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Intern  Joined: 08 Mar 2011
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Set A consists of all prime numbers between 10 and 25; Set B  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 67% (01:42) correct 33% (01:53) wrong based on 472 sessions

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Set A consists of all prime numbers between 10 and 25; Set B consists of consecutive even integers, and set C consists of consecutive multiples of 7. If all the three sets have an equal number of terms, which of the following represents the ranking of these sets in an ascending order of the standard deviation?

(A) C, A, B
(B) A, B, C
(C) C, B, A
(D) B, C, A
(E) B, A, C

Originally posted by punyadeep on 14 Mar 2011, 08:05.
Last edited by Bunuel on 16 Jun 2013, 10:46, edited 1 time in total.
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Set A consists of all prime numbers between 10 and 25; Set B consists of consecutive even integers, and set C consists of consecutive multiples of 7. If all the three sets have an equal number of terms, which of the following represents the ranking of these sets in an ascending order of the standard deviation?

(A) C, A, B
(B) A, B, C
(C) C, B, A
(D) B, C, A
(E) B, A, C

Set A - {11, 13, 17, 19, 23};
Set B - {5 consecutive even integers}, for example - {12, 14, 16, 18, 20};
Set C - {5 consecutive multiples of 7}, for example - {7, 14, 21, 28, 35}.

Now, 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.

You can see that set C is most widespread and set B is least widespread, so the correct answer is: B, A, C.

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thnx so much..........oa is incorrect then...!!
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A-> 11,13,17,19,23

B-> 0,2,4,6,8

C -> 7,14,21,28,35

So the answer is E, as C hax maximum gap between elements, and A has slightly more than B because of the last number - 23.

The OA seems to be wrong. Just curious to know where is this question from; I've seen two SD questions with wrong OA now.
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the question is from 700-800 level questions.........however there is no source,,,if u wish i can upload the document cos i find this document very good...!!!
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SD will be high if the sample is not compact since SD is a measure of compactness.

Mean will fall in the middle of the highest and lowest. So more the distance from the mean - the higher the SD. Assuming all the data is positive the SD will be proportional to the range (highest - smallest)

Set A {11 13 17 19 23} range = 12
Se B {12 14 16 18 20} range = 8
Set C {14 21 28 35 42 } range = 28

SD(B) < SD(A) < SD(C)

Please correct me if this reasoning is wrong.
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the question is from 700-800 level questions.........however there is no source,,,if u wish i can upload the document cos i find this document very good...!!!

Just my 2 cents: there are a lot of "good" documents around.. but least we can do is be careful on our part. If others didnt testify the right answer, I would have missed my dinner!

Edit: I just found out, this question is from Veritas Prep "Statistics and Problem Solving" book and the OA is indeed E.
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the question is from 700-800 level questions.........however there is no source,,,if u wish i can upload the document cos i find this document very good...!!!

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@ fluke...two documents iam uploading......they were sent to me by a frnd who scored 750 and he just went through this document for quant twice.......i found it focussed and helpful too...!!
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@ fluke...here r the answwers to it...!!
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File comment: answers with detailed explanations BIBLE SOLUTIONS.pdf [1.95 MiB]

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Re: Set A consists of all prime numbers between 10 and 25; Set B  [#permalink]

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Bumping for review and further discussion.
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Re: Set A consists of all prime numbers between 10 and 25; Set B  [#permalink]

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Set A consists of all prime numbers between 10 and 25; Set B consists of consecutive even integers, and set C consists of consecutive multiples of 7. If all the three sets have an equal number of terms, which of the following represents the ranking of these sets in an ascending order of the standard deviation?

(A) C, A, B
(B) A, B, C
(C) C, B, A
(D) B, C, A
(E) B, A, C

Set A $$\to {11,13,17,19,23}$$

Fact: Addition/subtraction of any number from a given set doesn't change the S.D of the given set.

From Set A, subtract 11 across to represent $$Set A^'$$ as $$\to {0,2,6,8,12}$$. $$S.D of Set A = S.D of Set A^'$$

If you notice closely, Set $$A^'$$ is very close to Set B, just that Set B looks like $$\to{0,2,4,6,8}$$,i.e. a data-point of 12 is present instead of 4, which makes $$Set A^'$$ more spread-out then Set B.

Thus, $$S.D of Set B< S.D of Set A^'$$

Assume Set C$$\to {0,7,14,21,28}$$

S.D represents how far are the data points are from the mean of the set, we can see that Set C has the most spread-out data points and the correct order = B,A,C.

E.
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Originally posted by mau5 on 12 Jul 2013, 09:28.
Last edited by mau5 on 12 Jul 2013, 12:03, edited 1 time in total.
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Re: Set A consists of all prime numbers between 10 and 25; Set B  [#permalink]

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1
Set A consists of all prime numbers between 10 and 25; Set B consists of consecutive even integers, and set C consists of consecutive multiples of 7. If all the three sets have an equal number of terms, which of the following represents the ranking of these sets in an ascending order of the standard deviation?

(A) C, A, B
(B) A, B, C
(C) C, B, A
(D) B, C, A
(E) B, A, C

Hi,

few things to keep in mind.
=>std deviation depends on distance of each term from mean and number of terms.==>since number of terms are same..we are concerned only about distance of EACH TERM from MEAN.==more the distance more the deviation.
=>std deviation is always positive==>so not concerned whether numbers are positive or negative.

SET A==>(11,13,17,19,23)==>avg around 16==>you can see distance of 11,13,17,19,23 is 5,3,1,3,7....1)
SET B==>(CONSECUTIVE EVEN INTEGERS...)= ( N-4,N-2,N,N+2,N+4)===>mean=N==>DISTANCE FROM MEAN= 4,2,0,2,4
SET C==>MULTIPLES OF 7 ====N-14,N-7,N,N+7,N+14===>MEAN=N====>DISTANCE FROM MEAN=14,7,0,7,14.

if we compare all distance clearly we can say B<A<C===>HENCE OPTION E
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Re: Set A consists of all prime numbers between 10 and 25; Set B  [#permalink]

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gmat1220 wrote:
SD will be high if the sample is not compact since SD is a measure of compactness.

Mean will fall in the middle of the highest and lowest. So more the distance from the mean - the higher the SD. Assuming all the data is positive the SD will be proportional to the range (highest - smallest)

Set A {11 13 17 19 23} range = 12
Se B {12 14 16 18 20} range = 8
Set C {14 21 28 35 42 } range = 28

SD(B) < SD(A) < SD(C)

Please correct me if this reasoning is wrong.

Buneal, please could you provide more info on how the standard deviation is proportional to the range. Is this strategy useful when you are in stressed conditions?

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Re: Set A consists of all prime numbers between 10 and 25; Set B  [#permalink]

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Bunuel wrote:
Set A consists of all prime numbers between 10 and 25; Set B consists of consecutive even integers, and set C consists of consecutive multiples of 7. If all the three sets have an equal number of terms, which of the following represents the ranking of these sets in an ascending order of the standard deviation?

(A) C, A, B
(B) A, B, C
(C) C, B, A
(D) B, C, A
(E) B, A, C

Set A - {11, 13, 17, 19, 23};
Set B - {5 consecutive even integers}, for example - {12, 14, 16, 18, 20};
Set C - {5 consecutive multiples of 7}, for example - {7, 14, 21, 28, 35}.

Now, 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.

You can see that set C is most widespread and set B is least widespread, so the correct answer is: B, A, C.

Great explanation...
But you don't even have to list them out..

we know that each prime number greater than 3 can be expressed in the form 6n + 1 or 6n - 1
Clearly the difference will be less than 7

and talking about A, the difference will be 2 units.

Therefore C is our winner, followed by B and then A. Re: Set A consists of all prime numbers between 10 and 25; Set B   [#permalink] 18 Jun 2020, 05:25

# Set A consists of all prime numbers between 10 and 25; Set B   