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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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
_________________
(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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
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EMPOWERgmatRichC
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Last visit: 31 Dec 2023
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Expert reply
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.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
General Discussion
sterling19
Joined: 14 Sep 2014
Last visit: 03 Jun 2015
Posts: 97
Concentration: Technology, Finance
WE:Analyst (Other)
Posts: 97
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
The correct answer is E.
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
The correct answer is E.
(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.
Answer E
(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.
Answer E
I think the answer is E;
We need to know the number of elements in the data set.
We need to know the number of elements in the data set.
EMPOWERgmatRichC
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Last visit: 31 Dec 2023
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GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
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
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
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?
Bunuel
MAGOOSH OFFICIAL SOLUTION:
Attachment:
greateststandarddeviation_text.PNG [ 17.56 KiB | Viewed 16666 times ]
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viktorija
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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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
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
saikiransomala
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Products:
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
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
1) Multiple of 3 is in the first set. We dont know how many. Insufficient
2) Multiple of 9 in the second set. We don't know how many. Insufficient
Combining both, we still don't know many
Answer is E.
2) Multiple of 9 in the second set. We don't know how many. Insufficient
Combining both, we still don't know many
Answer is E.
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