8.
MATHEMATICAL TREATMENT OF SYSTEMATIC ERRORS.
a. Definitions.
(1) Quantitative error - differences between known or certain value
and measured value given in units of quantity.
(2) Percentage error - ratio of quantitative error to the measured
values times 100.
(3) Maximum systematic error - total systematic error present in a
setup, assuming the worst possible conditions.
(4) Symbols.
(a) r = result of an individual reading.
(b) a = quantitative error involved in an individual reading.
(c) e = percentage error involved in a single reading.
(d) R = result of calculation.
(e) A = total quantitative error of system.
(f) E = total percentage error of system
b. Maximum systematic error.
(1) Maximum
systematic
error
may
be
calculated
by
the
following
rules:
WHEN THE ANSWER IS OBTAINED BY:
THE MAXIMUM ERROR IS THE:
The sum or difference of measurements.
Sum of the absolute quantitative
errors (disregarding sign).
Multiplication or division of
Sum of the percentage errors
measurements
(disregarding sign).
Measurements taken to a power
Multiplication of the power and
the percentage error.
(2) Once the maximum error (either quantitative or percentage) is
calculated, the unknown type of error is computed with the formula E =
A/Rx100%. Where E is the total percentage systematic error, A is the
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