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Math Expert V
Joined: 02 Sep 2009
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Question Stats: 65% (00:47) correct 35% (00:56) wrong based on 83 sessions

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Each term of set $$T$$ is a multiple of 5. Is standard deviation of $$T$$ positive?

(1) Each term of set $$T$$ is positive

(2) $$T$$ consists of one term

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Math Expert V
Joined: 02 Sep 2009
Posts: 58434

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Official Solution:

The standard deviation of a set 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, which means that the standard deviation of any set is greater than or equal to zero: $$SD \ge 0$$.

Next, the standard deviation of a set is zero if and only the set consists of identical numbers (or which is the same if the set consists of only one number).

(1) Each term of set $$T$$ is positive. If $$T=\{5\}$$ then then $$SD=0$$ but if set $$T=\{5, 10\}$$ then $$SD \gt 0$$. Not sufficient.

(2) Set $$T$$ consists of one term. Any set with only one term has the standard deviation equal to zero. Sufficient.

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I think this question is good and helpful.
Intern  Joined: 14 May 2014
Posts: 39
Schools: Broad '18 (WA\$)
GMAT 1: 700 Q44 V41 GPA: 3.11

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Bunuel wrote:
Official Solution:

The standard deviation of a set 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, which means that the standard deviation of any set is greater than or equal to zero: $$SD \ge 0$$.

Next, the standard deviation of a set is zero if and only the set consists of identical numbers (or which is the same if the set consists of only one number).

(1) Each term of set $$T$$ is positive. If $$T=\{5\}$$ then then $$SD=0$$ but if set $$T=\{5, 10\}$$ then $$SD \gt 0$$. Not sufficient.

(2) Set $$T$$ consists of one term. Any set with only one term has the standard deviation equal to zero. Sufficient.

dont we consider 0 as a positive no..? in that case both statements would be sufficient. pls help.
Math Expert V
Joined: 02 Sep 2009
Posts: 58434

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riyazgilani wrote:
Bunuel wrote:
Official Solution:

The standard deviation of a set 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, which means that the standard deviation of any set is greater than or equal to zero: $$SD \ge 0$$.

Next, the standard deviation of a set is zero if and only the set consists of identical numbers (or which is the same if the set consists of only one number).

(1) Each term of set $$T$$ is positive. If $$T=\{5\}$$ then then $$SD=0$$ but if set $$T=\{5, 10\}$$ then $$SD \gt 0$$. Not sufficient.

(2) Set $$T$$ consists of one term. Any set with only one term has the standard deviation equal to zero. Sufficient.

dont we consider 0 as a positive no..? in that case both statements would be sufficient. pls help.

You should brush up fundamentals.

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Check more here: number-properties-tips-and-hints-174996.html
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I think this is a high-quality question and I agree with explanation.
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It is very tricky because of two crucial facts:
(1) SD is never negative. Think of its formula. SD is zero when single or same elements.
(2) Zero is neither positive nor negative.
Intern  Joined: 25 Dec 2015
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Bunuel wrote:
Official Solution:

The standard deviation of a set 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, which means that the standard deviation of any set is greater than or equal to zero: $$SD \ge 0$$.

Next, the standard deviation of a set is zero if and only the set consists of identical numbers (or which is the same if the set consists of only one number).

(1) Each term of set $$T$$ is positive. If $$T=\{5\}$$ then then $$SD=0$$ but if set $$T=\{5, 10\}$$ then $$SD \gt 0$$. Not sufficient.

(2) Set $$T$$ consists of one term. Any set with only one term has the standard deviation equal to zero. Sufficient.

Are we not required to find whether the SD is positive or not and from the answer you have provided does not A give us SD>0 ?
So should not the answer be D instead of B ?
Math Expert V
Joined: 02 Aug 2009
Posts: 7991

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soumya90 wrote:
Bunuel wrote:
Official Solution:

The standard deviation of a set 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, which means that the standard deviation of any set is greater than or equal to zero: $$SD \ge 0$$.

Next, the standard deviation of a set is zero if and only the set consists of identical numbers (or which is the same if the set consists of only one number).

(1) Each term of set $$T$$ is positive. If $$T=\{5\}$$ then then $$SD=0$$ but if set $$T=\{5, 10\}$$ then $$SD \gt 0$$. Not sufficient.

(2) Set $$T$$ consists of one term. Any set with only one term has the standard deviation equal to zero. Sufficient.

Are we not required to find whether the SD is positive or not and from the answer you have provided does not A give us SD>0 ?
So should not the answer be D instead of B ?

Hi,
we are required to find out if SD is positive...
but we do not get a clear answer from A..
1) if there is only one element, or all elements are same say 5,5,5.. SD = 0..
2) if more than one and different, SD>0..

so SD can be 0, which is neither positive or negative or SD >0..
that is why insuff..
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I think this is a high-quality question and I agree with explanation.
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Intern  B
Joined: 22 Dec 2017
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Each term of set T is a multiple of 5. Is standard deviation of T positive?

(1) Each term of set T is positive

(2) T consists of one term
Hi,
the first statement is clearly not sufficient to answer the question about the SD.
The second SD=0 and 0 is neither positive nor negative , so that still didn't answer our question whether SD is positive or negative .
Please explain how statement 2 is sufficient.
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Joined: 01 Apr 2018
Posts: 11
Location: India
WE: Consulting (Consulting)

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I think this is a high-quality question and I agree with explanation.
Intern  B
Joined: 15 Oct 2017
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Bunuel wrote:
Official Solution:

The standard deviation of a set 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, which means that the standard deviation of any set is greater than or equal to zero: $$SD \ge 0$$.

Next, the standard deviation of a set is zero if and only the set consists of identical numbers (or which is the same if the set consists of only one number).

(1) Each term of set $$T$$ is positive. If $$T=\{5\}$$ then then $$SD=0$$ but if set $$T=\{5, 10\}$$ then $$SD \gt 0$$. Not sufficient.

(2) Set $$T$$ consists of one term. Any set with only one term has the standard deviation equal to zero. Sufficient.

Bunuel

What i dont understand is that why shouldnt the answer be D. since from both we can answer the question whether the result is positive or not
Math Expert V
Joined: 02 Sep 2009
Posts: 58434

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chinmay96 wrote:
Bunuel wrote:
Official Solution:

The standard deviation of a set 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, which means that the standard deviation of any set is greater than or equal to zero: $$SD \ge 0$$.

Next, the standard deviation of a set is zero if and only the set consists of identical numbers (or which is the same if the set consists of only one number).

(1) Each term of set $$T$$ is positive. If $$T=\{5\}$$ then then $$SD=0$$ but if set $$T=\{5, 10\}$$ then $$SD \gt 0$$. Not sufficient.

(2) Set $$T$$ consists of one term. Any set with only one term has the standard deviation equal to zero. Sufficient.

Bunuel

What i dont understand is that why shouldnt the answer be D. since from both we can answer the question whether the result is positive or not

The question asks whether SD is positive. From (2) in one case, when $$T=\{5\}$$ the $$SD=0$$ (so NOT positive) and in another case, when $$T=\{5, 10\}$$ the $$SD \gt 0$$ (so positive). Two answers. Not sufficient.
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