Estimation and error intervals
Objective. Use rounded information to describe possible values.
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- 2. Worked example
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Learn: the key idea
When a measurement is rounded, an error interval describes the range of possible exact values that could have produced that rounded figure. For a value rounded to the nearest unit, the true value lies within half a unit above and below the rounded figure, written using inequality notation with a lower bound included and an upper bound excluded. Example: a length given as 7 cm to the nearest centimetre has a true value satisfying 6.5 ≤ length < 7.5. These bounds judge the reliability of calculations made using rounded figures.
Worked example
A mass is recorded as 24 kg to the nearest kilogram. Write the error interval showing the bounds of estimation for the true mass.
- 1Rounding is to the nearest kilogram, so half a unit is 0.5 kg.
- 2Subtract 0.5 from 24 for the lower bound: 24 − 0.5 = 23.5.
- 3Add 0.5 to 24 for the upper bound: 24 + 0.5 = 24.5.
- 4The error interval is 23.5 kg ≤ mass < 24.5 kg.
Answer: 23.5 kg ≤ mass < 24.5 kg
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Start practisingCommon mistake. Pupils often use the rounded value itself as both bounds instead of finding half a unit either side; always calculate half of the rounding unit to establish the correct lower and upper bounds.
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