Question

In

Ohm's experiments, the values of
the unknown resistances were found
to be 6.12 12 , 6.09 Q2, 6.22 12, 6.15 .
Calculate the absolute error, relative
error and percentage error in these
measurements.​

Answer 1

Answer ⇒  Mean absolute error = 0.04, Relative error = 0.00651 and % Relative error = 0.651 %.

Explanation ⇒ Given data,

6.12 , 6.09 , 6.22 , 6.15

Mean Value = (6.12 + 6.09 + 6.22 + 6.15)/4

x = 6.145    

For absolute error in each term,

x₁ = |6.145 - 6.12| = 0.025

x₂ = |6.145 - 6.09| = 0.055

x₃ = |6.145 - 6.22| = 0.075

x₄ = |6.145 - 6.15| = 0.005

Mean absolute error = (0.025 + 0.055 + 0.075 + 0.005)/4

Δx = 0.16/4

Δx = 0.04

Now, Relative error = Mean Absolute Error/Mean Value.

∴ Relative error = Δx/x

∴ Relative error = 0.04/6.145

∴ Relative error = 0.00651

% Relative error = Relative Error × 100%

∴ % Relative error = 0.00651 × 100

∴ % Relative error = 0.651%

Hope it helps.