Question

Three measurements of the time for 20 oscillations of a pendulum give $t_1=39.6s,t_2=39.9s$ and $t_3=39.5s$. What is the precision in the measurements? What is the accuracy of the measurements?

Answer 1

precision is given by least count of the instrument { e.g., pendulum}

here, least of $20$ oscillation $=0.1sec$

so, least count of $1$ oscillation $=\frac{0.1}{20}=0.005sec$

hence, precision in measurements $=0.005sec$

observations are $39.6sec,39.9sec,39.5sec$

mean of observations $=\frac{(39.6+39.9+39.5)}{3}$

$=\frac{\left(119\right)}{3}\approx 39.6sec$

now, maximum error in $20$ oscillations $=$ observation of highest value - mean of observations

$=39.9-39.6=0.3sec$

so, max absorbed error in $1$ oscillation $=\frac{0.3}{20}=0.015sec$

hence, accuracy of measurements is $0.015sec$