Graphs are a visual representation of trends in data.

  • Graphical techniques are an effective means of communicating the effect of an independent variable on a dependent variable and can lead to determination of physical quantities.
  • The independent variable is the cause and is plotted on the horizontal axis. The dependent variable is the effect and is plotted on the vertical axis.
  • Sketched graphs have labelled but unscaled axes, and are used to show qualitative trends, such as variables that are proportional or inversely proportional.
  • Drawn graphs have labelled and scaled axes and are used in quantitative measurements.
  • When drawing graphs:
    • Give the graph a title (always based on y versus $x$), and label the axis with both quantities and units.
    • Use the available space as effectively as possible and use sensible scales – there should be no uneven jumps.
    • Plot all the points correctly.
    • Identify any points which do not agree with the general trend.
    • Think carefully about the inclusion of the origin. The point $(0, 0)$ can be the most accurate data point or it can be irrelevant.
  • You should be able to give a qualitative physical interpretation of a particular graph.
  • A ‘best-fit’ straight line does not have to go through all the points but should show the overall trend.
  • The equation for a straight line is:
    $y = mx + c$.
    $x$ is the independent variable,
    $y$ is the dependent variable,
    $m$ is the gradient
  • $m = \Delta y/\Delta x$
    $m$ has units of $y /x$
  • c is the intercept on the vertical axis and has the units of $y$.
  • A systematic error produces a displaced line.
  • Random uncertainties lead to points on both sides of the perfect line.
  • The gradient of a curve is given by the gradient of the tangent at that point.
  • The process of assuming that the trend line applies between two points is called interpolation.
  • A line is extrapolated when it is extended beyond the range of measurement.