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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