Repeated observations in an experiment gave the values `1.29 , 1.33 , 1.34 , 1.35 , 1.32 , 1.36, 1.30, and 1.33`. Calculate the mean value, absolute eror , relative error, and percentage error.

Explanation

Here, mean value
`x_(m)=(1.29+1.33+1.34+1.35+1.32+1.36+1.30+1.33)/(8)`
`=1.3275 = 1.33` (rounded off to two places of decimal)
Absolute errors in measurement are
`{:(Deltax_(1)=|1.33-1.29|=0.04 ,Deltax_(2)=|1.33 -1.33|=0.00 ,),(Deltax_(3)=|1.33-1.34|=0.01 ,Delta x_(4)=|1.33-1.35|=0.02 ,),(Deltax_(5)=|1.33-1.32|=0.01 , Delta x_(6)=|1.33-1.36|=0.03 ,),(Deltax_(7)=|1.33-1.30|=0.03 , Deltax_(8)=|1.33-1.33|=0.00 ,):}`
mean absoute error
`bar(Deltax_(m))=(0.04+0.00+0.01+0.02+0.01+0.03+0.03+0.00)/(8)`
`=0.0175`
`= 0.02` (rounded off to two places of decimal)
Relative error `= pm (bar(Deltax_(m')))/(x_(m))=pm(0.02)/(1.33)=pm 0.01503=pm 0.02`
(rounded off two placed of decimal)
Percentage error `= pm 0.01503 xx100=pm 1.503=pm1.5 %`