Finding Mean, Median, Mode

Date: 03/29/98 at 18:29:10
From: Adam White
Subject: Mean of scores

I have been out of school for 8 years and I am trying to get my 
diploma. On one of my practice tests it said to get the mean, median, 
and mode of scores. However in my textbook there are no examples to 
show me how to do it. The scores are: 100, 78, 93, 84, 91, 100, 82, 79. 
I would greatly appreciate if someone would show me how to do them.

Thank you,
Adam

Date: 03/29/98 at 20:40:34
From: Doctor Sam
Subject: Re: Mean of scores

Adam,

The mean of the scores is another name for their average. Just add 
them up and divide by the number of scores:

     mean = (100+78+93+84+91+100+82+79)/8   
          = 88.375                          

The median of the scores is "the number in the middle" when the scores 
are sorted in order.  In your example:

     100 100 93 91 84 82 79 78

If there is an even number of scores (as in your example) there is no 
number in the middle so the two numbers in the middle are averaged:

     median = (91 + 84)/2 = 87.5

The mean of the numbers can be misleading. If I tell you the mean 
income in my neighborhood is 1 million dollars a year you might think 
that I am wealthy. But maybe the neighborhood is a poor one with one 
very rich person making many millions of dollars a year. The average 
will be large because one number is very large.  

The median and the mean together give a better idea of the spread of 
the numbers. If there were one really wealthy person then the median 
income would be quite low. In your case the median is quite near to 
the mean, which suggests that the spread is probably evenly balanced.

The mode of a set of numbers is the number that occurs most often.  
In your example:

   mode = 100

The mode may help to correct false impressions if you know the mean 
and the median but don't actually see the data.  

For example, if I tell you the mean of four numbers is 50.5 and the 
median is 50 you may think that the four numbers are close to one 
another, like the numbers in your example. In fact, however, I am 
thinking of:
  
     101  99   1    1  

The mean is (101 + 99 + 1 + 1)/4 = 202/4 = 50.5 and the median = 
(99+1)/2 = 50. But the mode here is 1. If you know that, you will know 
that 1 is repeated more than once in the data and, since the mean is 
near 50 with only four numbers, that might give you the idea that the 
data include several large numbers and several small numbers rather 
than four numbers close to one another.

I hope that helps.

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