Precision Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

medium
A student measures a pencil three times and gets 15.215.2 cm, 15.115.1 cm, 15.315.3 cm. Another instrument gives 15.1815.18 cm, 15.2015.20 cm, 15.1915.19 cm. Which set of measurements is more precise? Which is more accurate if the true length is 15.515.5 cm?

Solution

  1. 1
    Precision concerns spread (consistency): Set 1 ranges from 15.115.1–15.315.3 cm (range =0.2= 0.2 cm). Set 2 ranges from 15.1815.18–15.2015.20 cm (range =0.02= 0.02 cm). Set 2 is more precise.
  2. 2
    Accuracy concerns closeness to the true value (15.515.5 cm): Mean of Set 1 =15.2= 15.2 cm; mean of Set 2 =15.19= 15.19 cm. Both are far from 15.515.5 cm, but Set 1 is slightly closer on average.
  3. 3
    Conclusion: Set 2 is more precise (tightly clustered) but neither set is very accurate.

Answer

Set 2 is more precise; neither set is highly accurate relative to the true length of 15.515.5 cm.
Precision measures repeatability (how close repeated measurements are to each other), while accuracy measures correctness (how close measurements are to the true value). A measurement can be precise but inaccurate (systematic error) or accurate but imprecise (random error).

About Precision

The degree of exactness in a measurement or calculation, reflected in the number of significant digits reported.

Learn more about Precision →

More Precision Examples

Example 2 hard

Add [formula] cm and [formula] cm, applying the rule for precision in addition.

Example 3 easy

Which measurement is more precise: [formula] m, [formula] m, or [formula] m? How many significant fi

Example 4 medium

Multiply [formula] cm [formula] [formula] cm, applying the significant figures rule for multiplicati

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