Question

A student performed an experiment and found following values of the refrective index of a liquid : 1.29, 1.33, 1.34, 1.35, 1.32, 1.36, 1.30, 1.33. Find the mean value of refrective index the mean absolute error the relative error and the percentage error ​

Answer 1

Explanation:

Mean value of quantity measured, V=

(1.29+1.33+1.34+1.35+1.32+1.36+1.30+1.33) / 8

x=1.3275=1.33(round off to two places of decimal). Absolute errors in measurement are:

Δx1 = (1.33−1.29) =0.04;

Δx2= (1.33−1.33) =0.00

Δx3= (1.33−1.34) =−0.01;

Δx4= (1.33−1.35) =−0.02

Δx5= (1.33−1.32) =+0.01;

Δx6= (1.33−1.36) =−0.03

Δx7= (1.33−1.30) =+0.03;

Δx8= (1.33−1.33) =0.00

Mean absolute error,

Δx= { i=n,i=l ∑ ∣ (Δx)i | } / n

= (0.04+0.00+0.01+0.02+0.01+0.03+0.03+0.00) / 8

= (0.14)/ 8

= 0.0175

=0.02

Relative error= ±Δx/x. = ± 0.02/1.33 =±0.015 =±0.02

Percentage error=±0.015×100=1.5%