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Manager  Joined: 07 Nov 2009
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If M is a negative integer and K is a positive integer, which of the  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 54% (01:29) correct 46% (01:47) wrong based on 535 sessions

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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}?

I. -1.5
II. -2
III. 0

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) None
Math Expert V
Joined: 02 Sep 2009
Posts: 61549
Re: If M is a negative integer and K is a positive integer, which of the  [#permalink]

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rohitgoel15 wrote:
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}?
I. -1.5
II. -2
III. 0

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

Important note: SD is always >=0. SD is 0 only when the list contains all identical elements (or which is same only 1 element).

So the answer is clearly E, none.

To elaborate more: Standard deviation shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So, basically we can say that it in a sense measures the distance and the distance cannot be negative. Also if you look at the formula for the standard deviation you'll see that it's square root of some number (variance) and the square root can never be negative.

Check this for more: math-standard-deviation-87905.html

Hope it helps.
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Re: If M is a negative integer and K is a positive integer, which of the  [#permalink]

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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
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Re: If M is a negative integer and K is a positive integer, which of the  [#permalink]

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Bunuel wrote:
So, basically we can say that it in a sense measures the distance and the distance cannot be negative.

Hope it helps.

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?
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Re: If M is a negative integer and K is a positive integer, which of the  [#permalink]

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1
abhishek911 wrote:
Bunuel wrote:
So, basically we can say that it in a sense measures the distance and the distance cannot be negative.

Hope it helps.

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.veritasprep.com/blog/2016/0 ... oots-gmat/
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Re: If M is a negative integer and K is a positive integer, which of the  [#permalink]

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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.

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Re: If M is a negative integer and K is a positive integer, which of the  [#permalink]

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1
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.
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Re: If M is a negative integer and K is a positive integer, which of the  [#permalink]

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Top Contributor
rohitgoel15 wrote:
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}?

I. -1.5
II. -2
III. 0

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

Property 1: The standard deviation of a set of values is always greater than equal to 0
Property 2: If all values in a set are equal, the standard deviation of the set equals 0
Property 3: If the values in a set are NOT all equal, the standard deviation of the set is greater than 0

Now examine the statements...
I. -1.5 standard deviation cannot be negative.
II. -2 standard deviation cannot be negative.
III. 0 since the values are not all equal, the standard deviation cannot be zero.

Cheers,
Brent
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Re: If M is a negative integer and K is a positive integer, which of the  [#permalink]

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