Table 1.

Summary of mathematical terms and symbols.

Symbol or term	Description
y	Quantity to be determined, or measurand
x, x1, x2, xi, xn	Value for a given ‘x’ variable
s	Sample standard deviation
σ	Population standard deviation
s(x1), s(x2), s(xi), s(xn)	Sample standard deviation for a given ‘x’ variable
s2	Sample squared standard deviation or variance
σ2	Population squared standard deviation or variance
s2(x1), s2(x2), s2(xi), s2(xn)	Sample squared standard deviation for a given ‘x’ variable
u	Standard uncertainty
u2	Squared standard uncertainty, equivalent to variance
u(y)	Standard uncertainty in y (measurand)
u2(y)	Squared standard uncertainty in y, or variance of uncertainty in y
u(x1), u(x2), u(xi), u(xn)	Standard uncertainty in a given ‘x’ variable
u2(x1), u2(x2), u2(xi), u2(xn)	Standard uncertainty squared for a given ‘x’ variable
y = f (xi)	Functional relationship between output ‘y’ and input variable ‘xi’
r	Correlation coefficient
rx1,x2 or r1,2	Correlation coefficient for the variables x1 and x2
Z-score, Z-value	The number of standard deviations that an observation or value is from the mean- a standardised variable
k	Coverage factor, the number of standard deviations or Z-scores required to include a stated proportion of values
ν	Degrees of freedom
Error	True value – measured value
Population covariance (x1, x2)	$$\frac{1}{N}\left[{\sum }_{i=1}^N\left(x_{1,i}-{\overline{x}}_1\right)\left(x_{2,i}-{\overline{x}}_2\right)\right]$$
∂y/∂xi	Partial derivative of y with respect to xi
log10(y), log10(xi)	Logarithm to the base 10
ln(y), ln(xi)	Logarithm to the base e