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# DS: STDs (m08q09)

Author Message
Manager
Joined: 10 Jan 2011
Posts: 240
Location: India
GMAT Date: 07-16-2012
GPA: 3.4
WE: Consulting (Consulting)
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Kudos [?]: 63 [0], given: 25

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11 Apr 2012, 00:23
HG wrote:
Standard deviation is always postivie . It's a average distance from mean. Distance can't be negative

1 - Suff
2- St dev is 0 - Suff

D

Yes St daviation can be positive or zero. Please note that zero is neighter positive nor negative.

A is not suff as STD can be positive or negative
B is suff as STD is 0

IMO ANS B
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-------Analyze why option A in SC wrong-------

Manager
Status: I will not stop until i realise my goal which is my dream too
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Schools: Johnson '15
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Kudos [?]: 53 [0], given: 16

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12 Apr 2012, 07:12
snkrhed wrote:
I'm not going to go into "how to solve" since many others are do it much better than I do.

I think for this question the key factors to know are:
1) definition of standard definition
2) definition of "0"

remember, when all numbers are the same or if there is one number in the set, the standard deviation is 0.
0 is not a positive integer. (positive integer is > 0).

SD problems are the ones i miss and i failed here too....
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Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

Satyameva Jayate - Truth alone triumphs

Math Expert
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Posts: 39065
Followers: 7757

Kudos [?]: 106583 [0], given: 11630

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11 Apr 2013, 05:09
Set $$T$$ consists of odd integers divisible by 5. Is standard deviation of $$T$$ positive?

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

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

On a side note, when a question tells you a set S has numbers x,y,z - do we assume that x y z will always be different numbers? or can they be the same number, but repeated 3 times.

BELOW IS REVISED VERSION OF THIS QUESTION:

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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Kudos [?]: 53 [0], given: 9

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11 Apr 2013, 05:21
Question: Is SD > 0?
S1: T = {5} => SD = 0 => No
T = (5, 15, 35} => SD > 0 => Yes
S1 is not sufficient.

S2: T = {5) => SD = 0 => No
T = (15) => SD = 0 => No
T = (25) => SD = 0 => No
S2 is sufficient.

B is correct.
Manager
Joined: 31 May 2011
Posts: 203
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Kudos [?]: 2 [0], given: 4

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11 Apr 2013, 05:47
snkrhed wrote:
I'm not going to go into "how to solve" since many others are do it much better than I do.

I think for this question the key factors to know are:
1) definition of standard definition
2) definition of "0"

remember, when all numbers are the same or if there is one number in the set, the standard deviation is 0.
0 is not a positive integer. (positive integer is > 0).

Sorry but is there some mistake here.
Thought this helpful set of Bunuel

math-number-theory-88376.html

Then positive number is a real number greater than 0
And 0 is not negative or positive number. Then in (2) SD = 0 => Why 0 is a positive number.

I find out this revise of Bunuel
ds-stds-m08q09-73347-20.html#p1210600
He also says the answer is B.
Could anyone here explain for me?
Math Expert
Joined: 02 Sep 2009
Posts: 39065
Followers: 7757

Kudos [?]: 106583 [1] , given: 11630

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11 Apr 2013, 05:51
1
KUDOS
Expert's post
thaihoang305 wrote:
snkrhed wrote:
I'm not going to go into "how to solve" since many others are do it much better than I do.

I think for this question the key factors to know are:
1) definition of standard definition
2) definition of "0"

remember, when all numbers are the same or if there is one number in the set, the standard deviation is 0.
0 is not a positive integer. (positive integer is > 0).

Sorry but is there some mistake here.
Thought this helpful set of Bunuel

math-number-theory-88376.html

Then positive number is a real number greater than 0
And 0 is not negative or positive number. Then in (2) SD = 0 => Why 0 is a positive number.

I find out this revise of Bunuel
ds-stds-m08q09-73347-20.html#p1210600
He also says the answer is B.
Could anyone here explain for me?

From (2) we get that SD=0, thus the answer to the question "is SD positive" is NO, which makes the second statement sufficient.
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Kudos [?]: 2 [0], given: 4

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11 Apr 2013, 05:54
Bunuel wrote:
thaihoang305 wrote:
snkrhed wrote:
I'm not going to go into "how to solve" since many others are do it much better than I do.

I think for this question the key factors to know are:
1) definition of standard definition
2) definition of "0"

remember, when all numbers are the same or if there is one number in the set, the standard deviation is 0.
0 is not a positive integer. (positive integer is > 0).

Sorry but is there some mistake here.
Thought this helpful set of Bunuel

math-number-theory-88376.html

Then positive number is a real number greater than 0
And 0 is not negative or positive number. Then in (2) SD = 0 => Why 0 is a positive number.

I find out this revise of Bunuel
ds-stds-m08q09-73347-20.html#p1210600
He also says the answer is B.
Could anyone here explain for me?

From (2) we get that SD=0, thus the answer to the question "is SD positive" is NO, which makes the second statement sufficient.

Thank you so much Bunuel
Manager
Joined: 15 Aug 2012
Posts: 110
Location: India
Concentration: Technology, Strategy
Schools: Merage '15 (A)
GPA: 3.6
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Kudos [?]: 47 [0], given: 22

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11 Apr 2013, 07:29
Set T consists of odd integers divisible by 5. Is standard deviation of positive?

1. All members of T are positive
2. consists of only one member

for 1. the SD can be 0(all same) or positive(all different). Hence Not Sufficient
for 2. the SD is 0 so sufficient.

Hence IMO B
Intern
Joined: 11 Jan 2010
Posts: 38
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Kudos [?]: 53 [0], given: 9

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11 Apr 2013, 08:18
Although it's true that this problem is tests on the concept or definition of the standard deviation, I think that I'd like to further break up my the evaluation of the two statements. Using the concept, here is how I'd solve this:

Set T = {5 * I} where I = 1, 3, 5, 7, ..., or n
Question: Is SD = positive?
S1: All member of T are positive.
Here are some of rules:
If the set consists of only one item, then SD = 0 (because mean is same as the item).
If the set consists of evenly distributed number, then SD > 0
So, making use of these two rule, we know that this answer is not sufficient.

S2: T consists of only one number.
In this case, we know that SD is always 0. So, the answer to the question is always no.
Therefore, S2 is sufficient.

Re: DS: STDs (m08q09)   [#permalink] 11 Apr 2013, 08:18

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# DS: STDs (m08q09)

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