Consider a series of measurements of the length of a box in an experiment. The readings are 2.4 ~m , 2.5 ~m , 2.6 ~m , 2.8 ~m , 3.0 ~m . What would be the relative error?

Step-by-step solution

Given that, number of observations, n=5 aligned & a₁=2.4 ~m , a₂=2.5 ~m , a₃=2.6 ~m , a₄=2.8 ~m , & a₅=3.0 ~m aligned Mean value of observations, aligned a & = a₁+a₂+a₃+a₄+a₅ 5 a & = 2.4+2.5+2.6+2.8+3.0 5 & = 13.3 5 =2.66 aligned Absolute errors in individual observed value aligned & | a₁ |= |a₁- a |=|2.4-2.66|=|-0.26|=0.26 & | a₂ |= |a₂- a |=|2.5-2.66|=|-0.16|=0.16 & | a₃ |= |a₃- a |=|2.6-2.66|=|-0.06|=0.06 & | a₄ |= |a₄- a |=|2.8-2.66|=0.14 & | a₅ |= |a₅- a |=|3.0-2.66|=0.34 aligned Mean absolute error, aligned a