Use percentage difference to compare your result to a known or theoretical value
Measurements & Uncertainties - OCR A-Level Physics
Key Definition
Percentage difference
A measure of the accuracyHow close a measurement is to the true or accepted value. of a measurement. It expresses the gap between your experimental result and the accepted (true) value as a percentage of the accepted value. The smaller the percentage difference, the more accurate the measurement.
A measure of the accuracyHow close a measurement is to the true or accepted value. of a measurement. It expresses the gap between your experimental result and the accepted (true) value as a percentage of the accepted value. The smaller the percentage difference, the more accurate the measurement.
$$\% \text{ difference} = \frac{|\text{measured value} - \text{true value}|}{\text{true value}} \times 100\%$$
- Use percentage difference to compare a single result against a known or theoretical value (for example, $g = 9.81 \text{ m s}^{-2}$ or the refractive index of glass = 1.5).
- If the percentage difference is less than the percentage uncertaintyThe range of confidence in a measurement, written as ± a value giving the upper and lower bounds within which the true value is expected to lie., the accepted value lies within your experimental range and the result is consistent.
- If the percentage difference is greater than the percentage uncertainty, the gap is too large to be explained by random scatter alone, so a systematic errorAn error that shifts every reading by the same predictable amount, usually due to calibration faults or zero error. is likely.
- Worked example: measured $g = 10.1 \text{ m s}^{-2}$ with 5% uncertainty. Accepted value = $9.81 \text{ m s}^{-2}$. $\% \text{ difference} = \frac{|10.1 - 9.81|}{9.81} \times 100\% = 3.0\%$. Since $3.0\% < 5\%$, the result is consistent with the accepted value.
Common Mistake
MEDIUM
Wrong: Calling a result "accurate" or "inaccurate" without comparing the percentage difference to the percentage uncertainty. Or dividing by the measured value instead of the true value.
Right: State the percentage difference, compare it to the percentage uncertainty, and write a conclusion. Always divide by the accepted (true) value, never your own measurement.
Right: State the percentage difference, compare it to the percentage uncertainty, and write a conclusion. Always divide by the accepted (true) value, never your own measurement.
Examiner Tips and Tricks
- OCR often asks "Is your result consistent with the accepted value?" The answer needs three parts: the percentage difference, the percentage uncertainty, and a comparison.
- "It is close" is not a conclusion. Use phrases like "consistent within experimental uncertainty" or "outside the range of uncertainty, suggesting a systematic error".