# 2.1.2 Errors & Uncertainties

### 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

Representing precision and accuracy on a graph

#### Zero error

• This is a type of systematic error which occurs when an instrument gives a reading when the true reading is zero
• This introduces a fixed error into readings which must be accounted for when the results are recorded

### Precision & Accuracy

• Precision of a measurement: this is how close the measured values are to each other; if a measurement is repeated several times, then they can be described as precise when the values are very similar to, or the same as, each other
• The precision of a measurement is reflected in the values recorded – measurements to a greater number of decimal places are said to be more precise than those to a whole number
• Accuracy: this is how close a measured value is to the true value; the accuracy can be increased by repeating measurements and finding a mean average

The difference between precise and accurate results

#### Exam Tip

It is very common for students to confuse precision with accuracy – measurements can be precise but not accurate if each measurement reading has the same error. Precision refers to the ability to take multiple readings with an instrument that are close to each other, whereas accuracy is the closeness of those measurements to the true value.

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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