1.2.3 Plotting & Interpreting Graphs

• When plotting graphs, it is important to consider the importance of the following factors:
  • Selecting appropriate scales
  • Labelling axes with quantities and units
  • Carefully plotting the points
  • Measurement of gradients and intercepts

Choice of Scale

• When choosing a scale, it must be big enough to accommodate all the collected values using as much of the graph paper as possible
• At least half of the graph grid should be occupied in both the x and y directions
• Scales should be clearly indicated and have suitable, sensible ranges that are easy to work with
  • For example, scales with multiples of 3 should be avoided

• The scales should increase outwards and upwards from the origin
• Each axis should be labelled with the quantity that is being plotted, along with the correct unit

Labelling the Axes

• Label each axis with the name of the quantity and its unit
  • For example, F / N means force measured in Newtons

• The convention is that a forward slash ( / ) is used to separate the quantity and the unit
• In general:
  • The independent variable goes on the x-axis
  • The dependent variable goes on the y-axis

Plotting the Points

• Points should be plotted so that they all fit on the graph grid and not outside it
• All values should be plotted, and the points must be precise to within half a small square
• Points must be clear, and not obscured by the line of best fit, and they need to be plotted with a sharp pencil so that they are thin
• There should be at least six points plotted on the graph, with any major outliers identified

Line or Curve of Best Fit

• There should be equal numbers of points above and below the line of best fit
  • Using a clear plastic ruler will help with this

• Not all lines will pass through the origin and nor should they be forced to
• The line (or curve) of best fit should not be too thick or joined dot-to-dot like a frequency polygon
• Anomalous values that have not been identified during the implementation stage should be ignored if they are obviously incorrect
  • This is because they will have a large effect on the gradient of the line of best fit

Calculating the Gradient

• The gradient can be calculated by dividing the rise (change in y) by the run (change in x)

• The calculation needs to be shown, including the correct substitution of identified plotted points from the axes into the equation
• The triangle used to calculate the gradient should be drawn on the graph and it needs to be as large as possible
  • Small triangles are not acceptable for working out a gradient

• When using the results from a table of values, the triangle that is used to obtain the gradient can utilise points that lie on the line of best fit but not values that lie away from the line

Determining the y-intercept

• The y-intercept is the y value obtained where the line crosses the y-axis at x = 0
• Values should be read accurately from the graph, with the scale on the y-axis being interpreted correctly

Step 1: Identify the independent and dependent variables

• • Independent variable = blade angle / °
  • Dependent variable = voltage / V

Step 2: Choose an appropriate scale

• • The range of the blade angle is 0 – 90°
  • Ideally, every small square represents 10°

• • The range of the voltage is 0 – 2.2 V
  • Ideally, each small square represents 0.5 V

• • Both axes should occupy at least 50% of the grid

Step 3: Label the axes

• • The dependent variable (voltage / V) goes on the y-axis
  • The independent variable (blade angle / °) goes on the x-axis
  • Both axes should be labelled with a quantity and a unit

Step 4: Plot the points

• • Each point should be accurate within half a small square

Step 5: Draw a curve of best fit

• • The curve should be smooth with a roughly equal distribution of points on either side of the curve
  • It must start at (0,0) and peak at (20, 2.2)