# Graph Construction by Hand

While computer programs can conveniently construct graphs from data, hand construction of a graph remains an important means of analyzing and appreciating the value and patterns present in data.  Follow the following rules in order to produce a properly sized and accurately plotted graph.

1.  DETERMINE THE RANGE LIMITS OF THE X-AXIS AND THE Y-AXIS

Examine the data set and note the minimum and maximum values:
X-axis:     ordinate (independent or known variable):       time, added concentration, etc.
Y-axis:     abscissa (dependent or unknown variable):     what was measured: weight, A660 etc

(If the zero value of X or Y is important for your graph, it should be included in the limits.)

2.  DETERMINE THE LIMITS OF YOUR GRAPH PAPER

Count the number of squares available for the X and Y axes, leaving at least 3 square at the bottom and sides, and 9 squares at the top.  Graph-lined composition notebooks with 5 X 5 quad ruling allow for a graph of no more than 35 squares wide and 40 squares tall.

3.  ASSIGN VALUES TO AXES WHICH INCLUDE THE RANGE LIMITS

Assign values to the coordinates which meet the following requirements:

a.  They include the limits determined in step 1.
b.  They make an adequately large graph as large as the available space will accommodate.
c.  They do not exceed the space available on the page.

Divide the value of the range by the number of squares available along the given axis.  Round up so that the first significant figure of the result equals 1, 2, 5 or 10 units per square. For example, if you have Y axis range from 0.000 to 1.212, divide the 1.212 by the 40 squares available, which equals 0.0303/square.  This would be rounded up to 0.05/square.  Memorize the 1, 2, 5 and 10 values per square.  Other values will make plotting the data difficult, and it will cost you points when graded.  The quantity zero should often be the space most to the left and/or bottom.

Here is a page from a notebook illustrating the parameters for sizing a graph to a page.

4.  CONSTRUCT AXES, MARK WITH REGULAR VALUES

Draw lines for the X-axis below and the Y-axis to the left of the selected open area on the graph paper.  Label each axis.  Mark off the selected regular values (often every 5 or 10 squares) with a small line corresponding to units/square selected in step 2.  Label each small line with its corresponding value.  (Do not label every square.)   Be certain to maintain linearity: all spaces must have equal value.

5.  ENTER DATA POINTS

For the first point, locate the appropriate value along the X axis and then follow that line up until the appropriate value of Y is reached.  Double check that you have not shifted from the desired location, and make a small dot at the point.  Draw a small circle around the point, making it easier to see, but preserving the integrity of the point.  Repeat until all data have been entered.  Did you include the zero point if it is a significant data point?  Use squares to indicate a second data set, triangles the third, etc.

6.  CONNECT THE CIRCLES

If the function you are graphing is linear, carefully connect the circles by lining a ruler up with the points and drawing a line between them.  (Do not violate the interior of the circles so that the value of the point will remain clear.)  Alternatively, if the function is non linear, you may either connect the circles or approximate the curve plots with a “best fit” curve.

7. TITLE THE GRAPH AND AXES

Create a title which is meaningful and explicitly reflects the value of the experimental data you have graphed.  Place it in CAPITAL LETTERS as the title of the page.  Below the title, indicate from where the original data came with a cross reference.  Be certain that the axes are correctly labeled.  Label any significant break points or phases in the curve, briefly indicate their meaning, if known.