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

Question

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

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

Bunuel · Accepted Answer

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.

Answer: E.

punyadeep · Answer

thnx so much..........oa is incorrect then...!!

subhashghosh · Answer

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.

punyadeep · Answer

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...!!!

gmat1220 · Answer

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.

gmatpapa · Answer

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.

fluke · Answer

Please do so. thanks.

punyadeep · Answer

@ 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...!!

punyadeep · Answer

@ fluke...here r the answwers to it...!!

Bunuel · Answer

Bumping for review and further discussion.

mau5 · Answer

Set A  	o {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  	o {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  	o{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 	o {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.

blueseas · Answer

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 BHENCE OPTION E

Alchemist14 · Answer

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?

Thanks in Advance

D4kshGargas · Answer

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.

750Barrier · Answer

hello , how do you know there are only 5 numbers in second and third set. understand that in first set, a restriction is given. nothing of such sort is given for 2nd and 3rd set. 
in that case.. answer should be C. 
please clarify !

Bunuel · Answer

Check the highlighted part in the stem.

bumpbot · Answer

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

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

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