If M is a negative integer and K is a positive integer, which of the

SD cant be negative. SD=0 if all the numbers are the same, or it is only one number in the set

So,E is the answ


hm...cant be before Bunuel trying, but still cant be hehe

Hi Bunuel , understand that SD is always greater than or equal to 0. But you say that the square root can never be negative, there always seems to be some confusion regarding this. Can you please direct me to any material which helps in understanding when to consider +/- {square root} and when not to?

Also, check out this post:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2016/0 ... oots-gmat/

Solution

Standard deviation formula is the mean of square of difference between mean and each element of the set which can either be positive or 0.



Thus, SD can either be 0 or positive.
Now, standard deviation is 0 when x= x ̅ or when mean and all the elements of the set are equal.
However, in the set {-7, -5, -3, M, 0, 1, 3, K, 7} all the elements of the given set are not equal.
Thus, none of the given number can be the mean of the set {-7, -5, -3, M, 0, 1, 3, K, 7}.
Hence, the correct answer is option E.

Answer: E

This is just a test of whether you know some properties of standard deviation.

Property 1: Standard deviation is 0 if and only if all of the members of the set are equal to one another.
Property 2: Standard deviation is always positive EXCEPT if Property 1 applies (all members of the set are equal to one another)

Why? You calculate standard deviation by squaring then square rooting a bunch of numbers (Plus a few more steps) (purposely non-exact - I'll follow up on this in a second). The result of the square root of a squared term is always positive (none of the other steps ever change this).

As you know, the GMAT isn't a test of your ability to calculate but rather your ability to think. Pro tip - if you find yourself calculating standard deviation you've indubitably missed an easier, faster solution. Of the three standard deviation questions in the problem solving section of the 2019 OG, none requires calculation. 68 can be solved by estimation, 151 involves three impossible answer choices (probably strategically best to guess between the remaining two), and 166 is really just quick algebra.

We don't need to think about different possible values of M and K, rather we cant decide only by observing the Three Options and checking those with properties of Standard Deviation.

I. Standard deviation can't be negative.
II. Standard deviation of a set can be Zero if all numbers of a set are equal. In the Given set, all numbers are not equal.

The answer is E.

Asked: If M is a negative integer and K is a positive integer, which of the following could be the standard deviation of a set {-7, -5, -3, M, 0, 1, 3, K, 7}?

Standard deviation of a set >=0 and is 0 only if all the elements are equal.

I. -1.5
II. -2
III. 0

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) None

IMO E

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