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Manager
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Which set has the greatest standard deviation? I. 1, 3, 5, 7, 9 II. 2, 4, 6, 8, 10 III. 1, -1, -3, -5, -7 (A) I (B) II (C) III (D) I and II (E) none Source: GMAT Club Tests - hardest GMAT questions Current explanation implies one would calculate the stddev for the sequence. Alternate explanation: They're all just skip+1 sets of the form f(n)=kn+x, k=2, no need to calculate stddev.
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CIO
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dzyubam wrote: It actually doesn't say that you have to calculate the standard deviation. One should know that if two sets have the same number of terms and the difference between any successive terms is equal in all sets, then standard deviation for these sets is equal. I must admit, stats is not my strongest area. I just considered the difference between the terms and chose E, while I should have considered the number of items too. Good thing no harm was done.
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vaibhavtripathi wrote: dzyubam wrote: It actually doesn't say that you have to calculate the standard deviation. One should know that if two sets have the same number of terms and the difference between any successive terms is equal in all sets, then standard deviation for these sets is equal. I must admit, stats is not my strongest area. I just considered the difference between the terms and chose E, while I should have considered the number of items too. Good thing no harm was done. I did the same thing and counted the difference to get E. What would have happened if there were fewer terms in one of the answer choices?
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I'm trying to not just answer the problem but to explain how I came up with my answer. If I am incorrect or you have a better method please PM me your thoughts. Thanks!
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Manager
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why wasn't the ans c.stndrd deviation is the max deviation nnumbers in the set are having from the mean.mean is 5 and set 3 is having max deviation.
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Manager
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E. All three have same standard deviation as they have the same pattern (difference of 2 amongst the sequence of numbers) Posted from my mobile device 
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hello to all. i will go with C. before calculating Standard Deviation, one should know how to calculate it. here is the link: http://www.icoachmath.com/SiteMap/Stand ... ation.htmlExplanation: Case 1: 1,3,5,7,9 mean=5, deviation from Mean: -4,-2,0,2,4 STandard Deviation =Sqrt[{(-4^2)+(-2^2)+(0)+(2^2)+(4^2)}/5] =2Sqrt2. Case 2: 2,4,6,8,10 Mean = 6 deviation from Mean: -4,-2,0,2,4 STandard Deviation =Sqrt[{(-4^2)+(-2^2)+(0)+(2^2)+(4^2)}/5] =2Sqrt2. Case 3: 1,-1,-3,-5,-7 Mean = 7.5 deviation from Mean: -6.5,-8.5,-10.5,-12.5,14.5 on calculating Standard Deviation ; you will get a higher value 2Sqrt2. so, Final Ans is C. --------------------- give me kudos, if you like my post  thanx for correcting me. the mean will be -7.5 instead of 7.5 in case 3. every thing is correct now.
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Last edited by 321kumarsushant on 16 Nov 2010, 02:23, edited 1 time in total.
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321kumarsushant wrote: Case 3: 1,-1,-3,-5,-7
Mean = 7.5
deviation from Mean: -6.5,-8.5,-10.5,-12.5,14.5
There is a problem here in your solution. pls check. hint: re calculate mean (re look at the number in the denominator) (I think I deserve a kudo now )
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sleekmover wrote: 321kumarsushant wrote: Case 3: 1,-1,-3,-5,-7
Mean = 7.5
deviation from Mean: -6.5,-8.5,-10.5,-12.5,14.5
There is a problem here in your solution. pls check. hint: re calculate mean (re look at the number in the denominator) (I think I deserve a kudo now ) thnx for correcting me.
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Quote: thanx for correcting me.
the mean will be -7.5 instead of 7.5 in case 3.
every thing is correct now. the mean will be -3 (you seems to be using 3 as denominator while 5 should be used)
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sleekmover wrote: Quote: thanx for correcting me.
the mean will be -7.5 instead of 7.5 in case 3.
every thing is correct now. the mean will be -3 (you seems to be using 3 as denominator while 5 should be used) Ohh Crap!!! thnx buddy, the mean will be -3 and i was using 2 as denominator. Anyway, this would go like this: CASE 3: mean = -3 deviation will be: 4,2,0,-2,-4. Standard Deviation: 2Sqrt2. same as A, B & C.
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Thus the answer is none (E)?
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answer is E ........:D
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Clearly,
E.
Number of terms are the same. Difference between the terms are the same. Hence the Standard deviation is going to be the Same.
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Answer is E. It doesn't matter how many terms there are if all are evenly spaced.
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scorcho wrote: Which set has the greatest standard deviation? I. 1, 3, 5, 7, 9 II. 2, 4, 6, 8, 10 III. 1, -1, -3, -5, -7 (A) I (B) II (C) III (D) I and II (E) none Source: GMAT Club Tests - hardest GMAT questions Current explanation implies one would calculate the stddev for the sequence. Alternate explanation: They're all just skip+1 sets of the form f(n)=kn+x, k=2, no need to calculate stddev. BELOW IS REVISED VERSION OF THIS QUESTION: Which of the following sets has the standard deviation greater than the standard deviation of set X={-19, -17, -15, -13, -11}I. A={1, 3, 5, 7, 9} II. B={2, 4, 6, 8, 10} III. C={1, -1, -3, -5, -7} A. Set A only B. Set B only C. Set C only D. Sets A, B and C E. None of the sets If we add or subtract a constant to each term in a set the standard deviation will not change.Since each set can be obtained by adding some constant to each term of set X (20 for set A, 21 for set B and 12 for set C), then the standard deviations of all sets are the same. Answer: E.
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