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If M is a negative integer and K is a positive integer

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If M is a negative integer and K is a positive integer  [#permalink]

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New post 31 Jan 2012, 00:08
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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
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If M is a negative integer and K is a positive integer  [#permalink]

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New post 31 Jan 2012, 00:56
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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.

Answer: E.

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

PS questions on SD: ps-questions-about-standard-deviation-85897.html
DS questions on SD: ds-questions-about-standard-deviation-85896.html

Hope it helps.
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Re: M is a negative integer and K is a positive integer  [#permalink]

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New post 31 Jan 2012, 00:57
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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 :lol: trying, but still cant be hehe
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Re: M is a negative integer and K is a positive integer  [#permalink]

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New post 31 Jan 2012, 21:36
Thanks Bunnel and Rohit for this good post and explanation
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Re: If M is a negative integer and K is a positive integer  [#permalink]

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New post 12 Aug 2013, 03:49
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


SD is always positive ...hence E.

IF the question would have been that what could be themedian.in that case answer would be C.
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Re: If M is a negative integer and K is a positive integer  [#permalink]

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New post 26 Aug 2015, 19:36
Bunuel wrote:
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.

Answer: E.

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.


Hope it helps.

_________________________________________________________________________________________




Hi,

I understood that SD cant be negative,
but SD can be zero, because SD <= 1/2 Range and if the range of a set is ZERO then SD will also be ZERO (I read this somewhere).

Please comment
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Re: If M is a negative integer and K is a positive integer  [#permalink]

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New post 26 Aug 2015, 23:47
gaganjyot11 wrote:
Bunuel wrote:
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.

Answer: E.

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.


Hope it helps.

_________________________________________________________________________________________




Hi,

I understood that SD cant be negative,
but SD can be zero, because SD <= 1/2 Range and if the range of a set is ZERO then SD will also be ZERO (I read this somewhere).

Please comment


SD is 0 only when the list contains all identical elements (or which is same only 1 element).

Check for more here: statistics-made-easy-all-in-one-topic-203966.html
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Re: If M is a negative integer and K is a positive integer  [#permalink]

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New post 04 Dec 2015, 19:05
good one..very tricky
SD can never be negative, thus I and II out
SD will be 0 only when all the elements of the set are equal. thus, in our case, it can't be 0.
if m is -1 and k is 5, then SD would be between 1 and 2.
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Re: If M is a negative integer and K is a positive integer  [#permalink]

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New post 18 Feb 2018, 02:07
-1.5,-2 cannot be the standard deviation,Because standard deviation can never be a negative number. SD>=0
SD=0 only when all the terms are equal.Irrespective of M and K all terms are not equal.So SD cannot be equal to 0 also.
So answer is none (E)
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Re: If M is a negative integer and K is a positive integer  [#permalink]

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New post 17 Jun 2018, 23:09
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  [#permalink]

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New post 17 Jun 2018, 23:16
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?


What is confusing there? Yes, SD as well as the even roots (such as square root of a number) is 0 or positive.
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Re: If M is a negative integer and K is a positive integer  [#permalink]

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New post 18 Jun 2018, 00:12
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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  [#permalink]

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New post 20 Jun 2018, 22:15
VeritasPrepKarishma wrote:
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/


Thanks. This was the confusion!
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Re: If M is a negative integer and K is a positive integer  [#permalink]

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New post 20 Jun 2018, 22:36

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.

Image

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
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Re: If M is a negative integer and K is a positive integer  [#permalink]

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New post 11 Sep 2018, 10:10
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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


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.

Answer: E

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Re: If M is a negative integer and K is a positive integer   [#permalink] 11 Sep 2018, 10:10
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