a 
half‑width of a rectangular distribution of possible values of input quantity
X_{i}:

a_{+} 
upper bound, or upper limit, of input quantity
X_{i}

a_{−} 
lower bound, or lower limit, of input quantity
X_{i}

b_{+} 
upper bound, or upper limit, of the deviation of input quantity
X_{i}
from its estimate
x_{i}:

b_{−} 
lower bound, or lower limit, of the deviation of input quantity
X_{i}
from its estimate
x_{i}:

c_{i} 
partial derivative or sensitivity coefficient:

f 
functional relationship between measurand
Y
and input quantities
X_{i}
on which
Y
depends, and between output estimate
y
and input estimates
x_{i}
on which
y
depends

∂f∕∂x_{i} 
partial derivative with respect to input quantity
X_{i}
of functional relationship
f
between measurand
Y
and input quantities
X_{i}
on which
Y
depends, evaluated with estimates
x_{i}
for the
X_{i}:

k 
coverage factor used to calculate expanded uncertainty
U = ku_{c}(y)
of output estimate
y
from its combined standard uncertainty
u_{c}(y),
where
U
defines an interval
Y = y ± U
having a high level of confidence

k_{p} 
coverage factor used to calculate expanded uncertainty
U_{p} = k_{p}u_{c}(y)
of output estimate
y
from its combined standard uncertainty
u_{c}(y),
where
U_{p}
defines an interval
Y = y ± U_{p}
having a high, specified level of confidence
p

n 
number of repeated observations

N 
number of input quantities
X_{i}
on which measurand
Y
depends

p 
probability; level of confidence:

q 
randomly varying quantity described by a probability distribution

q^{‾‾‾} 
arithmetic mean or average of
n
independent repeated observations
q_{k}
of randomly‑varying quantity
q 
estimate of the expectation or mean
μ_{q}
of the probability distribution of
q
 
q_{k} 
kth independent repeated observation of
randomly‑varying quantity
q

r(x_{i}, x_{j}) 
estimated correlation coefficient associated with input estimates
x_{i}
and
x_{j}
that estimate input quantities
X_{i}
and
X_{j}:

r(X^{‾‾‾}_{i}, X^{‾‾‾}_{j}) 
estimated correlation coefficient of input means
X^{‾‾‾}_{i}
and
X^{‾‾‾}_{j},
determined from
n
independent pairs of repeated simultaneous observations
X_{i, k}
and
X_{j, k}
of
X_{i}
and
X_{j}:

r(y_{i}, y_{j}) 
estimated correlation coefficient associated with output estimates
y_{i}
and
y_{j}
when two or more measurands or output quantities are determined in the same measurement

s^{2}_{p} 
combined or pooled estimate of variance

s_{p} 
pooled experimental standard deviation, equal to the positive square root of
s^{2}_{p}

s^{2}(q^{‾‾‾}) 
experimental variance of the mean
q^{‾‾‾}

estimate of the variance
σ^{2}⁄n
of
q^{‾‾‾}:
 
estimated variance obtained from a Type A evaluation
 
s(q^{‾‾‾}) 
experimental standard deviation of the mean
q^{‾‾‾},
equal to the positive square root of
s^{2}(q^{‾‾‾})

biased estimator of
σ(q^{‾‾‾})
(see C.2.21, note)
 
standard uncertainty obtained from a Type A evaluation
 
s^{2}(q_{k}) 
experimental variance determined from
n
independent repeated observations
q_{k}
of
q

estimate of the variance
σ^{2}
of the probability distribution of
q
 
s(q_{k}) 
experimental standard deviation, equal to the positive square root of
s^{2}(q_{k})

biased estimator of the standard deviation
σ
of the probability distribution of
q
 
s^{2}(X^{‾‾‾}_{i}) 
experimental variance of input mean
X^{‾‾‾}_{i},
determined from
n
independent repeated observations
X_{i, k}
of
X_{i}

estimated variance obtained from a Type A evaluation
 
s(X^{‾‾‾}_{i}) 
experimental standard deviation of input mean
X^{‾‾‾}_{i},
equal to the positive square root of
s^{2}(X^{‾‾‾}_{i})

standard uncertainty obtained from a Type A evaluation
 
s(q^{‾‾‾}, r^{‾‾‾}) 
estimate of the covariance of means
q^{‾‾‾}
and
r^{‾‾‾}
that estimate the expectations
μ_{q}
and
μ_{r}
of two randomly‑varying quantities
q
and
r,
determined from
n
independent pairs of repeated simultaneous observations
q_{k}
and
r_{k}
of
q
and
r

estimated covariance obtained from a Type A evaluation
 
s(X^{‾‾‾}_{i}, X^{‾‾‾}_{j}) 
estimate of the covariance of input means
X^{‾‾‾}_{i}
and
X^{‾‾‾}_{j},
determined from
n
independent pairs of repeated simultaneous observations
X_{i, k}
and
X_{j, k}
of
X_{i}
and
X_{j}

estimated covariance obtained from a Type A evaluation
 
t_{p}(v) 
t‑factor from the
t‑distribution for
v
degrees of freedom corresponding to a given probability
p

t_{p}(v_{eff}) 
t‑factor from the
t‑distribution for
v_{eff}
degrees of freedom corresponding to a given probability
p,
used to calculate expanded uncertainty
U_{p}

u^{2}(x_{i}) 
estimated variance associated with input estimate
x_{i}
that estimates input quantity
X_{i}
NOTE When
x_{i}
is determined from the arithmetic mean or average of
n
independent repeated observations,
u^{2}(x_{i}) = s^{2}(X^{‾‾‾}_{i})
is an estimated variance obtained from a Type A evaluation.

u(x_{i}) 
standard uncertainty of input estimate
x_{i}
that estimates input quantity
X_{i},
equal to the positive square root of
u^{2}(x_{i})
NOTE When
x_{i}
is determined from the arithmetic mean or average of
n
independent repeated observations,
u(x_{i}) = s(X^{‾‾‾}_{i})
is a standard uncertainty obtained from a Type A evaluation.

u(x_{i}, x_{j}) 
estimated covariance associated with two input estimates
x_{i}
and
x_{j}
that estimate input quantities
X_{i}
and
X_{j}
NOTE When
x_{i}
and
x_{j}
are determined from
n
independent pairs of repeated simultaneous observations,
u(x_{i}, x_{j}) = s(X^{‾‾‾}_{i}, X^{‾‾‾}_{j})
is an estimated covariance obtained from a Type A evaluation.

u^{2}_{c}(y) 
combined variance associated with output estimate
y

u_{c}(y) 
combined standard uncertainty of output estimate
y,
equal to the positive square root of
u^{2}_{c}(y)

u_{cA}(y) 
combined standard uncertainty of output estimate
y
determined from standard uncertainties and estimated covariances obtained from Type A evaluations alone

u_{cB}(y) 
combined standard uncertainty of output estimate
y
determined from standard uncertainties and estimated covariances obtained from Type B evaluations alone

u_{c}(y_{i}) 
combined standard uncertainty of output estimate
y_{i}
when two or more measurands or output quantities are determined in the same measurement

u^{2}_{i}(y) 
component of combined variance
u^{2}_{c}(y)
associated with output estimate
y
generated by estimated variance
u^{2}(x_{i})
associated with input estimate
x_{i}:

u_{i}(y) 
component of combined standard uncertainty
u_{c}(y)
of output estimate
y
generated by the standard uncertainty of input estimate
x_{i}:

u(y_{i}, y_{j}) 
estimated covariance associated with output estimates
y_{i}
and
y_{j}
determined in the same measurement

u(x_{i})∕ │x_{i}│ 
relative standard uncertainty of input estimate
x_{i}

u_{c}(y)∕ │y│ 
relative combined standard uncertainty of output estimate
y

[u(x_{i})∕x_{i}]^{2} 
estimated relative variance associated with input estimate
x_{i}

[u_{c}(y)∕y]^{2} 
relative combined variance associated with output estimate
y


estimated relative covariance associated with input estimates
x_{i}
and
x_{j}

U 
expanded uncertainty of output estimate
y
that defines an interval
Y = y ± U
having a high level of confidence, equal to coverage factor
k
times the combined standard uncertainty
u_{c}(y)
of
y:

U_{p} 
expanded uncertainty of output estimate
y
that defines an interval
Y = y ± U_{p}
having a high, specified level of confidence
p,
equal to coverage factor
k_{p}
times the combined standard uncertainty
u_{c}(y)
of
y:

x_{i} 
estimate of input quantity
X_{i}
NOTE When
x_{i}
is determined from the arithmetic mean or average of
n
independent repeated observations,
x_{i} = X^{‾‾‾}_{i}.

X_{i} 
ith input quantity on which measurand
Y
depends
NOTE X_{i}
may be the physical quantity or the random variable (see 4.1.1,
Note 1).

X^{‾‾‾}_{i} 
estimate of the value of input quantity
X_{i},
equal to the arithmetic mean or average of
n
independent repeated observations
X_{i, k}
of
X_{i}

X_{i, k} 
kth independent repeated observation of
X_{i}

y 
estimate of measurand
Y

result of a measurement
 
output estimate
 
y_{i} 
estimate of measurand
Y_{i}
when two or more measurands are determined in the same measurement

Y 
a measurand


estimated relative uncertainty of standard uncertainty
u(x_{i})
of input estimate
x_{i}

μ_{q} 
expectation or mean of the probability distribution of randomly‑varying quantity
q

v 
degrees of freedom (general)

v_{i} 
degrees of freedom, or effective degrees of freedom, of standard uncertainty
u(x_{i})
of input estimate
x_{i}

v_{eff} 
effective degrees of freedom of
u_{c}(y),
used to obtain
t_{p}(v_{eff})
for calculating expanded uncertainty
U_{p}

v_{effA} 
effective degrees of freedom of a combined standard uncertainty determined from standard uncertainties obtained
from Type A evaluations alone

v_{effB} 
effective degrees of freedom of a combined standard uncertainty determined from standard uncertainties obtained
from Type B evaluations alone

σ^{2} 
variance of a probabiIity distribution of (for example) a randomly‑varying quantity
q,
estimated by
s^{2}(q_{k})

σ 
standard deviation of a probability distribution, equal to the positive square root of
σ^{2} 
s(q_{k})
is a biased estimator of
σ
 
σ^{2}(q^{‾‾‾}) 
variance of
q^{‾‾‾},
equal to
σ^{2}∕n,
estimated by
s^{2}(q^{‾‾‾}) = s^{2}(q_{k})∕n

σ(q^{‾‾‾}) 
standard deviation of
q^{‾‾‾},
equal to the positive square root of
σ^{2}(q^{‾‾‾}) 
s(q^{‾‾‾})
is a biased estimator of
σ(q^{‾‾‾})
 
σ^{2}[s(q^{‾‾‾})] 
variance of experimental standard deviation
s(q^{‾‾‾})
of
q^{‾‾‾}

σ[s(q^{‾‾‾})] 
standard deviation of experimental standard deviation
s(q^{‾‾‾})
of
q^{‾‾‾},
equal to the positive square root of
σ^{2}[s(q^{‾‾‾})]

* Footnote to the 2008 version:
When the GUM was first published, there was an editorial rule in effect which prohibited the use of an Annex I.
That is why the annexes go from Annex H directly to Annex J.