Problem Solving

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

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.

Thanks Raleigh

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.

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.

so the answer to this question is there is no mode? sorry, but I am a little slow sometimes..

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?

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."