Name: James Barton
Who is asking: Teacher
Level: All

Question: I have always been told that a mode is the "one" number that appears most in the set of numbers: ex.{1,3,4,6,3,2} the mode is 3. What if you have {1,1,3,4,5,5}is there a mode. I was taught long ago that there is no mode, Not i am having to teach there is two modes. 1 and 5. If this is the case if we have {1,1,2,2,3,3,4,4,5,5} that every number is the mode. True or false. This is being ambigiuous if we say all are the mode. Because no one number is used more than the others.

Sincerely,
James Barton
Kerrville Tivy HIgh School

I also heard both versions. This might be a good example to illustrate the fact that people do not always agree on the meaning of the terms they use, and this can cause confusion and conflict. In your example some people would say that {1,1,3,4,5,5} has two modes (bimodal), and other people would say that it has no mode, depending on the definition they give to the word "mode". As another example, people might argue about which city has the biggest airport, Calgary or Edmonton. Of course, this depends on the meaning they give to "biggest airport": does it depend on surface area, traffic flow, number of runways,... Instances of such disagreements are frequent in life, so it might be helpful for students to encounter it in a harmless context, such as the precise statistical meaning of the word "mode".

I agree with Claude's answer. I took five statistics books off my bookshelf and looked up mode.

• Two of them mentioned bimodal and multimodal, more than one mode, and would say that your example {1,1,2,2,3,3,4,4,5,5} has five modes. They both said that if each item appears exactly once, as in (1,2,3,4,5} then there is no mode.
   
  
• One book said that if one item occurs more than any other, it is the mode. In all other situations there is no mode. So {1,1,3,4,5,5}, {1,1,2,2,3,3,4,4,5,5} and {1,2,3,4,5} have no mode.
   
  
• The remaining two books only talked about mode in the context of a histogram. The class with the most items is the modal class and the class value is the mode. They both mentioned bimodal histograms, that is histograms with two modes.