(d) precision and accuracy of measurements and data, including margins of…

The idea

Precision describes how closely repeated measurements agree with each other, while accuracy describes how close a measurement is to the true value. A set of readings can be precise yet inaccurate if a systematic error, such as a zero error on a balance, shifts every value the same way. Uncertainty in apparatus is the doubt in a single reading, often taken as half the smallest scale division for an analogue instrument or the stated tolerance for a digital one. Margin of error is the range within which the true value is expected to lie. Percentage error compares the uncertainty with the measured value: percentage error = (uncertainty ÷ measured value) × 100.

For example: A 0.01 cm³ uncertainty on a 2.00 cm³ reading gives (0.01 ÷ 2.00) × 100 = 0.5%, but the same uncertainty on 0.20 cm³ gives 5%, so small readings carry larger percentage errors.

What earns the marks

• Distinguishes precision (agreement between repeat readings) from accuracy (closeness to the true value).
• Explains that a systematic error can make precise readings inaccurate because all values are shifted in the same direction.
• States that apparatus uncertainty is the doubt in a reading, e.g. half the smallest division for an analogue scale or the manufacturer's tolerance for a digital instrument.
• Defines margin of error as the range within which the true value is expected to lie.
• Calculates percentage error as (uncertainty ÷ measured value) × 100 and recognises that the same absolute uncertainty gives a larger percentage error for a smaller reading.
• Selects the correct interpretation when given a set of readings, e.g. identifying low spread but a consistent offset from the true value.

Common mistakes and how to put them right

• Treating precision and accuracy as synonyms.

  Put it right by defining precision as agreement between repeats and accuracy as closeness to the true value.

• Assuming repeated readings that agree must be accurate.

  Put it right by explaining that a systematic error shifts all readings equally, so they can be precise but inaccurate.

• Using the whole smallest scale division as the uncertainty for an analogue instrument.

  Put it right by using half the smallest division unless the question states otherwise.

• Dividing the measured value by the uncertainty when calculating percentage error.

  Put it right by using (uncertainty ÷ measured value) × 100.

Exam tips

• Read the stem carefully to see whether it asks about spread of repeats (precision) or closeness to a true value (accuracy) before choosing an option.
• When a percentage error option is offered, estimate the size of the reading first: a small reading with a fixed uncertainty must give a larger percentage error.
• Eliminate options that confuse margin of error with uncertainty in a single reading, since the margin describes the range around the true value.