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### 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,

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Definitions
Middle School Definitions
Middle School Statistics

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