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# Which data set has the greater standard deviation, data set K or data

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Math Expert
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Which data set has the greater standard deviation, data set K or data  [#permalink]

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26 Feb 2015, 05:36
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Which data set has the greater standard deviation, data set K or data set L?

(1) Every element in data set K is a multiple of 3.

(2) Every element in data set L is a multiple of 9.

Kudos for a correct solution.

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Re: Which data set has the greater standard deviation, data set K or data  [#permalink]

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26 Feb 2015, 19:35
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Hi viktorija,

Since the GMAT is NEVER going to ask you to calculate the Standard Deviation, you have to think about what this question is REALLY testing you on. It's really about your basic understanding of the concept of Standard Deviation and how "spread out" a group of numbers is.

Given the minor 'restrictions' in the prompt and two Facts, the REAL issue is whether the elements in each set are duplicates or not.

The prompt tells us that there are two sets of numbers: Set K and Set L. But we're not told ANYTHING about those Sets. We're asked which has the larger Standard Deviation.

I think that most Test Takers can see that each of the two Facts (individually) just tells us a little bit about each Set of values. So both Facts are INSUFFICIENT.

Combined, we know...
Every element in Set K is a multiple of 3
Every element in Set L is a multiple of 9

Here are two simple examples:
Set K: {3, 3]
Set L: {9, 18]
Set L has the larger Standard Deviation.

Set K: {3, 6]
Set L: {9 9}
Set K has the larger Standard Deviation.
Combined, INSUFFICIENT

In the first example, I could have put 100s of numbers into Set K - if they were all 3s, then the Standard Deviation would still be the same (it would be 0, since all the elements are the same).
In the second example, I could have 100s of numbers into Set L - if they were all 9s, then the Standard Deviation would still be the same (it would be 0).
Thus, in THIS question, the number of terms really isn't the issue.

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Which data set has the greater standard deviation, data set K or data  [#permalink]

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26 Feb 2015, 09:15
1
Each statement alone provides information on only one data set, so alone each statement is insufficient.
Combining the statements is still not sufficient. We do not know anything about how far apart the values of each set are from their respective means.

Example 1:
Set K = {3, 6, 9} with a standard deviation of 3
Set L = {9, 9, 9} with no standard deviation

Example 2:
Set K = {3, 3, 3} with no standard deviation
Set L = {9, 18, 27} with a standard deviation of 9

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Which data set has the greater standard deviation, data set K or data  [#permalink]

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26 Feb 2015, 09:25
1
(1) Insufficient. Information is given only about the set K.
(2) Insufficient. Information is given only about the set L.

(1)+(2) Insufficient. We don't know how many elements are in the set K and in the set L.

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Re: Which data set has the greater standard deviation, data set K or data  [#permalink]

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26 Feb 2015, 11:32
I think the answer is E;

We need to know the number of elements in the data set.
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Re: Which data set has the greater standard deviation, data set K or data  [#permalink]

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26 Feb 2015, 11:43
1
Hi samichange,

Standard Deviation is really about how "spread out" the terms are. The number of terms may or may not be a factor.

For example:

{3, 3, 3} has a Standard Deviation of 0 since all of the terms are the same.
{3, 6} has a Standard Deviation > 0 since the terms are different.
{3, 6, 9, 12, 18} also has a Standard Deviation > 0 for the same reason.

Here, the number of terms was not a factor.

While calculating Standard Deviation in a real-world scenario involves a complicated calculation, the GMAT will never ask you to do that. The subject is rare on Test Day (you'll likely see it just once), but you have to be clear on the basic concepts if you want to get that question correct.

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Re: Which data set has the greater standard deviation, data set K or data  [#permalink]

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26 Feb 2015, 15:39
EMPOWERgmatRichC wrote:
Hi samichange,

Standard Deviation is really about how "spread out" the terms are. The number of terms may or may not be a factor.

For example:

{3, 3, 3} has a Standard Deviation of 0 since all of the terms are the same.
{3, 6} has a Standard Deviation > 0 since the terms are different.
{3, 6, 9, 12, 18} also has a Standard Deviation > 0 for the same reason.

Here, the number of terms was not a factor.

While calculating Standard Deviation in a real-world scenario involves a complicated calculation, the GMAT will never ask you to do that. The subject is rare on Test Day (you'll likely see it just once), but you have to be clear on the basic concepts if you want to get that question correct.

GMAT assassins aren't born, they're made,
Rich

EMPOWERgmatRichC,

Could you please elaborate more on your comment? How come that in order to compare the set K and set L we don't need to know the number of elements of those sets?
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Re: Which data set has the greater standard deviation, data set K or data  [#permalink]

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02 Mar 2015, 06:50
Bunuel wrote:
Which data set has the greater standard deviation, data set K or data set L?

(1) Every element in data set K is a multiple of 3.

(2) Every element in data set L is a multiple of 9.

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

greateststandarddeviation_text.PNG [ 17.56 KiB | Viewed 8532 times ]

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Re: Which data set has the greater standard deviation, data set K or data  [#permalink]

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03 Mar 2015, 12:47
viktorija wrote:
EMPOWERgmatRichC wrote:
Hi samichange,

Standard Deviation is really about how "spread out" the terms are. The number of terms may or may not be a factor.

For example:

{3, 3, 3} has a Standard Deviation of 0 since all of the terms are the same.
{3, 6} has a Standard Deviation > 0 since the terms are different.
{3, 6, 9, 12, 18} also has a Standard Deviation > 0 for the same reason.

Here, the number of terms was not a factor.

While calculating Standard Deviation in a real-world scenario involves a complicated calculation, the GMAT will never ask you to do that. The subject is rare on Test Day (you'll likely see it just once), but you have to be clear on the basic concepts if you want to get that question correct.

GMAT assassins aren't born, they're made,
Rich

EMPOWERgmatRichC,

Could you please elaborate more on your comment? How come that in order to compare the set K and set L we don't need to know the number of elements of those sets?

You don't need to know the number of elements because there isn't enough language to define what those elements in the set are.

With the current wording:

Statement (1) can have 1 or 100 elements. It fails to define the elements you can have 3 repeated 100 times, or 3,6,9,12....etc. -insufficient.

Statement (2) the same logic applies as in statement one. - insufficient.

A counter example may be:

St(1) Set X consists of 5 consecutive positive multiples of 3, beginning with 3.

St(2) Set Y consists of 5 consecutive positive multiples of 9, beginning with 9.

These statements offer enough "definition" to accurately determine the standard deviation, or infer which set would have a larger standard deviation. In this counter example both statement are necessary to answer the question "Which set has the largest standard deviation" - Set Y.

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Re: Which data set has the greater standard deviation, data set K or data  [#permalink]

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30 Apr 2015, 23:04
if
K: 3,3,3
L: 9,9,9 their SD=0

if
K: 3,6,9
L: 9,9,9 SD of K>SD of L

if
K: 3,3,3
L: 9,18,27 SD of L>SD of K

E
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Re: Which data set has the greater standard deviation, data set K or data  [#permalink]

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28 Oct 2015, 06:51
Hi,

Other way to look at this question is both the sets can contain all the elements as "Zero" or "any multiples of their respective series". Plus we do not have any specific information on the number of elements.

Hence the appropriate solution is "E"

Regards
Sai Kiran
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Re: Which data set has the greater standard deviation, data set K or data  [#permalink]

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15 Jul 2019, 03:33
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Re: Which data set has the greater standard deviation, data set K or data   [#permalink] 15 Jul 2019, 03:33
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