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What is the mode of this set ?

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by goelmohit2002 » Mon Jul 20, 2009 1:31 pm
Hi All,

Can someone please tell what is the mode of the following set of numbers:

(1,2,3).

Basically when no number is repeated, then is the mode:

a) not defined
b) does not exist.
c) is equal to all the numbers in the set i.e. (1,2,3)

Thanks
Mohit
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by raleigh » Mon Jul 20, 2009 1:53 pm
The mode is defined to be the number in a number set that occurs most frequently.

The most frequent a number appears in this set is 1 time. Numbers 1, 2, and 3 satisfy this so this set has 3 modes: 1, 2, and 3.
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by goelmohit2002 » Tue Jul 21, 2009 11:20 am
Thanks Raleigh
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by Stuart@KaplanGMAT » Tue Jul 21, 2009 12:02 pm
raleigh wrote:The mode is defined to be the number in a number set that occurs most frequently.

The most frequent a number appears in this set is 1 time. Numbers 1, 2, and 3 satisfy this so this set has 3 modes: 1, 2, and 3.
I disagree.

Sets can me modal, multimodal or non-modal.

If every number in a set occurs with the same frequency, there is no mode. As long as 1 number occurs with different frequency, there is at least one mode.

For example:

{1, 2, 2, 3} has a mode of 2.

{1, 2, 2, 3, 3} is called "bimodal" and has modes of 2 and 3.

{1, 1, 2, 2, 3, 3} has no mode, since all of the terms occur with equal frequency.
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by goelmohit2002 » Tue Jul 21, 2009 12:06 pm
Stuart Kovinsky wrote:
raleigh wrote:The mode is defined to be the number in a number set that occurs most frequently.

The most frequent a number appears in this set is 1 time. Numbers 1, 2, and 3 satisfy this so this set has 3 modes: 1, 2, and 3.
I disagree.

Sets can me modal, multimodal or non-modal.

If every number in a set occurs with the same frequency, there is no mode. As long as 1 number occurs with different frequency, there is at least one mode.

For example:

{1, 2, 2, 3} has a mode of 2.

{1, 2, 2, 3, 3} is called "bimodal" and has modes of 2 and 3.

{1, 1, 2, 2, 3, 3} has no mode, since all of the terms occur with equal frequency.
Awesome Stuart !!!

Thanks a lot for clearing this doubt so nicely.
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by ajlcalbanese1 » Tue Jul 21, 2009 1:00 pm
so the answer to this question is there is no mode? sorry, but I am a little slow sometimes..
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by raleigh » Tue Jul 21, 2009 1:17 pm
I haven't seen a formal definition -- just what they list in say PR or Kaplan, and what I've read from my Google searches.

The best source that I found is the wikipedia page for mode(https://en.wikipedia.org/wiki/Mode_%28st ... efinedness). However, this does not answer the question. It says that the mode for a finite set is one of the elements of the set. So it implies that the mode exists for a finite set. In that case, the mode of {1,2,3} would be 1,2, and 3.


Contary to the wiki, I read
(https://mathforum.org/library/drmath/view/61375.html - this definitely isn't a 100% credible source) that a set has no mode if every number in the set occurs once. If any number in a finite set occurs more than once, then the set has a mode. Moreover, the mode is the number(s) that occurs most frequently.

{1,2,3} has no mode because 1,2, and 3 only occur once. However, the set {1,1,2,2,3,3} has 3 modes: 1,2, and 3.

Stuart, can you link to a formal definition that supports your claim? I know you have a lot of credibility on this forum, but you basically said I was wrong because your definition of mode differs from mine. You didn't even state your definition, and all of these claims do not agree. Can you define mode, and give a source that confirms it?
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by Stuart@KaplanGMAT » Tue Jul 21, 2009 1:41 pm
Well, my original source is my high school math teacher, but that may not seem credible!

Sadly, the Official Guide, which addresses mode on page 115, doesn't discuss the issue at all.

However, Kaplan tells us:

"A set may have more than one mode if two or more terms appear an equal number of times within the set, and each appears more times than any other term." [emphasis mine]

Further, Kaplan says:

"If every element in the set occurs an equal number of times, then the set has no mode."
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by Ian Stewart » Tue Jul 21, 2009 2:26 pm
If every number in a set occurs equally often, the set is considered not to have a mode; any decent stats book will confirm that. The good news is, it doesn't matter - I can promise you will never, ever see a GMAT question that tests whether you know this. These days, I'd be surprised if you even see a question about modes at all, actually.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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