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"," "t_(1)=39.6s,t_(2)=39.9 s and t_(3)=39.5 s`
Least count of measuring instrument=`0.1 s`
(As measurements have only one decimal place)
Precision in the measurment = Least count of the measuring instrument =`0.1 s`
Mean value of time for 20 oscillations is given by
`t=(t_(1)+t_(2)+t_(3))/3`
`=(39.6+39.9+39.5)/3=39.7 s `
Absolute errors in the measurements
`Deltat_(1)=t-t_(1)=39.7-39.6=0.1 s`
`Deltat_(2)=t-t_(2)=39.7-39.9=-0.2 s`
`Deltat_(3)=t-t_(3)=39.7-39.5=0.2 s`
`"Mean absolute error "=(|Deltat_(1)|+|Deltat_(2)|+|Deltat_(3)|)/3`
`=(0.1+0.2+0.2)/3`
`=(0.5)/3=0.17approx0.2" ""(rounding off upto one decimal place)"`
`therefore" Accuracy of measurement "=+-0.2 s`