Question

The readings of the measurements of a simple pendulum experiment are 2.43s, 2.56s,

2.42s, 2.71s and 2.90s. Calculate the absolute errors, relative error or percentage error.​

Answer 1

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Answer 2

Given :

a₁ = 2.43s

a₂ = 2.56s

a₃ = 2.42s

a₄ = 2.71s

a₅ = 2.90s

To find :

Absolute errors , relative error and percentage error.

Solution :

Absolute errors :

a_mean = (2.43s + 2.56s + 2.42s + 2.71s + 2.90s) / 5

a_mean = 2.604s

|Δa₁| = |a_mean - a₁| = |2.604s - 2.43s| = 0.174s

|Δa₂| = |a_mean - a₂| = |2.604s - 2.56s| = 0.044s

|Δa₃| = |a_mean - a₃| = |2.604s - 2.42s| = 0.184s

|Δa₄| = |a_mean - a₄| = |2.604s - 2.71s| = 0.106s

|Δa₅| = |a_mean - a₅| = |2.604s - 2.90s| = 0.296s

Mean Absolute Error :

Δa_mean = (|Δa₁| + |Δa₂| + |Δa₃| + |Δa₄| + |Δa₅|) / 5

Δa_mean = 0.1608s

Relative Error :

Relative error = Δa_mean / a_mean

Relative error = 0.1608s / 2.604s

Relative error = 0.06175

Percentage Error :

δa = (Δa_mean / a_mean) × 100%

δa = (0.1608s / 2.604s) × 100%

δa = 6.175%