Question

radius of sphere measured repeatedly readings are 5.62m,5.54m,5.56m,5.40m,5.30m, determine mean value mean absolute error relative error percentage error

Answer 1

Answer :

Values = 5.62 m, 5.54 m, 5.56 m, 5.40 m, 5.30 m.

The mean value = (5.62 + 5.54 + 5.56 + 5.40 + 5.30)/5

= 27.42/5

= 5.484 m.

Absolute errors:-

5.62 - 5.484 = 0.136

5.54 - 5.484 = 0.056

5.56 - 5.484 = 0.076

5.40 - 5.484 = |−0.084| = 0.084

5.30 - 5.484 = |−0.184| = 0.184

Absolute mean error = (0.136 + 0.056 + 0.076 + 0.084 + 0.184)/5

= 0.536/5

= 0.1072 m.

So, the Relative error:- ∆a_mean/a_mean

= 0.1072/5.484

= 0.0195 m.

Hence, the percentage error = 0.0195 * 100 = 1.95 %.