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.

Options

A. `(2.48pm0.01)m, 0.40%`
B. `(3.48pm0.02)m,0.45%`
C. `(2.48pm0.01)m,0.45%`
D. `(3.48pm0.02)m,045%`

Answer

A

Explanation

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