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Comparing results with accepted values and drawing conclusions

Edexcel IAL Physics · WPH13 Practical Skills in Physics I

Experiments end with a judgement: is the result consistent with the accepted value or the prediction? Examiners want numbers, not opinions.

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Using limits

1. Find the percentage uncertainty of your calculated value (not of the accepted value).

2. Work out the limits: value ± (percentage / 100 x value).

3. State whether the accepted value lies within these limits.

4. Conclude: if it does, your result is consistent with (accurate to) the accepted value; if not, there is probably a systematic error or a wrong assumption.

The most common examiner complaint is calculating limits from the accepted value's uncertainty instead of your own.

Percentage difference

percentage difference = |measured - accepted| / accepted x 100%, with the accepted value on the bottom.

Writing the conclusion

Always write an explicit comparison: 'The upper limit is 9.86 m/s2 and the lower limit 9.38 m/s2; 9.81 m/s2 lies between them, so the result is consistent with the accepted value.' A correct calculation without the comparison sentence regularly loses a mark.

Improvements

Base improvements on your evidence: target the measurement with the largest percentage uncertainty, or the likely systematic error. 'Use a micrometer instead of a ruler for the diameter, because the diameter contributes most of the uncertainty' beats 'be more careful'.

Worked example

A student finds g = 9.62 m/s2 with a percentage uncertainty of 2.5%. Is this consistent with 9.81 m/s2?

  1. Absolute uncertainty = 2.5 / 100 x 9.62 = 0.24 m/s2
  2. Limits: 9.38 m/s2 to 9.86 m/s2
  3. 9.81 m/s2 lies within these limits.

Answer: Yes: the result is consistent with the accepted value

Key idea: Limits from your own percentage uncertainty; check whether the accepted value is inside; say so explicitly. Or compare the percentage difference (accepted value on the bottom) with your percentage uncertainty.

Check yourself

  1. A measured speed of sound is 334 m/s with a percentage uncertainty of 2.0%. Find the upper limit in m/s, to 3 s.f.
    Show answer

    341 m/s. 334 x 1.020 = 340.68, so 341 m/s.

  2. A measured speed of sound is 334 m/s ± 2.0% (limits 327 m/s to 341 m/s). The accepted value is 343 m/s. What should the conclusion be?
    • Consistent, as 334 is close to 343
    • Consistent, as the uncertainty is small
    • No conclusion is possible
    • Not consistent: 343 m/s lies outside the limits
    Show answer

    Not consistent: 343 m/s lies outside the limits. 343 m/s is above the upper limit of 341 m/s.

  3. A measured value of g is 9.62 m/s2 and the accepted value is 9.81 m/s2. Find the percentage difference, to 2 s.f.
    Show answer

    1.9 %. |9.62 - 9.81| / 9.81 x 100 = 1.9%.

  4. A Young modulus is measured as 1.18 x 1011 Pa with a percentage uncertainty of 6%. Find the upper limit, in units of 1011 Pa, to 3 s.f.
    Show answer

    1.25 x 1011 Pa. 1.18 x 1.06 = 1.2508, so 1.25 x 1011 Pa.

  5. The Young modulus of copper is 1.30 x 1011 Pa. A wire's measured value has limits 1.11 x 1011 Pa to 1.25 x 1011 Pa. What can be deduced?
    • The wire is probably not copper, as 1.30 x 1011 Pa is outside the limits
    • The wire is copper
    • The wire is copper, as the values are similar
    • Nothing, since the uncertainty is 6%
    Show answer

    The wire is probably not copper, as 1.30 x 1011 Pa is outside the limits. 1.30 is above the upper limit of 1.25, so the result is not consistent with copper.

  6. When testing whether a result agrees with an accepted value, whose percentage uncertainty should be used to set the limits?
    • The uncertainty of the accepted value
    • The uncertainty of the least precise instrument only
    • The uncertainty of your own calculated result
    • A standard 5% in every case
    Show answer

    The uncertainty of your own calculated result. Limits come from your own result; examiners report this as the commonest error.

  7. In a Young modulus experiment, the percentage uncertainties are: length 0.1%, diameter 2.5%, extension 1.5%. Which improvement would reduce the overall uncertainty most?
    • Measure the diameter more precisely
    • Measure the length more precisely
    • Use a heavier mass hanger
    • Repeat the length measurement
    Show answer

    Measure the diameter more precisely. The diameter has the largest percentage uncertainty, so improving it helps most. (It is also squared in the formula, which at A2 you will see doubles its effect.)

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Last updated 8 November 2026. Spotted a mistake? Tell us.