Mean and Mode

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anubhavgulati: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Sun May 29, 2011 5:28 amFollowed by: 1 member; Thanked: 1 times

by anubhavgulati » Sun Aug 21, 2011 10:56 am

Hi,

Data Sufficiency Question.

Set of data consists of 3 integers.What is the Standard Deviation for this set of data ?
1) Average and Median are both 3.
2) Mode is 3.

Solution) I went for answer choice E (both are not sufficient), but when I cross checked answer was C(both statements together are sufficient).

As per statement 1, Its insufficient as sets can be {1,2,3} or {3,3,3}.
As per statement 2, As mode is 3, I think for the first set {1,2,3} we can also say mode is 1,2 or 3.
but as per the answer they have considered mode as 3 only for set {3,3,3}.

Can we say mode as 3 for the set {1,2,3}. This is where I get it wrong, but I have read that if set has unique elements, we can say that every element is a mode.

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Source: Beat The GMAT — Data Sufficiency | Sun Aug 21, 2011 10:56 am

beatthegmat.garry: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Tue Jul 12, 2011 1:07 pmFollowed by: 1 member; Thanked: 8 times

by beatthegmat.garry » Sun Aug 21, 2011 6:50 pm

Let n1, n2 and n3 be the 3 numbers:

statement 1: Mean=3 and Median=3

therefore,
(n1+n2+3)/3=3 .......n3=3.
n1+n2=6.
the possible combinations of n1 and n2 are (0,6)(1,5)(2,4)(3,3)

Statement 2:
Mode=3. Hence more than one number will be 3. Since n3 is assumed to be 3 we have either n1=n2=3.

Hence C.

Thanks !

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Mon Aug 22, 2011 1:59 am

Set of data consists of 3 integers.What is the Standard Deviation for this set of data ?
1) Average and Median are both 3.
2) Mode is 3.

from 1
the set can be 2,3,4 or 1,3,5 or 0,3,6 etc where average is 3 and median is 3. In-sufficient

from 2
the set can be 3,3,1 or 3,1,3 or 1,3,3 etc In-sufficient

from 1 and 2
the set should be 3,3,3. Sufficient!

Hope it helps!

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anubhavgulati: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Sun May 29, 2011 5:28 amFollowed by: 1 member; Thanked: 1 times

by anubhavgulati » Mon Aug 22, 2011 8:37 am

GmatKiss wrote:Set of data consists of 3 integers.What is the Standard Deviation for this set of data ?
1) Average and Median are both 3.
2) Mode is 3.

from 1
the set can be 2,3,4 or 1,3,5 or 0,3,6 etc where average is 3 and median is 3. In-sufficient

from 2
the set can be 3,3,1 or 3,1,3 or 1,3,3 etc In-sufficient

from 1 and 2
the set should be 3,3,3. Sufficient!

Hope it helps!

Appreciate your response, but still there is a doubt, let say if there are 3 unique elements in set, can we say that each element is mode.
If set is {1,2,3} can we say mode of this set is 1 or 2 or 3, as all occurs 1 time.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Aug 22, 2011 9:24 am

anubhavgulati wrote: Appreciate your response, but still there is a doubt, let say if there are 3 unique elements in set, can we say that each element is mode.
If set is {1,2,3} can we say mode of this set is 1 or 2 or 3, as all occurs 1 time.

Good question, anubhavgulati.

The set {1, 2, 3} has three modes. They are 1, 2 and 3.

So, can we say that the mode of this set is 3? Not really, since "the" implies that there is one unique mode, and the set {1, 2, 3} has three modes.

Can we say that a mode of this set is 3? Sure. 3 is one of the three modes of the set {1, 2, 3}.

Now in the original question, statement 2 reads "Mode is 3"
Does this mean the mode is 3 or a mode is 3? It's unclear.

Given this ambiguity, we can't really answer the question. Also know that the GMAT would never be so ambiguous.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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anubhavgulati: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Sun May 29, 2011 5:28 amFollowed by: 1 member; Thanked: 1 times

by anubhavgulati » Mon Aug 22, 2011 10:32 am

Brent@GMATPrepNow wrote:
anubhavgulati wrote: Appreciate your response, but still there is a doubt, let say if there are 3 unique elements in set, can we say that each element is mode.
If set is {1,2,3} can we say mode of this set is 1 or 2 or 3, as all occurs 1 time.
Good question, anubhavgulati.

The set {1, 2, 3} has three modes. They are 1, 2 and 3.

So, can we say that the mode of this set is 3? Not really, since "the" implies that there is one unique mode, and the set {1, 2, 3} has three modes.

Can we say that a mode of this set is 3? Sure. 3 is one of the three modes of the set {1, 2, 3}.

Now in the original question, statement 2 reads "Mode is 3"
Does this mean the mode is 3 or a mode is 3? It's unclear.

Given this ambiguity, we can't really answer the question. Also know that the GMAT would never be so ambiguous.

Cheers,
Brent

Ok, Thanks Brent for your solution.

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