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# Each term of set T is a multiple of 5. Is standard deviation

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Each term of set T is a multiple of 5. Is standard deviation  [#permalink]

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04 Sep 2009, 17:29
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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) Set T consists of one term

M08-09
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Re: Each term of set T is a multiple of 5. Is standard deviation  [#permalink]

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04 Sep 2009, 18:57
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4

1.) Let T = { 5,15}
Mean = 10
$$sd =\sqrt{\frac{((5 - 10)^2 + (15-10)^2)}{2}}$$

=>$$sd = 5$$ > 0

but, if T = {5,5}
Then Sd = 0 ,, uncertainity,,,hence, insufficient..

2.) T has only one member..
sd = 0 hence, sufficient.. sd is not positive..
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Re: Each term of set T is a multiple of 5. Is standard deviation  [#permalink]

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20 Oct 2012, 19:35
1
Ans is B

1) If pos nos are 5 10 15 the SD>0
If pos nos are same 15 15 15 SD= 0

SD=0 or SD>0

2) Only one number SD= 0
Hence suff to say SD is not greater than zero . SUFFICIENT
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Re: Each term of set T is a multiple of 5. Is standard deviation  [#permalink]

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20 Oct 2012, 23:32
1) If T is {5,10,15} then standard deviation is positive. If T is {5,5,5} then standard deviation is 0. Insufficient

2)T contains only one number. Hence standard deviation can only be 0. Sufficient.

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Re: Each term of set T is a multiple of 5. Is standard deviation  [#permalink]

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22 Oct 2012, 08:18
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Jivana wrote:
If set $$T$$ consists of odd integers divisible by 5, is the standard deviation of $$T$$ positive?

(1) All members of $$T$$ are positive
(2) $$T$$ consists of only one member

Revised version of this question is below:

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

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 can not be negative, which means that the standard deviation of any set is greater than or equal to zero: .

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>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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Re: Each term of set T is a multiple of 5. Is standard deviation  [#permalink]

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26 Feb 2013, 03:25
I am cheated and fail.

he he,

very easy to die if we are in the test room.

fluency on math must be high
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Re: Each term of set T is a multiple of 5. Is standard deviation  [#permalink]

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21 Apr 2013, 01:45
Bunuel wrote:
Jivana wrote:
If set $$T$$ consists of odd integers divisible by 5, is the standard deviation of $$T$$ positive?

(1) All members of $$T$$ are positive
(2) $$T$$ consists of only one member

Revised version of this question is below:

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

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 can not be negative, which means that the standard deviation of any set is greater than or equal to zero: .

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>0. Not sufficient.

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

But isn't 0 neither positive nor negative ?? i am confused!!
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Re: Each term of set T is a multiple of 5. Is standard deviation  [#permalink]

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21 Apr 2013, 01:49
shelrod007 wrote:
But isn't 0 neither positive nor negative ?? i am confused!!

Indeed my friend.

Bunuel says:

(2) Set T consists of one term --> any set with only one term has the standard deviation equal to zero. As YOU say 0 is neither positive nor negative, so is the standard deviation positive? NO . Sufficient.

The std deviation is 0 and because 0 is not positive or negative, this is sufficient to answer..

Hope this clarifies, let me know
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Re: Each term of set T is a multiple of 5. Is standard deviation  [#permalink]

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07 Sep 2014, 00:25
Jivana wrote:
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) Set T consists of one term

M08-09

1. say terms are 5,5,5,5,5 then SD=0 if 5,10,15 then SD is +ive.. Not suff

2. only one term then SD is zero. hence not +ive--- suff
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Re: Each term of set T is a multiple of 5. Is standard deviation  [#permalink]

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18 Oct 2015, 06:35
1
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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) Set T consists of one term

In the original condition, the question asks whether the standard deviation is positive, but standard deviations in general are always greater than or equal to 0. Only when the terms are all equal or when there is only one term will the standard deviation equal 0. Hence, as in condition 2, the set T consists of one term, the standard deviation becomes 0, and the answer to the question becomes 'no' so this is a sufficient condition.
In condition 1, we cannot know whether the terms are equal or different, so this is an insufficient condition, making the answer (B).
This type of question is not normally seen in tests.

Normally, questions regarding standard deviations have too much variables that make (E) the answer, or else the standard deviation becomes 0; only these types of question are normally seen in tests.
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Each term of set T is a multiple of 5. Is standard deviation  [#permalink]

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18 Oct 2015, 22:08
1
Jivana wrote:
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) Set T consists of one term

SD in layman terms is the distance between each term and the mean of the set

Given: Each term of the set is a multiple of 5
Required: SD of the set > 0?

Statement 1: Each term of the set is positive
There can be various versions of this set
Set 1: {5, 10, 15}
In this case, SD = 5 (Distance of the elements of the set from the mean)
Set 2: {5, 5, 5}
In this case, SD = 0 (Distance of the elements of the set from the mean)
No unique value of SD

INSUFFICIENT

Statement 2: Set T consists of one term
If there is only one element in the set, then SD = 0
Hence we have a unique value of SD

SUFFICIENT

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Each term of set T is a multiple of 5. Is standard deviation  [#permalink]

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15 Jul 2016, 09:44
Jivana wrote:
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) Set T consists of one term

M08-09

It's a tricky one.
Standard deviation is never negative. So SD can either be 0 or a positive value.

(1) Each term of set T is positive
{2,2,2,2}==> standard deviation is 0
{1,2,3,4,5} ==> standard deviation will be some positive value.. probably 2.17 or something
INSUFFICIENT

(2) Set T consists of one term
Now thats where it gets tricky .Since standard deviation is the square-root of the unbiased estimator of the variance; it has N-1 in the denominator, where N is the total number of samples; therefore when there is only one sample SD become undefined because N-1 become 1-1=0 and zero is the denominator means undefined values.

SO the answer of this question SHOULD BE E unless we assume that undefined means neither negative, nor positive, nor zero...nor infinity...

Bunuel can you look into the answer ... should w e mark it as B or E
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Re: Each term of set T is a multiple of 5. Is standard deviation  [#permalink]

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Re: Each term of set T is a multiple of 5. Is standard deviation   [#permalink] 15 Aug 2019, 00:41
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