The accuracy in the measurement of time for 20 oscillations of a...

Given, t₁ = 39.6 s

& & & & & & & & & & & & & & & & & & & & t₂ = 39.9 s

& & & & & & & & & & & & & & & & & & & & t₃ = 39.5 s &

Least count of measuring instrument = 0.1 s

[As measurements have only one decimal place] Precision in the measurement = Least count of the measuring instrument = 0.1 s

Mean value of time for 20 oscillations

$t = \dfrac{{t}_{1} + {t}_{2} + {t}_{3}}{3} = \dfrac{3 9 \text{.} 6 + 3 9 \text{.} 9 + 3 9 \text{.} 5}{3} = 3 9 \text{.} 7 \text{s}$

Absolute errors in the measurements

$$\begin{array}{ll}\Delta {t}_{1} = t - {t}_{1} = 3 9 \text{.} 7 - 3 9 \text{.} 6 = 0 \text{.} 1 \text{s} \\ \Delta {t}_{2} = t - {t}_{2} = 3 9 \text{.} 7 - 3 9 \text{.} 9 = - 0 \text{.} 2 \text{s} \\ \Delta {t}_{3} = t - {t}_{3} = 3 9 \text{.} 7 - 3 9 \text{.} 5 = 0 \text{.} 2 \text{s}\end{array}$$

$\text{Mean absolute error} = \dfrac{\left|\Delta {t}_{1}\right| + \left|\Delta {t}_{2}\right| + \left|\Delta {t}_{3}\right|}{3}$

$= \dfrac{0 \text{.} 1 + 0 \text{.} 2 + 0 \text{.} 2}{3} = \dfrac{0 \text{.} 5}{3} = 0 \text{.} 1 7 \approx 0 \text{.} 2 \left(\text{rounding-off upto one decimal place}\right) \text{.}$

∴ Accuracy of measurement $= \pm 0 \text{.} 2 \text{s}$