Bar Graphs vs. Histograms

Date: 09/05/2002 at 09:34:41
From: Michelle McCabe
Subject: Statistics

What is the difference between bar graphs and histograms? I have 
attended workshops with teachers and most teachers say that the main 
difference is that bars in a bar graph are not connected. However, in 
newspapers I have seen connected bar graphs.

Date: 09/05/2002 at 11:07:07
From: Doctor Mitteldorf
Subject: Re: Statistics

You're right. A histogram is a particular kind of bar graph. 

If you make a bar graph of the favorite colors of children in Mrs. 
Flaherty's 4th grade class (6 for pink, 8 for blue, 1 for black, etc.) 
that doesn't qualify as a histogram, because the colors don't 
correspond to any numerical values, and their order is arbitrary. A 
different kind of example: you could make a bar graph of monthly 
returns on your stock investment in January, February, etc. Here, 
there IS a natural order to the bars, but it still doesn't qualify as 
a histogram.

A histogram is a bar graph of frequencies of different numerical 
values within a population. The most straightforward kind of example 
is a bar graph of the number of 4th grade students by height:  

 how many between 4'   and 4'1" 
          between 4'1" and 4'2"
          between 4'2" and 4'3"
etc.

This is the particular kind of bar graph that qualifies as a 
histogram. You could make the monthly returns from above into a 
histogram like this:  

Over a 10 year period, how many months had a return 

   between -5% and -4%
   between -4% and -3%
   between -3% and -2%
   between -2% and -1%
   between -1% and 0%
   between  0% and 1%
   between  1% and 2%
   between  2% and 3%
   etc.

One more point about histograms: if you have a very large sample, you 
can make the slices thinner and thinner, and the bar graph may begin 
to look like a smooth curve. You could take your graph of the number 
of children by height, and use national statistics so that the numbers 
are very large. Then instead of plotting every one-inch interval, you 
might be able to plot 0.01" intervals, and the bar graph would look 
much like a smooth curve, in this case probably a bell-shaped curve.

- Doctor Mitteldorf, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 09/05/2002 at 16:28:13
From: Michelle McCabe
Subject: Statistics

Thank you so much for your speedy reply!  Before today, I had not 
heard a more complete or clear answer. 

Maybe you can help me clear up another statistics question. What is 
the best way to define scale and interval for a middle school student?

Date: 09/05/2002 at 17:36:55
From: Doctor Mitteldorf
Subject: Re: Statistics

These terms are used in lots of different contexts.  My suggestion is 
that you use lots of examples, including hands-on exercises.

I'm not sure I'd want to teach this material to middle school 
students, but if I did I'd start out having them make graphs by hand, 
then use a spreadsheet like Lotus or Excel, and teach them to make 
different kinds of graphs on the screen.

- Doctor Mitteldorf, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 09/06/2002 at 16:03:18
From: Michelle McCabe
Subject: Statistics

In our 6th grade curriculum, students are expected to make frequency 
tables and histograms. They have no problem making the tables or 
histograms; however, they have not as yet been given an actual 
definition of interval. I was just curious about a formal definition 
of intervals. I have found several but I was hoping for something that 
was clearer. But as you suggest, maybe the fact that they are 
choosing correct intervals when creating the table is good enough 
without an actual definition of interval.  

Here is an example of a definition I found:

When making a frequency table for data (5 to 18), first choose a scale 
for the data. The scale must include all the numbers. One scale that 
would allow you to record all of the numbers is 1 to 20. 

You must also decide on the interval.  The interval separates the 
scale into equal parts. One possible interval is 5. 

Thanks again for your time.