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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. |
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Answer» 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%` |
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