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DS: STDs (m08q09)

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Re: DS: STDs [#permalink] New post 10 Apr 2012, 23:23
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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Re: DS: STDs (m08q09) [#permalink] New post 12 Apr 2012, 06:12
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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Re: DS: STDs (m08q09) [#permalink] New post 11 Apr 2013, 04:09
Expert's post
bigfernhead wrote:
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

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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.

Answer: B.
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Re: DS: STDs (m08q09) [#permalink] New post 11 Apr 2013, 04:21
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.
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Re: DS: STDs (m08q09) [#permalink] New post 11 Apr 2013, 04:47
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?
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Re: DS: STDs (m08q09) [#permalink] New post 11 Apr 2013, 04:51
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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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: DS: STDs (m08q09) [#permalink] New post 11 Apr 2013, 04:54
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 :-D :-D :-D
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Re: DS: STDs (m08q09) [#permalink] New post 11 Apr 2013, 06:29
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
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Re: DS: STDs (m08q09) [#permalink] New post 11 Apr 2013, 07:18
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.

B is the correct answer.
Re: DS: STDs (m08q09)   [#permalink] 11 Apr 2013, 07:18
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