Histogram

Date: 04/16/2001 at 23:00:13
From: Kelly
Subject: Math Problems

What is a histogram?

Date: 04/17/2001 at 13:27:48
From: Doctor Ian
Subject: Re: Math Problems

Hi Kelly,

To make a histogram, first you count the occurrences of the different 
kinds of objects that you're keeping track of. For example, you might 
go around your classroom and write down the grade (A, B, C, D, or F) 
that everyone got on the latest test:

     Bill      B
     Betty     A
     Fernando  B
     Karen     B
     Joe       F
     Eliza     C
     Zbignew   A
     Kai       B
     Ellen     F
  
Another way to write this information is to organize it by grade, 
instead of by name:

     A   Betty, Zbignew
     B   Bill, Fernando, Karen, Kai
     C   Eliza
     D   
     F   Joe, Ellen

But for the purposes of creating a histogram, you're not interested in 
individuals, just numbers, so you can replace each list by the number 
of people it contains:

     A   2
     B   4
     C   1
     D   0
     F   2

The number next to each grade is the 'frequency' with which that grade 
occurs. That is, the frequency of 'A' grades is 2, the frequency of 
'B' grades is 4, and so on. The higher the frequency of a category, 
the more objects there are in the category.

In fact, at this point, you actually _have_ a histogram, but people 
prefer pictures to numbers, so it's normal to convert each number to a 
picture, in which the length of a line is proportional to the number 
it represents. So, for example, a line representing '6' would be twice 
as long as one representing '3':

     A  **
     B  ****
     C  *
     D
     E  **

Note that histograms are only interesting when the categories are 
defined so that several objects will fall into each one; the following 
histogram of weights doesn't tell you very much because the categories 
are too precise:

     Weight   Frequency
      100
      101      *
      102
      103
      104      *
      105      * 
      106
       :
      134
      135

Categories can also be too broad:

      Weight   Frequency
       0- 70
      70-140   **************************
     140-210     
  
The hardest thing about making a good histogram is choosing the right 
categories.  

I hope this helps. Be sure to write back if you have more questions, 
about this or anything else. 

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