Time intervals measured by a clock give 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 of the observations?
NEET 2020 (Phase 2)

Question

Time intervals measured by a clock give 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 of the observations? NEET 2020 (Phase 2)

TestHub · Accepted Answer

First, calculate the mean of observations,

$\Rightarrow A_{m} = \frac{1.25 + 1.24 + 1.27 + 1.21 + 1.28}{5}$ $= 1.25 \sec$ ,
it means, $∆ A_{1} = |1.25 - 1.25| s, ∆ A_{2} = |1.24 - 1.25| s, ∆ A_{3} = |1.27 - 1.25| s, ∆ A_{4} = |1.21 - 1.25| s & ∆ A_{5} = |1.28 - 1.25| s$

then calculates the mean of error,

$∆ A_{m} = \frac{0 + 0.01 + 0.02 + 0.04 + 0.03}{5}$ $= \frac{0.1}{5}$

$%$ error $\frac{∆ A_{m}}{A_{m}} = \frac{0.1 \times 100}{5 \times 1.25} = 1.6 %$

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