#### 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

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