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Range & SD (m03q34) [#permalink]
 26 Oct 2008, 23:39
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Which set(s) has the greatest standard deviation? 1. Set 1 consisting of 10 digits 2. Set 2 consisting of 10 first positive consecutive even numbers 3. Set 3 consisting of 10 first primes (A) set 1 (B) set 2 (C) set 3 (D) set 1 and 2 (E) set 1, 2, and 3 Source: GMAT Club Tests - hardest GMAT questions
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C.
all other things being equal. set of #s with greater differences has the greatest SD.
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How do you know that 10 digits in set 1 are not widely distributed as those in the set of prime numbers. There is no info which tells us this. S1 can be [1,2.....9,10] or [1,4, 23, 56,......1234] or anything else.
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Krishan,
what I know about digits (in this context) is they are 10 numbers that form other numbers: {0,1,2,3,4,5,6,7,8,9}
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Krishan,
That is exactly my question...
Can anyone pls explain how do we know what digits are to be selected for set one?
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Re: Range & SD (m03q34) [#permalink]
06 Oct 2010, 08:35
yes digit refers to number 0 through 9. The number 10 would be a two-digit number (1 and 0 being digits).
As such, a set of 10 digits would be consecutive in order to maximize the standard deviation (we only have ten digits to choose from [0 through 9] so any identical digits in the set would minimize the overall standard deviation of the set).
So, the max standard deviation for set 1 = 1
Set 2 = 2
Set 3 is more than 2 (no need to do the standard deviation calculations, especially on GMAT since it tests only that you know the concept of what it is) when you start getting into the bold parts of the set:
2,3,5,7,11,13,17,,19,21,23
Set three has highest standard deviation, as there are 4 numbers with 4 units between them
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Re: Range & SD (m03q34) [#permalink]
06 Oct 2010, 08:49
C is the answer .
Reason for my choice : In case of SD, the more the difference between numbers mean and number , highest the SD. So in case of C we have the highest SD
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Re: Range & SD (m03q34) [#permalink]
06 Oct 2010, 09:14
The question would have been more clear (i.e. more GMAT-like) if statement 1 said:
1. Set 1 consisting of 10 single-digit integers.
That being said, C is clearly the correct answer...
First 10 primes are 2, 3, 5, 7, 11, 13, 17, 23, 29, and 31.
First 10 positive consecutive even integers are 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20.
If you think about standard deviation as the "average difference between each number" (not technically true but sufficient for GMAT purposes) then the set of primes beats the set of even integers.
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Re: Range & SD (m03q34) [#permalink]
06 Oct 2010, 10:20
Easy one. Answer C. Only C with its set of 10 primes numbers are spaced widely apart and hence its variance and S.D is the highest.
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Re: Range & SD (m03q34) [#permalink]
06 Oct 2010, 10:38
abushey31 wrote: The question would have been more clear (i.e. more GMAT-like) if statement 1 said:
1. Set 1 consisting of 10 single-digit integers.
That being said, C is clearly the correct answer...
First 10 primes are 2, 3, 5, 7, 11, 13, 17, 23, 29, and 31.
First 10 positive consecutive even integers are 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20.
If you think about standard deviation as the "average difference between each number" (not technically true but sufficient for GMAT purposes) then the set of primes beats the set of even integers. Depends. There are numbers and there are digits. Numbers are made of digits ! Actually, there are only 10 digits in Mathematics.
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Re: Range & SD (m03q34) [#permalink]
06 Oct 2010, 10:42
It was easy but after understanding the !st point.Good one.Considered for KUDOS
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Re: Range & SD (m03q34) [#permalink]
06 Oct 2010, 11:05
adishail wrote: abushey31 wrote: The question would have been more clear (i.e. more GMAT-like) if statement 1 said:
1. Set 1 consisting of 10 single-digit integers.
That being said, C is clearly the correct answer...
First 10 primes are 2, 3, 5, 7, 11, 13, 17, 23, 29, and 31.
First 10 positive consecutive even integers are 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20.
If you think about standard deviation as the "average difference between each number" (not technically true but sufficient for GMAT purposes) then the set of primes beats the set of even integers. Depends. There are numbers and there are digits. Numbers are made of digits ! Actually, there are only 10 digits in Mathematics. Right. My point is that by definition Sets contain numbers or variables...saying that a set contains digits is not mathematically clear. Given the way the rest of the question is worded you can reason that that's what the creator of the question meant, but on a real GMAT question it should be more clear in my opinion.
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Re: Range & SD (m03q34) [#permalink]
06 Oct 2010, 11:11
abushey31 wrote: adishail wrote: abushey31 wrote: The question would have been more clear (i.e. more GMAT-like) if statement 1 said:
1. Set 1 consisting of 10 single-digit integers.
That being said, C is clearly the correct answer...
First 10 primes are 2, 3, 5, 7, 11, 13, 17, 23, 29, and 31.
First 10 positive consecutive even integers are 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20.
If you think about standard deviation as the "average difference between each number" (not technically true but sufficient for GMAT purposes) then the set of primes beats the set of even integers. Depends. There are numbers and there are digits. Numbers are made of digits ! Actually, there are only 10 digits in Mathematics. Right. My point is that by definition Sets contain numbers or variables...saying that a set contains digits is not mathematically clear. Given the way the rest of the question is worded you can reason that that's what the creator of the question meant, but on a real GMAT question it should be more clear in my opinion. I believe this is all part of the GMAT trick. A lot of the questions are missed because they are misunderstood. I agree with you, but I guess we have to get use to these tricks. Or at the least, see how we can be tricked. Good Luck !
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Re: Range & SD (m03q34) [#permalink]
07 Oct 2010, 03:27
The Correct Answer is C.
Set 1 ={0,1,2,3,4,5,6,7,8,9} i.e 10 digits
Set 2 ={ 2,4,6,8,10,12,14,16,18,20}
Set 3 ={2,3,5,7,11,13,17,19,23,29}
The S.D is higher for the series that has a higher range...
Just had a little doubt about the first set hope its correct.
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Re: Range & SD (m03q34) [#permalink]
07 Oct 2010, 12:23
Agree on the first set ambiguity. could be more cleare - set 1 consisting of the first 10 digits. C is the answer.
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Re: Range & SD (m03q34) [#permalink]
07 Oct 2010, 18:36
hmmmm i don't see much ambiguity with set 1, it doesn't say first 10 digits. All it says is "Set 1 consisting of 10 digits" which can mean anything. Given with that kind of info, I automatically knocked it out.
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Re: Range & SD (m03q34) [#permalink]
13 Oct 2010, 20:30
Should be C. Although A in theory could be it as its 10 random digits. But C is the only one that is explicitly correct.
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Re: Range & SD (m03q34) [#permalink]
10 Oct 2011, 05:29
Just to add in my point of looking at such questions. Stat2 & 3 are quite clear to everyone, so let me talk only about stat1.
Stmt1: Set 1 is 10 digits. There are two ways to knock this option off.
First, 'a digit' is always a single digit and thus can only be -9, -8, -7 .. to 7,8,9. You can assume that your number is a two-digit or three-digit, only when it is stated explicitly or when it is stated that the number is not a single digit number.
Second way of knocking this off (incase there is confusion on deciding what a digit can be), is to think of the statement in such a way that it holds true under all circumstances. That is, if you chose your numbers 2,3,4...consecutively, then you know your std deviation will be lesser than that of stmt3. However, if you chose your numbers as 1, 100, 3456, 46752, .... so on, you know it will yield a std deviation larger than stmt3.
Thus you will never be in a position to say that stmt will always be true. Hence it is incorrect.
Consider kudos if you liked my explanation...
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Re: Range & SD (m03q34) [#permalink]
10 Oct 2011, 08:46
study wrote: Which set(s) has the greatest standard deviation? 1. Set 1 consisting of 10 digits 2. Set 2 consisting of 10 first positive consecutive even numbers 3. Set 3 consisting of 10 first primes (A) set 1 (B) set 2 (C) set 3 (D) set 1 and 2 (E) set 1, 2, and 3 Source: GMAT Club Tests - hardest GMAT questions A digit in GMAT is always a non-negative single-digit integer Valid digits={0,1,2,3,4,5,6,7,8,9} 1. Set 1 consisting of 10 digits {0,0,0,0,9,9,9,9}- Believe this will give us the max deviation: 4.5 2. Set 2 consisting of 10 first positive consecutive even numbers {2,4,6,8,10,12,14,16,18,20} Diff= 9,7,5,3,1,1,3,5,7,9 3. Set 3 consisting of 10 first primes {3,5,7,11,13,17,19,23,29}. Mean=12 Approx Diff= 9,7,5,1,1,5,7,11,17 These numbers are bigger than their counterpart in 2. Deviation must be greater thus. Ans: "C"
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Re: Range & SD (m03q34) [#permalink]
24 Nov 2011, 15:00
Standard deviation is about the variety of range a set can expand....For ex- set a got (2 4 6 8) Set B got (2 5 7 11) B got the greater SD...
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Re: Range & SD (m03q34)
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24 Nov 2011, 15:00
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