Applying Limits of Accuracy

Applying Limits of Accuracy

GCSE(F) GCSE(H)

There are two types of measures.

Discrete measures can be counted (such as people, or cars).

Continuous measures involve measurement (such as the length of a car, or the weight of a person) where a single measure can fall into a range.

The accuracy of a continuous measurement depends upon the person or device making the measurement. In engineering, a measurement is often given with an error interval: a length may be given as 25 ±0.5mm.

Mathematically, that means the length can range from 25 - 0.5 = 24.5 mm to 25 + `0.4dot(9)`mm. It can also be written as 24.5 ≤ measurement < 25.5. Note greater than or equal to for the lower limit, and less than for the upper limit.

Another way of indicating the accuracy of a measurement is to give a tolerance. A tolerance is the range of accuracy around a measurement: half the tolerance will be higher than the measurement, and half the tolerance will be lower.

If m is the measurement and t is the tolerance, then:

lower bound = m - 0.5t; and

upper bound = m + 0.5t; and

the limits are m ±0.5t

remembering that the upper bound is not part of the measurement.

Examples

1. A car is 432cm long, measured with an error interval of 0.15cm. What are the upper and lower bounds of the length of the car? Write the answer as an inequality.

Answer: 431.85 ≤ length < 432.15 cm

Lower: 432 - 0.15 = 431.85

Upper: 432 + 0.15 = 432.15

2. A lorry makes a run from Manchester to Leeds and return three times over one week. The distance from Manchester to Leeds is 44.8 miles, with an error interval of 0.05 miles. What is the minimum distance the lorry could have travelled?

Answer: 268.5 miles

Minimum for one one-way journey: 44.8 - 0.05 = 44.75.

For six (three return) journeys = 44.75 x 6 = 268.5.