The dependent and independent variables

Visualising data: plotting a graph

Variables are any characteristics in an experiment that can change value, including mass, length, temperature, speed, radius, volume, rate of reaction or position. In a typical scientific experiment, we change the independent variable in a controlled way. A corresponding change in second variable is then measured, should it exist. If a change in the second variable is measured, then it is said to be dependent on the first variable.

An example experimental setup is shown below to illustrate how the extension of a spring depends on the mass suspended from it:

Three springs are shown. The first spring has no mass hanging from it, and it has no extension. The second spring has a mass hanging from it, and its length has increased by x. The third spring has two masses hanging from it, and it now has extension 2x. Extension x therefore depends on mass, with mass being the controlled or independent variable.

For example, a physicist wishes to understand if a particular spring obeys Hooke’s law. They expect a linear correlation between the mass suspended from the spring and the spring’s extension if Hooke’s law is obeyed. In their experiment, they control the mass hanging from the spring whilst measuring the spring’s extension. Mass is therefore our independent variable whilst the measured extension of the spring is the dependent variable. The physicist will likely present their experimental results on a graph as shown below:

A graph showing how the extension of a spring in meters correlates with the mass suspended from the spring. Data points are represented by blue crosses. The extension is seen to increase as more mass is suspended from the spring.

How can we interpret these results?

How do I read a graph and why is this important?

Curriculum

The dependent and independent variables

Visualising data: plotting a graph

Getting Involved

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