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 (i) mean value of refreactive index of glass (ii) mean absolute error (iii) relative error and (iv) percentage error are respectively.

Explanation

(i) Mean value of refractive index,
`mu_("mean")= (1.54 +1.53 +1.44 +1.54 +1.56 +1.45)/(6) = 1.51`
(ii) Taking `mu_("mean")` as the true value, the errors in the six measurements are
1.54 - 1.51 = +0.03, 1.53 - 1.51 = +0.02,
1.44 - 1.51 = -0.07
1.54 - 1.51 = +0.03, 1.56 - 1.51 = +0.05
and 1.45 - 1.51 = -0.06
The absolute errors are 0.03, 0.02, 0.07, 0.03, 0.05 and 0.06
(iii) Mean absolute error in the value of `mu` is
`Delta mu_("mean")= (0.03 +0.02 +0.07 +0.03 +0.05+0.06)/(6)= (0.26)/(6) = 0.04`
(iv) Relative error in the value of `mu, mu(Delta mu_("mean"))/(mu_("mean"))= (0.04)/(1.51)= 0.02649 = 0.03`. Percentage error in the value of `mu=0.03 xx 100 = 3%`