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

Explanation

Precision is the least measurable value with that instrument in our case precision is `pm 0.1 sec`.
Calculate of accuracy:
Average value of measurements
`=(39.6+39.9+39.5)/3=119/3=39.67`
Error in each measurement =
`Deltaa_1=39.67-39.6=0.07`,
`Deltaa_2=39.9-39.67=0.23,`
`Deltaa_3=39.67-39.5 =0.17`
`Deltaa_(mean)=(0.07+0.23+0.17)/3=0.156`
Precision `pm 1 sec`. In these measurements only two siginificant figures are believable. 3rd One is uncertain.
Adjustment of `Deltaa_(mean)` upto given significant figure =0.156 adjusted to 0.2. So our value is accurate upto `pm0.2`
So our result is 39.67 `pm` 0.2, when significant figures taken into account it is 39.7 `pm 0.2 sec.