In an experiment, the values of refractive index of glass were found to be 1.54, 1.53 , 1.44 and 1.54 , 1.56 and 1.45 in successive measurements . Calculate (i) Mean value of refractive index of glass (ii) Absolute error in each measurement (iii) Mean absolute error (iv) relative error and (v) Percentage error.

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) 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)`
(iv) Relative error in the value of `mu`,
`=(Delta_(mu_("mean") ))/( mu_("mean") ) = (0.04)/( 1.51)- 0.02649 = 0.03`
(v) Percentage error in the value of
`mu= 0.03 xx 100= 3%`