Question

In ohm's experiment , the value of the unknown resistance were found to be 6.12ohms, 6.09 ohm's,6.22ohms, 6.15ohms. calculate the absolute error, relative error and percentage error in these measurement

Answer 1

Answer:

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

Step-by-step explanation:

Given data:  

6.12 , 6.09 , 6.22 , 6.15  

Step 1- Find the mean value.

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

x = 6.145  

Step 2- Fine the absolute error.

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    

Step 3- Find mean absolute error  

= (0.025 + 0.055 + 0.075 + 0.005)/4

Δx = 0.16/4

Δx = 0.04

Step 4- Fine relative error = Mean Absolute Error/Mean Value.  

Relative error = Mean Absolute Error/Mean Value.  

Relative error = Δx/x

Relative error = 0.04/6.145

Relative error = 0.00651

Step 5- Find % Relative error  

% Relative error = Relative Error × 100%

% Relative error = 0.00651 × 100

% Relative error = 0.651%

Answer 2

Answer:

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

Step-by-step explanation:

Given data:  

6.12 , 6.09 , 6.22 , 6.15  

Step 1- Find the mean value.

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

x = 6.145  

Step 2- Fine the absolute error.

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    

Step 3- Find mean absolute error  

= (0.025 + 0.055 + 0.075 + 0.005)/4

Δx = 0.16/4

Δx = 0.04

Step 4- Fine relative error = Mean Absolute Error/Mean Value.  

Relative error = Mean Absolute Error/Mean Value.  

Relative error = Δx/x

Relative error = 0.04/6.145

Relative error = 0.00651

Step 5- Find % Relative error  

% Relative error = Relative Error × 100%

% Relative error = 0.00651 × 100

% Relative error = 0.651%