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first explain the deffrence between absolute and relative error

If x=2.5 and y=1.8 both corrected to 1 decimal place calculate the absolute and relative of X+Y corected to 2 decimal places.

2007-06-30 07:35:39 · 1 answers · asked by t_a_jd 2 in Science & Mathematics Engineering

1 answers

Absoute error is either the error which must be assumed by rounding (± half the unit value of the last digit) or the sum of the errors of a group of numbers. Relative error is the absolute error divided by the base value, usually expressed as a percent.
2.5 = 2.5 ± 0.5 (absolute) = 2.5 ± 20.0% (relative)
2.55+ would round to 2.56 and 2.45- would round to 2.40
1.8 = 1.8 ± 0.5 (absolute) = 1.8 ± 27.8% (relative)
Arithmetically,
x + y =
4.30 ± 1.00 (absolute) = 4.30 ± 23.26% (relative)
Statistically,
x + y =
4.30 + 0.71 (absolute) = 4.30 ± 16.44%

Introduction of a second decimal place is a mathematiclly invalid operation, since it implies a greater accuracy than actually exists.

2007-06-30 08:22:46 · answer #1 · answered by Helmut 7 · 0 0

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