Mean, Median, and Mode

Date: 07/15/98 at 20:39:08
From: Matthew
Subject: Finding the Mode

I understand the median, but I am having trouble understanding the 
mode. Can you please explain?

Date: 07/16/98 at 07:58:35
From: Doctor Anthony
Subject: Re: Finding the Mode

If you have a set of numbers, say the ages of pupils in a group, then 
there are 3 different ways of finding a single number to represent the 
whole group. The most common is the 'mean' or average. For the mean 
you add up all the ages and divide this total by the number of pupils.

The second way you could find a single representative number is to 
arrange all the pupils in a line in ascending order of age, with the 
youngest on the left and oldest on the right. You then go to the person 
standing in the exact middle of this line and find his/her age. This 
will be the median age. If there is an even number of pupils you 
will not have a single person at the midpoint, so you will take the 
middle pair and give the average of their ages as the median age.

The third way to find a single representative number is to group the 
pupils by age, so you could have 5 pupils of age 10, 8 pupils of age 
11, 14 pupils of age 12, 7 pupils of age 13, 2 pupils of age 14 and 3 
pupils of age 15. Looking at this distribution of ages you see that 
the biggest group is those of age 12, so you say the 'mode' of the 
distribution is 12. In short, the mode is the most frequently 
occurring value. If no value occurs more than once then you don't have 
a mode. Sometimes two values will occur at an equal but greater 
frequency than other values, and in this case we say that the 
distribution is bi-modal.

- Doctor Anthony, The Math Forum
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