Question

Repeated observations in an experiment gave the values $1.29,1.33,1.34,1.35,1.32,1.36,1.30$, and $1.33$. Calculate the mean value, absolute error, relative error, and percentage error.

Answer 1

Mean value of quantity measured, $V=\frac{1.29+1.33+1.34+1.35+1.32+1.36+1.30+1.33}{8}$$x=1.3275=1.33$(round off to two places of decimal).Absolute errors in measurement are:$\Delta x_1=1.33-1.29=0.04;$ $\Delta x_2=1.33-1.33=0.00$$\Delta x_3=1.33-1.34=-0.01;$ $\Delta x_4=1.33-1.35=-0.02$$\Delta x_5=1.33-1.32=+0.01;$ $\Delta x_6=1.33-1.36=-0.03$$\Delta x_7=1.33-1.30=+0.03;$ $\Delta x_8=1.33-1.33=0.00$

Mean absolute error, $\overline{\Delta x}=\frac{{\sum }_{i=l}^{i=n}|(\Delta x{)}_i|}{n}$$=\frac{0.04+0.00+0.01+0.02+0.01+0.03+0.03+0.00}{8}$$\frac{0.14}{8}=0.0175=0.02$

Relative error$=\pm \frac{\overline{\Delta x}}{x}=\pm \frac{0.02}{1.33}=\pm 0.015=\pm 0.02$

Percentage error$=\pm 0.015\times 100=1.5\%$