Precision, Accuracy & Errors
Practical Skills - OCR A-Level Physics
Key Definition
Precision
How close the measured values are to each other. Precise measurements show a small spread when repeated. A measurement to more decimal places (e.g. 2.456 m) is more precise than one to fewer (e.g. 2 m).
How close the measured values are to each other. Precise measurements show a small spread when repeated. A measurement to more decimal places (e.g. 2.456 m) is more precise than one to fewer (e.g. 2 m).
Key Definition
Accuracy
How close a measured value is to the true value. Accuracy can be increased by repeating measurements and finding a mean average.
How close a measured value is to the true value. Accuracy can be increased by repeating measurements and finding a mean average.
- A measurement can be precise but not accurate if there is a systematic error -- all readings are consistently wrong by the same amount.
- Think of a dartboard: precision is hitting the same spot repeatedly; accuracy is hitting the bullseye.
Random Errors
Key Definition
Random Error
Unpredictable fluctuations in readings caused by uncontrollable factors (e.g. temperature fluctuations, air currents, reaction time). Random errors affect precision.
Unpredictable fluctuations in readings caused by uncontrollable factors (e.g. temperature fluctuations, air currents, reaction time). Random errors affect precision.
- Random errors cause readings to scatter above and below the true value.
- They can be reduced by: taking repeat measurements and calculating a mean, or using data logging equipment to eliminate human reaction time.
Systematic Errors
Key Definition
Systematic Error
Errors arising from faulty instruments or flawed experimental methods. They shift all measurements by the same amount in the same direction, affecting accuracy.
Errors arising from faulty instruments or flawed experimental methods. They shift all measurements by the same amount in the same direction, affecting accuracy.
- Systematic errors cannot be reduced by repeating measurements -- the setup itself must be corrected.
- They can be reduced by: recalibrating instruments, checking for zero errorsWhen an instrument gives a non-zero reading when the true value is zero. This is a type of systematic error., and comparing results with known standards.
Zero Errors
- A zero error is a type of systematic error where an instrument gives a non-zero reading when the true value is zero.
- Examples: a balance reading 0.2 g with nothing on it, a voltmeter reading 0.1 V when disconnected.
- If the zero error is positive, subtract it from all measurements. If negative, add it to all measurements.
Percentage Uncertainty
- The uncertainty in an analogue measurement is half the smallest scale division.
- Percentage uncertainty is calculated using: $$\text{percentage uncertainty} = \frac{\text{uncertainty}}{\text{measured value}} \times 100\%$$
- For the same instrument, the larger the value measured, the smaller the percentage uncertainty.
- If the percentage error is too high, conclusions may need to be rejected or further testing may be required.
Common MistakeHIGH
Wrong: Believing that repeating measurements will reduce systematic errors.
Right: Repeating measurements reduces random errors only. Systematic errors require recalibration, checking for zero errors, or correcting the experimental method.
Right: Repeating measurements reduces random errors only. Systematic errors require recalibration, checking for zero errors, or correcting the experimental method.