# 1.2.1 Sources of Uncertainty

### 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 as 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 that 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 consistently 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 different instruments should be used

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

• Precise measurements are ones in which there is very little spread about the mean value, in other words, how close the measured values are to each other
• If a measurement is repeated several times, it 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

• A measurement is considered accurate if it is close to the true value
• The accuracy can be increased by repeating measurements and finding a mean of the results
• Repeating measurements also helps to identify anomalies that can be omitted from the final results

The difference between precise and accurate results

#### Repeatability

• A measurement is repeatable if the original experimenter repeats the investigation using the same method and equipment and obtains the same results

#### Reproducibility

• A measurement is reproducible if the investigation is repeated by another person, or by using different equipment or techniques, and the same results are obtained

#### Resolution

• Resolution is the smallest change in the quantity being measured of a measuring instrument that gives a perceptible change in the reading
• For example, the resolution of a wristwatch is 1 s, whereas the resolution of a digital stop-clock is typically 10 ms (0.01 s)
• In imaging, resolution can also be described as the ability to see two structures as two separate structures rather than as one fuzzy entity

Good resolution and poor resolution in an ultrasound scanner. The good image manages to resolve the two objects into two distinct structures whereas the poor image shows one fuzzy entity.

#### Exam Tip

It is a very common mistake to confuse precision with accuracy – measurements can be precise but not accurate if each measurement reading has the same error.

Make sure you learn that 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: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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