Uncertainty & Error

Uncertainties

  • Experiments involve using laboratory apparatus and taking measurements.
  • Almost all measurements have an inherent degree of uncertainty.
  • Uncertainty is a measure of the amount of error that might be present in the measurements you have taken.
  • Uncertainty is usually due to errors in experimental design and operation, of which there are two types.

Systematic errors

  • Source
    • Systematic errors occur due to a persistent flaw with equipment or incorrect use of equipment e.g. consistently taking a burette reading from a height (error of parallax) instead of at eye level.
  • How to identify
    • A systematic error would affect the entire data set so you would get a regular pattern but on analysis the pattern would not be the expected one.
    • Systematic errors reduce accuracy.
  • How to correct
    • Improvements in the experimental technique or by using apparatus with a greater degree of accuracy.
    • Measuring larger amounts decreases the uncertainty. For example in a rate of reaction experiment, increasing the length of time between measuring the amount of products formed will reduce the uncertainty.

Random errors

  • Source
    • Random errors occur due to issues over which the scientist has no direct control e.g. changes in room temperature when measuring the effect of heat on the rate of a reaction.
  • How to identify
    • A random error would usually show up as an anomalous result, which is a data point that does not fit the pattern.
    • Random errors reduce reliability.
  • How to correct
    • Using apparatus with a greater degree of accuracy, increasing the number of measurements taken or taking measurements more carefully.

Calculating Uncertainty

From an Instrument

  • The smallest change that an instrument can measure is called its resolution.
  • For example a thermometer that has a mark every 0.5°C has a resolution of 0.5°C and this is a higher resolution than a thermometer that has a mark every 1°C.
  • Uncertainties when mathematically calculated are represented using the symbol ± placed before the uncertainty.
  • The uncertainty of an instrument can be calculated using the equation:

Uncertainty =  Resolution ÷ 2

  • For a digital instrument the uncertainty is the value obtained when you divide the last displayed digit by 2.
  • For example a reading of 8.05g from a balance thus has an uncertainty of 0.052= ±0.025g.
  • This means that the true value lies somewhere between 8.025g and 8.075g.

From a Set of Results

  • Each time you take a measurement there is a level of uncertainty.
  • The mean calculated from a set of results also has an implicit level of uncertainty involved.
  • The uncertainty in a mean can be calculated using the following equation, where the range is the difference between the largest value and the smallest value:

% error =  Range ÷ 2

  • The larger the value of the range then the greater will be the level of uncertainty as the results are less precise .
  • Uncertainties when mathematically calculated are represented using the symbol ± placed before the uncertainty.
  • An answer of 10.0 with an uncertainty of ± 0.5 cm3 indicates that the actual “true” value lies somewhere between 9.50 and 10.50 cm3.

Example

acid base titration table, IGCSE & GCSE Chemistry revision notes

Need help?

AQA GCSE Chemistry Notes

Want to aim for a Level 9?

See if you’ve got what it takes. Test yourself with our topic questions.

Morgan Curtin Chemistry

Author: Morgan

Morgan’s passion for the Periodic Table begun on his 10th birthday when he received his first Chemistry set. After studying the subject at university he went on to become a fully fledged Chemistry teacher, and now works in an international school in Madrid! In his spare time he helps create our fantastic resources to help you ace your exams.