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The length of a rod as measured in an ex...

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

Text Solution

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Average length = Arithmetic mean of the measured values
`x_("mean")=(2.48+2.46+2.49+2.49+2.46)/5`
= `(12.38)/5m=2.476m`
`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")=0.01m`
Thus, `x=2.48pm0.01m`
Percentage error `deltax=(Deltax_("mean"))/x xx100=0.01/2.48xx100=0.40%`
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