If we remove 22 then the only way to remove a total of 26 will be to remove 4, so the only two numbers we can remove are 4 and 22 which leaves us with one single set M = {6, 8, 10, 12, 14, 16, 18, 20}. Sufficient.