It is important to process and present data in a way which makes it easy to analyse. It is also important to evaluate the quality of data before drawing a conclusion.

Depending on the data that has been obtained, there are mathematical techniques that can be used to further analyse the results.

From a straight-line graph the gradient can be calculated. The gradient of a distance-time graph is equal to the speed, and the gradient of a force-extension graph is equal to the spring constant.

The area under a graph can also be calculated. The area under a velocity-time graph will give the distance travelled.

Lines can be **extrapolated** in order to estimate a value beyond the measured values, and **interpolation** can be used to estimate a value between two known values.

The final step is to consider improvements that could be made to equipment and experimental procedure in order to increase the precision and accuracy of the data collected.

Things to consider when improving procedure are:

- Is the best piece of equipment being used? For example should Vernier callipers be used instead of a ruler when measuring a relatively short length? Would it be better to use a smaller diameter measuring cylinder when finding the volume of a small quantity of liquid?
- Should more repeats be taken? For example if three repeated readings are reliable, is it necessary to take any more?
- Could someone else reproduce the experiment?
- Were there any external conditions that could be controlled better? eg should a cooling experiment be conducted near a heater or near an frequently opened door?

It is important to reduce errors as much as possible in any investigation. Errors are not the same thing as making mistakes.

Random errors are present when any measurement is made and cannot be corrected for. Their effect can be reduced by taking more measurements and finding the mean. For example, measuring the time period of a pendulum will produce a random error as it is impossible to stop a timer at exactly the right moment every time.

Systematic errors are when a measured result differs consistently from the true result every time. For example, a zero error on a meter will produce a systematic error.