Question

In an experiment refractive index of glass was observed to be $1.45,1.56,1.54,1.44,1.54$ and $1.53$. The mean absolute error in the experiment is

• A. $0.04$
• B. $0.02$
• C. $0.03$
• D. $0.01$

Answer 1

Answer: (A)

$0.04$

$\begin{array}{c}{\mu }_1=1.45{\mu }_2=1.56\\ {\mu }_3=1.54{\mu }_3=1.44\\ {\mu }_5=1.54{\mu }_6=1.53\end{array}$

$\begin{array}{c}\mu =\text{refractive}\\ \text{index}\end{array}$

$\overline{u}=\frac{{\mu }_1+{\mu }_2+{\mu }_3+{\mu }_4+{\mu }_5+{\mu }_6}{6}$$=1.51$

$\begin{array}{c}\overline{\mu }-{\mu }_1=|1.5|-1.45\mid =0.06\\ \overline{\mu }-{\mu }_2=|1.51-1.56|=+0.05\\ \overline{\mu }-{\mu }_3=|1.51-1.54|=+0.03\\ \overline{\mu }-{\mu }_4=|1.51-1.44|=0.07\\ \overline{\mu }-{\mu }_r=|1.5|-1.54\mid =+0.03\\ \overline{\mu }-{\mu }_6=|1.51-1.53|=+0.02\end{array}$

$\Delta \overline{u}=(0.06+0.05+0.03+0.07+0.03+0.02)/6$$=0.043\approx 0.04$