DEFINITIONS OF IMPORTANT TERMS

Measurement work employs a number of terms which are defined below:
Measurand: The quantity or variable being measured is called measurand or measurement variable.
Accuracy: It is defined in terms of the closeness with which an instrument reading approaches
the true or expected (desired) value of the variable being measured.
Precision: It is measure of the consistency of reproducibility (repeatability) of the measurement
(i.e., the successive reading do not differ). For a given fixed value of an input variable, precision is a
measure of the degree to which successive measurement differ from one another.
Sensitivity: It is defined by the change in the output or response of the instrument for a unit
change of input or measured variable.
Resolution: Resolution is the smallest change in a measured variable (or measurand) to which the
instrument will respond.
True or Expected Value: The true or expected value of a quantity to be measured may be defined
as the average of an infinite number of measured values when the average deviation due to the various
contributing factors tends to zero. It also refers to a value of the quanity under consideration that would
be obtained by a method (known as exemplar method) agreed upon by experts. In other words, it is the
most probable value that calculations indicate and one should expect to measure.
Note that the value of the unknown obtained by making use of primary standards and measuring
instruments is considered to be its ture value.
Error: It is the deviation of the measured (or indicated) value from the true (or expected) value of
a quantity. In other words, error is the difference between the measured value and the true value of the
unknown quantity. It is also called absolute error are maximum possible error. Then error of measurements
is given by
∈A = Am – At ...(12.1)
where Am = measured value of the quantity
At = true value of the quantity
Absolute error, ∈0, is the limit of error in measurement. In other words, ∈A must not be higher
than ∈0.
Thus, |∈0| = max |Am – At| ...(12.2)
Note that the absolute error does not give any information about accuracy. For example, an error
of (–1) volt in measurement of 1000 volt is negligible, but the same error in measurement of 10 volts is
never acceptable. Thus, error is expressed in terms of another term called the relative error which is the
ratio of absolute error of the ture value of the quantity being measured. Therefore, the relative error, ∈R
is given by
∈R = Absolute error
True value
= 0
At
∈
= (Am – At)/ At ...(12.3)
The percentage relative error % ∈R = ∈R × 100.
Also, from Eqn. (12.3), we have
(1 + ∈r ) At = Am
or At =
1 [ ]
m
R
A
+ ∈
...(12.4)
If the absolute error ∈A is sufficiently small, then Eqn. (12.1) shows that
∈A = Am – At ≈ 0
or At ≅ Am ...(12.5)
That is, Am may be substituted for At in Eqn. (12.3) for practical purpose. Now in view Eqn. (12.3)
becomes ∈R = 0
Am
∈
...(12.6)
Correction: The difference between the true value and the measured value of the sought quantity
is defined as the reading correction or simply correction. That is, correction is negative or error. Thus,
δC = – ∈A ...(12.7)
= At – Am ...(12.8)
or At = expected value = Am + δC ...(12.9)
Therefore addition of correction in measured value gives the true (or accurate or expected) value.
Bandwidth: The bandwidth of an instrument relates to the maximum range of frequency over
which it is suitable for use. It is normally quoted in terms of 3 dB (dB = decibel) point. For an amplifier,
it is the range of frequencies between which the gain or amplitude ratio is constant to within 3 dB (this
corresponds 30% reduction in gain).
Significant Figures: An indication of the precision of the measurement is obtained from the
number of significant figures in which it is expressed.
Significant figures convey actual information regarding the magnitude and the measurement precision
of a quantity. The more is the significant figures, the greater will be the precision of measurement. For
example, if a resistor is specified as having a resistance of 105 Ω and 105.3 Ω, than in 105 Ω there are
three significant figures whereas in 105.3 Ω there are four. The later with more significant figures,
expresses a measurement of greater precision than the former.