Analysing graphical data

A graph helps to analyse data and can be used to draw a conclusion.

When plotting a graph:

  • choose axis scales so that the plotted points occupy at least half the space available (this will help make the graph easier to read)
  • label both axes, including the units
  • think about whether the line should pass through the origin (0,0)
  • choose intervals along the scale that make it easy to plot the points and read off values, eg increments of 2, 5 or 10
  • a point that is not near the best fit line is anomalous - it needs to be explained before it can be ignored
  • after plotting the point, draw a line of best fit - remember this can be curved
An anomalous point in the graph

Reading the shape of a graph

A lot can be learnt by looking at the shape of a graph. The gradient is the slope of the graph. For example, when looking at a graph of mass produced against time, the gradient of the graph shows the mass produced per second. This is the rate of reaction.

Example

Question

How does the rate of reaction change over time?

  • Imagine walking along the graph. Describe how the gradient changes:
    • it starts very steep and then gets gradually less steep until it is horizontal
  • Turn this into a description of the rate of reaction:
    • the rate of reaction is very fast at the start but gradually slows down until the reaction stops

Finding more data from a graph

Finding values within the range originally measured is called interpolation.

To interpolate a graph, read up from the horizontal axes, then across to find the new value.

No data was gathered for the mass produced by 25 seconds, but it can be interpolated from the graphNo data was gathered for the mass produced by 25 seconds, but it can be interpolated from the graph

Finding values beyond the range that was originally measured is called extrapolation.

To extrapolate a graph, first extend the line. Then read up from the horizontal axis and across to find the new value.

Data was only measured for 50 seconds but by extrapolating the line a value can be read for 60 seconds.Data was only measured for 50 seconds but by extrapolating the line a value can be read for 60 seconds