Question

In an experiment, the values of refractive indices of glass were found to be 1.54, 1.53, 1.44, 1.54,1.56 and 1.45 in successive measurements.

Find the following:

i) Mean value of refractive index of the glass

ii) Mean absolute error

iii) Relative error

iv) Percentage error

• A. 1.51, 0.04, 0.03, 3%
• B. 1.51, 3, 0.03, 0.04%
• C. 3, 0.04, 1.51, 0.03%
• D. 0.04, 1.51, 3, 0.03%

Answer 1

The correct option is A 1.51, 0.04, 0.03, 3%

$Mean=\frac{1.54+1.53+1.44+1.54+1.56+1.45}{6}$ $=1.51$

$\left|Meanabsoluteerror\right|=\sqrt{\frac{1}{6}\sum (\overline{x_1}-\overline{x}{)}^2}=0.04$

$Relativeerror=\frac{Absoluteerror}{Mean}=\frac{0.04}{1.51}=0.026\approx 0.03$

% $error=$ $Relative$ $error\times 100=3$%