Question

The refractive index ($\mu$) of glass is found to have the values $1.49,1.50,1.52,1.54and1.48$. Calculate mean absolute error.

• A. $0.02$
• B. $0.04$
• C. $0.08$
• D. $0.09$

Answer 1

The correct option is A $0.02$

Mean value of refractive index

$\begin{array}{c}\Rightarrow \frac{{\mu }_1+{\mu }_2+{\mu }_3+{\mu }_4+{\mu }_5}{5}\\ \Rightarrow \frac{1.49+1.50+1.52+1.54+1.48}{5}\\ \Rightarrow 1.51\end{array}$

$\Rightarrow \left|\Delta {\mu }_1\right|=|1.51-1.49|=0.02$

$\Rightarrow [\Delta {\mu }_2|=|1.51-1.50\mid =0.01$

$=>\left|\Delta {\mu }_3\right|=|1,5|-1,||5=0.01$

$\Rightarrow \left|\Delta {\mu }_4\right|=|1.51-1.54|=0.03$

$\Rightarrow \left|\Delta {\mu }_5\right|=|1.51-1.48|=0.03$

$\Rightarrow$ absolute error $=\frac{\left|\Delta {\mu }_1\right|+\left|\Delta {\mu }_2\right|+\left|\Delta {\mu }_3\right|+\left|\Delta {\mu }_4\right|+\left|\Delta {\mu }_5\right|}{5}$

$\Rightarrow \frac{0.02+0.01+0.01+0.03+0.03}{5}$

=> 0.02