Question

A child walking on a footpath notices that the width of the footpath is uneven. He reported this to his principal. What is the mean absolute error in width of footpath if width of footpath in 10 m length are noted as 5 m, 5.5m, 5m, 6m & 4.5m? *
1 point
(a) 0.44 m
(b) 0.46 m
(c) 0.54 m
(d) 0.52 m​

Answer 1

Given info : The width of footpath in 10 m length are noted as 5 m , 5.5 m , 5 m , 6m and 4.5 m.

To find : The mean absolute error in width of footpath is ...

solution : first find mean of all observations.

mean, μ = (5 + 5.5 + 5 + 6 + 4.5)/5

= 26/5

= 5.2 m

now ∆x₁ = |μ - x₁| = |5.2 - 5| = 0.2 m

∆x₂ = |μ - x₂| = |5.2 - 5.5| = 0.3 m

∆x₃ = |μ - x₃| = |5.2 - 5| = 0.2 m

∆x₄ = |μ - x₄| = |5.2 - 6| = 0.8 m

∆x₅ = |μ - x₅| = |5.2 - 4.5| = 0.7 m

mean absolute error = (∆x₁ + ∆x₂ + ∆x₃ + ∆x₄ + ∆x₅)/5

= (0.2 + 0.3 + 0.2 + 0.8 + 0.7)/5

= 2.2/5

= 0.44

Therefore mean absolute error in width of footpath is 0.44 m.

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