Using Mean, Mode, and Range

Date: 11/23/2002 at 17:42:01
From: Katy
Subject: Mean, Mode, Range

What is a mean? And why do we have to learn and use it? And what is 
the mode? I have no clue what it is. What is a range?

Date: 11/30/2002 at 21:59:54
From: Doctor Pepper
Subject: Re: Mean, Mode, Range

Hi Katy -

The mean, mode, and range are what we call sample statistics.  They
are important for describing large sets of data.  

Let's say there are 30 people in my math class. Just looking at
everyone's score on the latest test doesn't really tell me very much.
However, if I look at the mean and the mode I get a sense of how the
class did on average.

The range is the highest score minus the lowest score. It is a measure 
of dispersion and it tells us the spread of the scores - that is, did 
some people do really well while others did really badly, or are all 
the scores pretty close together? 

The mean is the average score. We find it by adding up all the scores 
and dividing by the total number of scores. 

The mode is the most frequently occurring score, that is, the score 
the most people got.  

That's how I think these concepts can most easily be explained, but I 
get to use them every day in my research. I am a graduate student in 
developmental psychology working in a lab that studies infants. The 
mean, mode, and range aren't really that exciting, but we need them to 
understand the data we collect.  

Just imagine having sheets and sheets of data. I don't know about you, 
but I definitely don't have the patience to look at how each baby did 
on our experiment. We see oodles of babies each day, and each is a lot 
of fun but also gives us a lot of data. I enter all the individual 
data into a statistics package and it spits out certain key statistics 
that I am interested in learning about.  

In terms of testing babies, we cannot ask them to tell us what they
think. Rather, we get a sense of what they are thinking by their
behavior. In one of my current studies we are looking at what makes a
face interesting. Thus we can show two different faces and see which
the baby prefers and looks at longer. I can find the mean looking
times for each face and make conclusions about which face in general
the babies prefer. I also can find the range to see how widely the
looking times vary.  

It's important to note that I also graph all my data. That way, I can
tell if there are any outliers. These are data points that stick way
out from the general trend and may affect my mean and range. The
great thing about the mode is that it isn't affected by outliers.

Let's suppose you're not interested in psychology but in sports.  
There are a lot of statistics involved in sports. I like baseball a 
lot. When a player gets up to bat we know his batting average - how
well he performs on average. That is, sometimes he may really rock
while other times he might not do so well. The average takes all the
times he has been up to bat, adds them up, and divides by the total
times he hit. It gives us the best indication of how he will do the
next time he's at bat.

Statistics play a huge part in our everyday life. These are important
concepts to learn because they will definitely come up again and will
give you a good idea of the big picture!
  
I hope this helps.

Best of luck,
- Doctor Pepper, The Math Forum
  http://mathforum.org/dr.math/