# 3.18 Plotting Graphs

## Plotting 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

#### 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 Example of labelled axes with the name of the variable, its symbol and its unit

#### 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

#### 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

#### Worked example

A student investigates the effect of placing an electric fan in front of a wind turbine. The wind turbine is connected to a voltmeter. When the wind turbine turns, it generates a voltage. The student obtains the following results: Plot the student’s results on the grid and draw a curve of best fit on the graph. 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) #### Exam Tip

Remember that 'sketching' and 'plotting' a graph are two different command words

• 'Sketch' means – Produce a freehand drawing. For a graph, this would require a line and labelled axis with important features indicated, the axes are not scaled.
• 'Plot' means – Produce a graph by marking points accurately on a grid from data that is provided and then drawing a line of best fit through these points. A suitable scale and appropriately labelled axes must be included if these are not provided in the question

The difference between these two command words is the use of scales. A plotted graph has a scaled axes, whilst a sketch doesn't have to be but both times the axes should be clearly labelled ### Get unlimited access

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