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Bar Graphs and Histograms

Date: 04/30/2008 at 22:16:02
From: Michelle
Subject: differences and similarities of bar graph vs. histogram

What is the difference between a bar graph and a histogram?  For
example, what are some similarities or which bar graph explains 
more details.

I'm confused about which graph touches with each other and how it 
shows details.  Let's say 6 girls love dogs, 5 love cats, and 2 love
hamsters, a bar graph would represent this data more than a histogram.



Date: 04/30/2008 at 23:31:48
From: Doctor Peterson
Subject: Re: differences and similarities of bar graph vs. histogram

Hi, Michelle.

A histogram is a KIND of bar graph; so everything that a bar graph is,
a histogram is too.  But there are special things about a histogram
that are not true of ordinary bar graphs, and these are the differences.

One big difference is what they are used for.  A bar graph can be used
to compare ANY group of numbers, as in your example of the numbers who
like different kinds of pets.  That is very much like the sort of
frequency distribution that histograms display, since you are graphing
"frequencies"; but the bars would represent categories, not numbers. 
A histogram is used ONLY when the bars will represent different
numbers or intervals along an axis.  For example, if 6 girls had pets
weighing 0 - 3 pounds, 5 had pets weighing 3 - 6 pounds, and 2 had
pets weighing 6 - 9 pounds, you could make a histogram of that.

As a result of this difference, we make the bars of a histogram touch
--that way, they illustrate the idea that they represent adjacent sets 
of numbers, and that together they cover an entire range of values.  
Discrete bar graphs represent separate entities, like your dogs, cats, 
and hamsters, and therefore are drawn separately, with space between.
 (Sometimes histograms are drawn with spaces, to indicate that they 
represent discrete numbers, that is, integers, rather than a 
continuous range of values.  Also, sometimes at higher levels, the 
intervals can be different sizes, so the bars have different widths.  
Regular bar graphs always have the same width, because the width 
doesn't stand for anything in particular.)

Also, the bars in a histogram ALWAYS represent frequencies (numbers of
data values that fall in the corresponding interval); other bar graphs
might represent other things such as the amount of money spent on
different pets.  (Actually, when bars can have different widths, it is
not the height, but the area of each bar that represents the frequency.)

There are some smaller differences relating to how they are drawn,
such as how the bars are labeled, but these are the main ideas.

See this page for a little more:

  Bar Graphs vs. Histograms
    http://mathforum.org/library/drmath/view/61175.html 

Here's an answer I found elsewhere:

  Math Central: Bar Graphs and Histograms
    http://mathcentral.uregina.ca/QQ/database/QQ.09.99/raeluck1.html 

This page explains a couple of the more advanced features I mentioned:

  Statistics Canada: Histograms and Histographs
    http://www.statcan.ca/english/edu/power/ch9/histograms/histo.htm 

If you have any further questions, feel free to write back.


- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Statistics
Middle School Statistics

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