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Set Q consists of the following five numbers

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Set Q consists of the following five numbers: Q = {5, 8, 13, 21, 34}. Which of the following sets has the same standard deviation as Set Q?

I. {35, 38, 43, 51, 64}
II. {10, 16, 26, 42, 68}
III. {46, 59, 67, 72, 75}

(A) I only
(B) I & II
(C) I & III
(D) II & III
(E) I, II, & III


For a detailed explanation of everything you need to understand about Standard Deviation for the GMAT, as well as a solution to this particular question, see
http://magoosh.com/gmat/2012/standard-d ... -the-gmat/

Mike :-)
[Reveal] Spoiler: OA

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mikemcgarry wrote:
Set Q consists of the following five numbers: Q = {5, 8, 13, 21, 34}. Which of the following sets has the same standard deviation as Set Q?

I. {35, 38, 43, 51, 64}
II. {10, 16, 26, 42, 68}
III. {46, 59, 67, 72, 75}

(A) I only
(B) I & II
(C) I & III
(D) II & III
(E) I, II, & III


For a detailed explanation of everything you need to understand about Standard Deviation for the GMAT, as well as a solution to this particular question, see
http://magoosh.com/gmat/2012/standard-d ... -the-gmat/

Mike :-)



Facts about Standard Deviation:
(1) Multiplying all the numbers change Standard Deviation
(2) Adding and subtracting all the numbers with the same number keeps the standard deviation same.
If you observe Set I and III are added versions of Set Q .
Set I: 5 has been added to the Set Q
Set III: Subtract each element from 80 and you would find a number there in the Set Q.
Set II: elements are multiplied by 2 and standard deviation changes.

Hence the answer is C.
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Hello from the GMAT Club BumpBot!

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New post 06 Sep 2016, 03:26
Bunuel Can you help us with a way as to how do we tackle such questions?

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New post 06 Sep 2016, 03:47
Keats wrote:
Bunuel Can you help us with a way as to how do we tackle such questions?


Please try to be a little bit more specific. For example, what part of the following solution is not clear: set-q-consists-of-the-following-five-numbers-147917.html#p1187415
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Keats wrote:
Bunuel Can you help us with a way as to how do we tackle such questions?

Dear Keats,
I see that the genius Bunuel answered your request briefly.

I will echo his concern. My friend, one of the habits of excellence is asking excellent questions. When you ask a vague one-line question, the presupposition behind that question is that responsibility for the process of education lies with the expert asked, in this case, Bunuel. In fact, 100% of the responsibility for your learning lies with you. One tangible way to demonstrate this responsibility is to ask thorough and detailed questions that make explicitly clear exactly what you understand and exactly what you don't understand. See:
Asking Excellent Questions

Wishing you excellence, my friend.

Mike :-)
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New post 26 Oct 2016, 14:38
Bunuel

Set Q consists of the following five numbers: Q = {5, 8, 13, 21, 34}. Which of the following sets has the same standard deviation as Set Q?

I. {35, 38, 43, 51, 64}
II. {10, 16, 26, 42, 68}
III. {46, 59, 67, 72, 75}

Can you please help in reaching out to why III is true?

S.D. remains same if we add/subtract a constant number from each element of the set. In Q = {5, 8, 13, 21, 34} , we are trying to subtract each of the element of Q from 80
80 - 5 = 75
80 - 8 = 72
80 - 13 = 67
80 - 21 = 59
80 - 34 = 46

Is it a right way to do this? What I know is that you add or subtract elements to set Q. Not the other way!

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New post 26 Oct 2016, 14:47
Also, Bunuel Can you please share a link, if any, for such problems?Thanks.

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Keats wrote:
Set Q consists of the following five numbers: Q = {5, 8, 13, 21, 34}. Which of the following sets has the same standard deviation as Set Q?

I. {35, 38, 43, 51, 64}
II. {10, 16, 26, 42, 68}
III. {46, 59, 67, 72, 75}

Can you please help in reaching out to why III is true?

S.D. remains same if we add/subtract a constant number from each element of the set. In Q = {5, 8, 13, 21, 34} , we are trying to subtract each of the element of Q from 80
80 - 5 = 75
80 - 8 = 72
80 - 13 = 67
80 - 21 = 59
80 - 34 = 46

Is it a right way to do this? What I know is that you add or subtract elements to set Q. Not the other way!

Dear Keats,

My friend, I'm happy to respond. I see you have requested the genius Bunuel, but I can help: I'm the author of this question.

One way to recognize that III is correct is to see the pattern of subtraction from 80. That's one way to do it, but not the only way.

Think about this. Look at at set Q = {5, 8, 13, 21, 34}. Subtract adjacent numbers to get the pattern of spacing between the numbers: 3-5-8-13. Those are the spaces between the individual data points.
Now, look at the pattern of spacing in III {46, 59, 67, 72, 75}--it's 13-8-5-3. That's the same pattern in reverse. In other words, the basic pattern of spacing in Q and III is the same. If the data points are spaced the same, it doesn't matter where they are on the number line, they have the same standard deviation.

This blog has two more practice problems on Standard Deviation:
Standard Deviation on the GMAT

Does this make sense?
Mike :-)
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Keats wrote:
Also, Bunuel Can you please share a link, if any, for such problems?Thanks.


Check below:

Hope it helps.
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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

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Re: Set Q consists of the following five numbers [#permalink]

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New post 26 Oct 2016, 23:57
mikemcgarry wrote:

Dear Keats,

My friend, I'm happy to respond. I see you have requested the genius Bunuel, but I can help: I'm the author of this question.

One way to recognize that III is correct is to see the pattern of subtraction from 80. That's one way to do it, but not the only way.

Think about this. Look at at set Q = {5, 8, 13, 21, 34}. Subtract adjacent numbers to get the pattern of spacing between the numbers: 3-5-8-13. Those are the spaces between the individual data points.
Now, look at the pattern of spacing in III {46, 59, 67, 72, 75}--it's 13-8-5-3. That's the same pattern in reverse. In other words, the basic pattern of spacing in Q and III is the same. If the data points are spaced the same, it doesn't matter where they are on the number line, they have the same standard deviation.

This blog has two more practice problems on Standard Deviation:
Standard Deviation on the GMAT

Does this make sense?
Mike :-)



Wohoo!! This is awesome to learn. It just simplifies. Thank You mikemcgarry. +1Kudos!

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New post 09 Nov 2016, 18:44
Another approach is to look at the sequence of differences between the numbers in the set and look for them in the other 3 sets, regardless of the order.

Q = {5, 8, 13, 21, 34}. Differences goes as 3 ,5 ,8, 13

I. {35, 38, 43, 51, 64} --> 3 ,5 ,8, 13 --> Same Std Dev.
II. {10, 16, 26, 42, 68} --> 6, 10, 16, 26 --> Different Std Dev.
III. {46, 59, 67, 72, 75} --> 13, 8, 5, 3 --> Same Std Dev.

Hence the answer is C.

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New post 14 Dec 2017, 17:18
niks18

Can you explain why are we focusing on patterns by difference between two adjacent no?
As per my understanding the SD should be approx difference of each no from mean.

Also note that adding / subtracting same integer will not change SD, but here we are adding
different numbers to the list. How can this be a conclusive factor to determine same SD?
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Set Q consists of the following five numbers [#permalink]

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New post 15 Dec 2017, 20:03
adkikani wrote:
niks18

Can you explain why are we focusing on patterns by difference between two adjacent no?
As per my understanding the SD should be approx difference of each no from mean.

Also note that adding / subtracting same integer will not change SD, but here we are adding
different numbers to the list. How can this be a conclusive factor to determine same SD?


Hi adkikani

At first I would suggest that you keep the property in mind as explained by mikemcgarry in his earlier post. it will save you from unnecessary calculation.

As you rightly mentioned that adding / subtracting same integer will not change SD. There is another property which says if you multiply each element of the set by \(k\), then you multiply the standard deviation by \(|k|\) (remember SD is always positive because it is square root of variance. Variance is the average of the squares of difference between each element and mean, so variance will always be positive)

Set Q {5, 8, 13, 21, 34}. let's assume it's SD is \(d\)

Set I, I hope is clear to you as you have used the addition property.

Set III {46, 59, 67, 72, 75}

Now add \(-80\) to each element of the set, you will get {-34,-21,-13,-8,-5}. Re-arrange (if may like to do so to see a pattern, otherwise not required) {-5,-8,-13,-21,-34}

This is same as set Q multiplied by \(-1\), so SD of this set will be \(d*|-1|=d=\) same as set Q

so we can also derive that if basic pattern of spacing between adjacent element of two sets are same then SD will be equal.

This question tests basically few properties of SD which you can easily deduce if you know the STEP TO CALCULATE SD of a given set

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