The length of a rod as measured in an experiment was found to be 2.48m, 2.46 m, 2.49 m, 2.50 m and 2.48m. Find the average length, absolute arror in each observation and the percentage error.

Explanation

Average length=Arithmetic mean of the measured values
`x_(mean)=(2.48+2.46+2.49+2.49+2.46)/(5)=(12.38)/(5)=2.476 m`
`therefore` True value, `x_(mean)=2.48m`
Absolute errors in various measurements,
`|Deltax_(1)|=|x_(1)=x_(mean)|=2.48-2.48=0.00m`
`|Deltax_(2)|=|2.46-2.48|=0.02m`
`|Deltax_(3)|=|2.49-2.48|=0.01m`
`|Deltax_(4)|=|2.49-2.48|=0.01m`
`|Deltax_(5)|=|2.46-2.48|=+0.02m`
Mean absolute error =`(|Deltax_(1)|+|Deltax_(2)|+|Deltax_(3)|+...+|Deltax_(5)|)/(5)`
`((0.00+0.02+0.01+0.01+0.02))/(5)=(0.06)/(5)`
`Deltax_(mean)=0.01 m`
Thus, `x=2.48pm0.01m`
Percentage error, `deltax=(Deltax_(mean))/(x)xx100`
`(0.01)/(2.48)xx100=0.40%`