Mean, Median, and Mode in Real Life

Date: 12/21/96 at 20:06:06
From: Brian Beck
Subject: Mode if more than 2 numbers repeat and if there are no 
repeated numbers.

I was teaching about mean, median and mode the other day, and 
everything was going well. The students seemed to understand what we 
were doing, although it was not clear why we needed to know three 
different methods for finding central tendencies. The question came 
up about how to determine the mode if there was more than one number 
in a list that repeated. My suggestion was that there could be more 
than one mode, and an answer in the teacher's guide also indicated the 
same thing. The other question asked how to figure out the mode if no 
numbers in the list repeated. Again, my answer (from the guide) was 
that there was no mode. Was I correct?  Please explain why.  If I was 
incorrect, please explain the correct responses.

Thank you.
Brian Beck
Grade 7 teacher

Date: 12/21/96 at 21:05:07
From: Doctor Ceeks
Subject: Re: Mode if more than 2 numbers repeat and if there are no 
repeated numbers.

Hi,

Identifying "the" mode is an attempt to answer the question: "Which 
occurs most frequently?" Sometimes there's a clear answer, other 
times there are a few answers, and sometimes everything comes up the 
same amount and there's no point in asking or answering that question.  
So your answers are fine.  You could also say that all the items in a 
list where no item is repeated are modes, but there's not much point.  
Anyway, the answer to "what is the mode" in such a non-repeating list 
is a technical matter, and it's more important to understand that the 
question itself becomes rather inapplicable in such situations.

Here are examples of situations to illustrate when the three different
methods of finding central tendencies are useful:

Fashion is generally an answer to the question, "What is the mode?"
e.g. "What's the most popular sneaker?" or "What shirt style would
most people want to wear?"

Of the two outcomes: "strike out" or "base hit or better," assigning
0 to "strike out" and 1 to "base hit or better" and then averaging is
more useful to a manager than determining the mode, which in pro 
baseball is for everybody to "get out."  (At least, I can't think of 
anybody with a batting average over 500... was there ever such a 
phenomenon?)

Knowing the median test score is important to people who want to think 
they are in the "better half of the population."

-Doctor Ceeks,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/