Precision and accuracy: close together, or close to the truth?

Arrows on a target

Precision is how close a group of measurements are to each other. Accuracy is how close a measured value is to the accepted or true value. They are separate ideas.

Fig. 1.15 shows arrows on a target. Arrows bunched together are precise. Arrows near the bullseye are accurate. Arrows bunched on the bullseye are both.

In measurement, the instrument sets the precision: the smaller the least count, the more precise. Accuracy depends on the fractional uncertainty, the uncertainty compared with the size of the reading.

So the smaller the quantity, the more precise the instrument it needs. More significant figures in a result show higher accuracy.

Precision: readings agree with each other; set by the least count. Accuracy: the reading matches the true value; judged by fractional uncertainty.

Key terms

Precision

How closely repeated measurements agree.

Accuracy

How close a measured value is to the true value.

Least count

The smaller it is, the more precise the instrument.

Fractional uncertainty

The uncertainty divided by the reading: a relative measure.

Short questions with model answers

1. Q1. The same metre rule (±0.05 cm) gives the line 10.3 cm and the rod 4.6 cm. Which result is more accurate?

   • 0.05 cm ÷ 10.3 cm ≈ 0.0049
   • 0.05 cm ÷ 4.6 cm ≈ 0.011

   The 10.3 cm line: same precision, but smaller fractional uncertainty. It also has 3 significant figures against 2.

2. Q2. Rank the metre rule, Vernier Callipers and screw gauge by precision.

   • 1 mm > 0.1 mm > 0.01 mm
   • Smallest least count = most precise.

   Screw gauge, then Vernier Callipers, then metre rule.

Common mistakes

• ✗ Using precise and accurate as if they mean the same.

  ✓ Precise readings agree with each other; accurate ones agree with the true value.

• ✗ Saying arrows bunched together must be on target.

  ✓ Fig. 1.15 (a): bunched but off-centre is precise, not accurate.

• ✗ Judging accuracy by the uncertainty alone, ignoring the size of the reading.

  ✓ Accuracy depends on the fractional uncertainty: divide by the reading.

MCQs

1. 1. Arrows close together but away from the bullseye are:

   1. (a) Accurate, not precise
   2. (b) Precise, not accurate
   3. (c) Accurate and precise
   4. (d) Neither
   Show answer

   (b) Fig. 1.15 (a).

2. 2. The precision of a measurement is determined by:

   1. (a) The true value
   2. (b) The number of readings
   3. (c) The size of the object
   4. (d) The instrument used
   Show answer

   (d) Smaller least count, more precise (p. 22).

3. 3. The most precise of these is:

   1. (a) Screw gauge
   2. (b) Vernier Callipers
   3. (c) Metre rule
   4. (d) Measuring tape
   Show answer

   (a) Least count 0.01 mm, the smallest.

4. 4. Accuracy depends on:

   1. (a) The least count only
   2. (b) The colour of the scale
   3. (c) The fractional uncertainty
   4. (d) The number of students
   Show answer

   (c) The relative measurement matters (p. 22).

5. 5. Higher accuracy is shown by:

   1. (a) A bigger unit
   2. (b) More significant figures
   3. (c) Fewer readings
   4. (d) A larger uncertainty
   Show answer

   (b) The larger the number of significant figures, the higher the accuracy.

Quick revision

• Precision: readings close to each other. Accuracy: close to the true value.
• A smaller least count gives more precision; screw gauge beats Vernier beats rule.
• Accuracy follows fractional uncertainty and shows in more significant figures.