Percentage Relative Error in Time Readings – Rankers Physics
Topic: Unit And Dimensions
Subtopic: Error Analysis

Percentage Relative Error in Time Readings

The intervals measured by a clock given the following readings: 1.25 s, 1.24 s, 1.27 s, 1.21 s and 1.28 s. What is the percentage relative error in the observations?

[2020-Covid]

4%
16%
1.6%
2%

Solution:

Mean value \(\bar{t} = (1.25+1.24+1.27+1.21+1.28)/5 = 1.25\text{ s}\). Mean absolute error \(\delta\bar{t} = (|0|+|0.01|+|0.02|+|0.04|+|0.03|)/5 = 0.1/5 = 0.02\text{ s}\). Percentage relative error \( = (\Delta\bar{t} / \bar{t}) \times 100% = (0.02 / 1.25) \times 100% = 1.6%\).

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