Graphical representation of data
To explain the relationship between two or more variables investigated in an experiment, data should be presented in such a way as to make any patterns and trends more evident. Although tables are an effective means of recording data, they may not be the best way to show trends, patterns or relationships. Graphical representations can be used to more clearly show whether any trends, patterns or relationships exist. The type of graphical representation used by students will depend upon the nature of the investigation and the type of variables investigated:
- pie graphs and bar charts can be used to display data in which one of the variables is categorical
- line graphs can be used to display data in which both the independent and dependent variables are continuous
- lines of best fit can be used to illustrate the underlying relationship between variables
- scattergrams can be used to show an association between two variables
- sketch graphs (not necessarily on a grid; no plotted points; labelled axes but not necessarily scaled) can be used to show the general shape of the relationship between two variables.
When drawing graphs, students should note that:
- the independent variable is represented on the horizontal axis while the dependent variable is represented on the vertical axis
- the existence of a correlation does not necessarily establish that there is a causal relationship between two variables
- not all experiments will show a correlation between variables
- common types of relationships in physics include linear, power and sometimes exponential.
Students should understand why it is important not to ‘force data through zero’. In drawing conclusions they should examine patterns, trends and relationships between variables with the limitations of the data in mind. Gradients and y-intercepts should be considered in terms of what these may indicate about the relationship between independent and dependent variables. Conclusions drawn from data must be limited by, and not go beyond, the data available.
Representation of uncertainties in graphs
Absolute uncertainties can be represented on graphs using error bars. Students should normally include vertical error bars; at times, horizontal error bars may also be appropriate. A trend line (if used) should lie within the region of the error bars. Deviation of trend lines should be discussed in the analysis of results.
Further information relating to uncertainty is provided in Experimental uncertainty and errors.