Question

A student performing an experiment to find the period of second pendulum obtained the following results. 1.96 a, 2.00 s, 1.94 s, 2.04 s and 2.06 s. Find absolute error, relative error, percentage error in the measurement.

Answer 1

$1.96,\mathrm{2.001.94},2.04,2.06$

$\to$ Arithmetic mean $=\frac{1.96+2.00+1.94+2.04+2.06}{5}=\frac{1.10}{5}=2$

$\to$ Absolute error

${△}_{a1}=1.96-2=-0.04$

${△}_{a2}=2.00-2=0$

${△}_{a3}=1.94-2=0.06$

${△}_{a4}=2.04-2=0.4$

${△}_{a5}=2.06-2=0.6$

Mean of absolute error $=\frac{{△}_{a1}+{△}_{a2}+{△}_{a3}+{△}_{a4}+{△}_{a5}}{5}$

$=\frac{-0.04+0-0.06+0.4+0.6}{5}=\frac{0.9}{5}=0.18$

Relative error $=\frac{0.18}{2}=0.09$

$x$ of relative error $=\frac{0.18}{2}\times 100=9x$