IB Chemistry home > Syllabus 2016 > Data Processing > Random uncertainties and systematic errors

Syllabus ref: 11.1

The term 'random' means something that happens by chance. When experiments are carried out there are many unforeseen situations that could affect the recorded data.

Error and uncertainty

Errors in experiments arise from three general sources:

  1. 1 Instrumental inaccuracy
  2. 2 Human limitations
  3. 3 Experimental design

The goal of any good investigator is to minimise and quantify the errors whenever possible. To do this the investigator has to understand where and how the errors arise. This is the purpose of the evaluation.

Errors or uncertainties may be broadly categorised as either random or systematic. In the following sections we will take a look at how errors arise in experiments and what may be done to minimise them.


Instrumental accuracy

The instrumental accuracy must be considered for every piece of apparatus used. Good laboratory apparatus usually has the tolerance marked on it by the manufacturer. For example, a grade 'B' 50ml pipette may have the marking 50ml ± 0.07 @ 20ºC.

The uncertainty in a piece of apparatus is often called the 'tolerance'. The manufacturer includes the tolerance of the measuring instrument, assuming that it is used as per the instructions.

All measurements have an associated random uncertainty. We are limited by both the accuracy of the instruments that are used in measurement and by our own capabilities.

Even electronic instrumentation has to 'decide' on the final decimal place. If an electronic balance measures to two decimal places, it has to choose the second decimal place by considering the (unseen) third decimal. If the third is 5 or greater then the second decimal is 'rounded up' If the third decimal is 4 or less, the second is left unchanged. We don't see this operation in practice, but it means that there is always an uncertainty of +/- 0.005 in a two decimal place measure.

Glassware used to measure volume of solutions may be measuring cylinders, pipettes or burettes. All of these instruments require human judgement to gauge exactly at which level the solution lies. A solution is measured to a given 'mark' on the glassware. This requires our senses to be as accurate as possible, but everybody has human limitations. We just have to accept that there is an uncertainty when we record our results.

Similarly the manufacturer of the glassware is conditioned by the accuracy of the manufacturing process; the machines made to manufacture instrumentation also have their own inaccuracy.

And the conditions affect the measurements. Pipettes, for example are calibrated to measure solutions at 20ºC. This is rarely the exact temperature of a solution, once again introducing an inaccuracy.

So what do we do with all of this inaccuracy? The answer is that we have to accept and record it as part of our experimentation, to understand that it is ever-present and to try and quantify it so that we know the upper and lower limits of each measurement taken.


Human limitations

This is not what students usually understand by the term. Human error does not necessarily indicate that a mistake has been made. To differentiate between mistakes in experimentation and normal human limitation, some authors use the term 'blunders' instead of error to mean mistakes. This gives a sense that the experimenter has done something that he/she should not have, ie spilled some solution to be titrated, or dropped something onto the floor.

Unfortunately the term is often used in everyday life to suggest an incorrect action taken, or mistake made. "The crash was caused by human error"

In scientific terms, human error means the limitations inherent in measurements made by human agency, such as timing the disappearance of a cross drawn onto the side of a beaker due to the formation of a precipitate, judging the end-point of a titration etc.


Systematic errors

These are errors that are consistently produced in the course of an experiment by poor design, or some inherent fault or limitation in the apparatus. They may also be due to poor experimental techniques.

These errors can never be quantified completely, nor can the experiments be made more reliable by repetition. However, they can be improved by changing the experimental design, by improving the measuring techniques etc.

Typical systematic errors include


Definitions Summary

Systematic errors: - An error that is repeated throughout the course of an experiment is said to be a systematic error. These may be due to inaccuracy in the apparatus, or in the techniques applied.

Precision:- This refers to how close the measured values are to one another. Readings may be very precise, but wildly inaccurate.

Accuracy:- This refers to how close the precise values are to the literature accepted values.

Repeatable:- This is linked to precision in that if one person is conducting the same experiment and produces precise results the experiment is said to be repeatable.

Reproducible:- The is effectively the same as repeatable, but for other groups, or studies that produce the same precise results.

Tolerance:- The accepted accuracy of a piece of apparatus when used in the manner described by the manufacturer.