Errors & Uncertainties (Cambridge (CIE) AS Physics)

Random & systematic errors

• Measurements of quantities are made with the aim of finding the true value of that quantity

• In reality, it is impossible to obtain the true value of any quantity, there will always be a degree of uncertainty

• The uncertainty is an estimate of the difference between a measurement reading and the true value

• Random and systematic errors are two types of measurement errors which lead to uncertainty

Random error

• Random errors cause unpredictable fluctuations in an instrument’s readings as a result of uncontrollable factors, such as environmental conditions

• This affects the precision of the measurements taken, causing a wider spread of results about the mean value

• To reduce random error: repeat measurements several times and calculate an average from them

Systematic error

• Systematic errors arise from the use of faulty instruments used or from flaws in the experimental method

• This type of error is repeated every time the instrument is used or the method is followed, which affects the accuracy of all readings obtained

• To reduce systematic errors: instruments should be recalibrated or the technique being used should be corrected or adjusted

A graph showing the precision and accuracy of different sets of measurements

Precision can only be used to describe multiple measurements - it tells us how close together those measurements are. Imprecise measurements will have a large range, as shown by the accurate but imprecise black line. 

Zero error

• Zero error is a type of systematic error which occurs when an instrument gives a non-zero reading when the true reading is zero

  • An example may be a set of mass scales showing a reading of 0.200 g when nothing is on the scales

• This introduces a fixed error into readings which must be accounted for when the results are recorded

Precision & accuracy

Precision

• The precision of a measurement is how close the measured values are to each other; if a measurement is repeated several times, then it can be described as precise when the values are very similar to, or the same as, each other

Accuracy

• The accuracy of a measurement is how close a measured value is to the true value; the accuracy can be increased by repeating measurements and finding a mean average

Diagram showing the difference between accurate results and precise results

Random errors can affect precision - the quantity is being measured accurately but each measurement is affected differently, spreading the results out. Systematic errors can lead to precise inaccurate results, by adding 0.5 to each value, for example, the precise results are moved away from the true value.