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The graph above is an example of a properly prepared graph of the data from the Period vs. Mass for a pendulum experiment described earlier. Note that it contains each of the characteristics of good graphs, which are described in detail below.
A title that describes the experiment. This title should be descriptive of the experiment and should indicate the relationship between the variables. It is conventional to title graphs with DEPENDENT VARIABLE vs. INDEPENDENT VARIABLE. For example, if the experiment was designed to show how changing the mass of a pendulum affects its period, the mass of the pendulum is the independent variable and the period is the dependent variable. A good title might therefore be PERIOD vs. MASS FOR A PENDULUM.
The graph should fill the space allotted for the graph. If you have reserved a whole sheet of graph paper for the graph then it should be as large as the paper and proper scaling techniques permit.
The graph must be properly scaled. The scale for each axis of the graph should always begin at zero. The scale chosen on the axis must be uniform and linear. This means that each square on a given axis must represent the same amount. Obviously each axis for a graph will be scaled independently from the other since they are representing different variables. A given axis must, however, be scaled consistently.
Scale each axis so as to take up a maximum amount of the space available while still maintaining divisions that will make plotting the graph as easy as possible. Increments on an axis of 1, 2, or 5 are easy to use when plotting points. For larger numbers 10, 20 or 50 or possibly 100, 200, or 500 might work and so on. For smaller numbers 0.1, 0.2, or 0.5 might work or maybe 0.01, 0.02, or 0.05. A good way to choose the scale for an axis is to identify the largest data point that will be plotted on that axis. Then count the number of squares on your graph paper that are available for plotting the variable on that axis. Divide the maximum data value by the number of squares. This will give you smallest value that each square could possible have as its increment. Since the result of this division will most likely not be a convenient number, you should then round up to the nearest convenient value. Once you have chosen a scale, you do not have to label each square with its value. Label enough values on the axis to make it clear what scale you are using.
Scaling Example: In a given experiment in which the length is being measured, the largest length that was measured was 455.2 m. The graph paper being used has 25 squares that could be used for the length axis. The minimum scaling increment for this graph paper would then be 455.2 m divided by 25 squares or 18.2 m per square. Since 18.2 is not a convenient number to use for the increment (it would be very difficult to plot such a graph) then you should round the value up to the next higher convenient number. This would be 20 m per square. Since each square is worth 20 and the largest value you need to plot on the axis is 455.2, you could label the axis every fifth square with 5 times 20 or 100.
Each axis should be labeled with the quantity being measured and the units of measurement. The independent variable is plotted on the horizontal (or x) axis and the dependent variable is plotted on the vertical (or y) axis. The units on an axis must be consistent with the variables being plotted on that axis.
Each data point should be plotted in the proper position. You should plot a point as a small dot at the position of the of the data point and you should circle the data point so that it will not be obscured by your line of best fit. These circles are called point protectors.
A line of best fit. This line should show the overall tendency (or trend) of your data. If the trend is linear, you should draw a straight line that shows that trend using a straight edge. If the trend is a curve, you should sketch a curve that is your best guess as to the tendency of the data. This line (whether straight or curved) does not have to go through all of the data points and it may, in some cases, not go through any of them.
Do not, under any circumstances, connect successive data points with a series of straight lines, dot to dot. This makes it difficult to see the overall trend of the data that you are trying to represent.
If you are plotting the graph by hand, you will choose two points for all linear graphs from which to calculate the slope of the line of best fit. These points should not be data points unless a data point happens to fall perfectly on the line of best fit. Pick two points which are directly on your line of best fit and which are easy to read from the graph. Mark the points you have chosen with a +.
Do not do other work in the space of your graph such as the slope calculation or other parts of the mathematical analysis.
If your graph does not yield a straight line, you will be expected to manipulate one (or more) of the axes of your graph, replot the manipulated data, and continue doing this until a straight line results. In general it will probably not take more than three graphs to yield a straight line.
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