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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?
$1.6$
$2$
$4$
$16$
Solution
The arithmetic mean of given values is taken as true value.
$t _{\text {mean }}=\frac{t_{1}+ t _{2}+ t _{3}+ t _{4}+ t _{5}}{5}$
$t_{\text {mean }}=\frac{1.25+1.24+1.27+1.21+1.28}{5}$
$t_{\text {mean }}=1.25 s$
$\Delta t_{\text {mean }}=\frac{\left|\Delta t_{1}\right|+\left|\Delta t_{2}\right|+\left|\Delta t_{3}\right|+\left|\Delta t_{4}\right|+\left|\Delta t_{5}\right|}{5}$
$\Delta t_{\text {mean }}=\frac{0+0.01+0.02+0.04+0.03}{5}=0.02 s$
Percentage error $=\frac{\Delta t_{\operatorname{mean}}}{t_{\text {mean }}} \times 100=\frac{0.02}{1.25} \times 100$
$=1.6 \%$
