Time for 20 oscillations of a pendulum is measured as `t_1 = 39.6 s , t_2 = 39.9 s , t_3 = 39.5.` What is the precision in the measurements ? What is the accuracy of the measurement ?

Explanation

Given, no of oscillations, N= 20
Time taken for 20 oscillations,
`t_(1)= 39.6s, t_(2)= 39.9s " and "t_(3)= 39.5s`
The precision in the time measurement is equal to the least count of measuring instrument which is 0.1s.
Mean value of time per 20 oscillations is
t mean `=(t_(1)+t_(2)+t_(3))/(3)`
`=(39.9+39.9+39.5s)/(3)`
`=39.7s`
Absolute error in each measurement is
`triangle t_(1)= t_("mean")-t_(1)`
`=39.7-39.6= 0.1s`
`trianglet_(2)= t_("mean")-t_(2)`
`=39.7-39.9= -0.2s`
`trianglet_(3)= t_("mean")- t_(3)`
`=39.7-39.5=0.2s`
Mean absolute error is
`trianglet_("mean")= (|trianglet_(1)|+|trianglet_(2)|+|trianglet_(3)|)/(3)`
`=(0.1+0.2+0.2)/(3)`
`=0.17s = 0.2s` (1 significant figures)
Accuracy of measurement `= pm 0.2 s`