Refractive index of a flint glass (mu) was measured in an experiment and was found to be 1.655,1.667, 1.655, 1.659, 1.669" and "1.654. Find (i) the mean value of mu (ii) mean absolute error (iii) relative error (iv) percentage error.

Refractive index of a flint glass (mu) was measured in an experiment a

1.	Refractive index of a flint glass (mu) was measured in an experiment and was found to be 1.655,1.667, 1.655, 1.659, 1.669" and "1.654. Find (i) the mean value of mu (ii) mean absolute error (iii) relative error (iv) percentage error.
Answer» SOLUTION :Given, `mu_(1)=1.655, mu_(2)=1.667, mu_(3)=1.655, mu_(4)=1.659, mu_(5)= 1.669, mu_(6)=1.654` (i) Mean value of `mu` is `mu_(m)=(mu_(1)+mu_(2)+mu_(3)+mu_(4)+mu_(5)+mu_(6))/(6)` `=(1.655+1.667+1.655+1.659+1.669+1.654)/(6)=1.6598` `=1.660` (Rounded off to 4 significant figures) ABSOLUTE errors in the different measurments are `triangle mu_(1)= mu_(m)-mu_(1)` `=1.660-1.655=0.005` `triangle mu_(2)= 1.660-1.667= -0.007` `triangle mu_(3)= 1.660-1.655=0.005` `triangle mu_(4)= 1.660- 1.659= 0.001` `triangle mu_(5)= 1.660- 1.669= -0.009` `triangle mu_(6)= 1.660- 1.654= 0.006` Mean absolute ERROR `triangle bar(mu)= (sum\|triangle mu_(i)\|)/(6)` `=(0.005+0.007+0.005+0.001+0.009+0.006)/(6)` `=0.0055=0.006` (Rounded off to 1 significant figure) (iii) Relative error `triangle mu= (triangle bar(mu))/(mu_m)=(0.006)/(1.660)=0.0036` `=0.004` (iv) percentage error `= (triangle bar(mu))/(mu_m)xx100%= 0.4%`.