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How Do You Make a Circle Graph or Pie Chart?

Date: 12/16/2003 at 21:33:46
From: twa
Subject: circle graph

How do I make a circle graph using these numbers?  I'm thinking of a
circle and it has each percent inside and a key.

body part                weight (pounds)
head                        10.5
neck and trunk              70.0
arms                        16.5
hands                        2.5
legs                        47.5
feet                         5.0



Date: 12/17/2003 at 11:39:42
From: Doctor Jason
Subject: Re: circle graph

Hi Twa,

Of all of the different types of graphs, circle graphs are one of the 
more complicated ones to make.  They are sometimes called pie charts.

Instead of using your information, let's look at an example using the
following set of data regarding eye color of students in a class:

   Eye color  | # of Students
   ---------------------------
   Brown      |     15
   Blue       |      9
   Green      |      6

To make a circle graph using this set of data, the first thing I would
do is make each of the numbers into a fraction out of the total number
of students.  There is a total of 30 students in the class (15 + 9 + 6):

   Eye color  | # of Students | Fraction 
   -------------------------------------
   Brown      |     15        |  15/30
   Blue       |      9        |   9/30
   Green      |      6        |   6/30
   -------------------------------------
   Total      |     30        |  30/30

The circle graph will have 3 "pie pieces," one for each eye color. 
The part representing brown eyes will be 15/30 of the circle, the part
representing blue eyes will be 9/30 of the circle, and the part
representing green eyes will be 6/30 of the circle.  

How do we know how much 15/30 of the circle is?  The answer lies in
the fact that a circle is 360 degrees.  If we multiply the fraction 
representing the part of the circle times 360, we will then have the 
angle measure of the respective part.  It may be easier to work with 
decimals instead of fractions, so I divided out the fractions and 
entered them in our table:

   Eye color  | # of Students | Fraction | Decimal  
   ------------------------------------------------
   Brown      |     15        |  15/30   |  0.5
   Blue       |      9        |   9/30   |  0.3
   Green      |      6        |   6/30   |  0.2 
   ------------------------------------------------
   Total      |     30        |  30/30   |  1.0

Multiplying the decimal number times 360 gives us the angle measure 
of each part of the graph:

                360 * 0.5 = 180 (Brown)

                360 * 0.3 = 108 (Blue)

                360 * 0.2 =  72 (Green)

Entering these values into the table:

  Eye color  | # of Students | Fraction | Decimal | Angle Measure 
  ----------------------------------------------------------------
  Brown      |     15        |  15/30   |   0.5   |  180 degrees
  Blue       |      9        |   9/30   |   0.3   |  108 degrees
  Green      |      6        |   6/30   |   0.2   |   72 degrees
  ----------------------------------------------------------------
  Totals     |     30        |  30/30   |   1.0   |  360 degrees
     
Now we can construct our graph.  We need to draw a circle with one
radius.  Using the radius as one leg of the angle, draw the second 
segment of the angle using a protractor and one of the angle measures 
from the table.  If we use 180 degrees as the first angle, our circle 
should be cut in half, since 180 is a straight line.

Next, we use one of the remaining angle measures to draw another
angle.  One of the legs of this angle needs to be one of the 2 radii
already drawn (but not drawn as part of the 180 degree "brown" piece,
meaning don't overlap the angles). 

After that, the remaining piece should have the angle measure of the
remaining angle in the table (It would be a good idea to check!).

Finally, give the graph a name and provide a key or labels.  You may 
also want to color the graph.
 
I hope this helps!  Let me know if there is anything else I can do.

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

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