Question

The radius of a sphere measured repeatedly yields values 5.63 m, 5.54 m, 5.44 m, 5.40 m and 5.35 m. Determine the most probable value of radius and the mean absolute, relative and percentage errors.

Answer 1

Given: a₁ = 5.63 m, a₂ = 5.54 m, a₃ = 5.44 m

a₄ = 5.40 m, a₅ = 5.35 m,

To find:

(i) Most probable value (Mean value)

(ii) Mean absolute error

(iii) Relative error

(iv) Percentage error

From formula (ii),

Absolute errors:

From formula (ii),

= 0.0904 m

From formula (iii),

Relative error = \(\frac{0.0904}{5.472}\)

= 1.652 × 10^-2

(after rounding off to correct significant digits)

= 1.66 × 10^-2

= 0.0166

∴ Percentage error = 1.66 × 10^-2 × 100 = 1.66%

(i) The mean value is 5.472 m. 

(ii) The mean absolute error is 0.0904 m. 

(iii) The relative error is 0.0166. 

(iv) The percentage error is 1.66%

[Note: Answer to relative error is rounded off using rules of significant figures and of rounding off]