Typically an estimate of an unknown response curve f(x) is obtained with an associated function describing the standard uncertainty of the estimate at each value of x. Often the quantity of interest will be a functional of f(x), such as a derivative or integral. In such a case the standard uncertainty cannot be calculated without knowledge of the correlation between and for all relevant pairs of points (x_i, x_j). This information might be stored as a two-dimensional function in the continuous case or as a matrix (u_ij) in the discrete case, but this will often be impractical. The difficulty can often be avoided by instead storing the 'random' and 'systematic' components of uncertainty, which is a concept that is familiar but out of favour. This step enables the calculation of standard uncertainty for many functionals of f(x) from numerical data and from a graphical representation. Three examples are given illustrating these concepts. The paper also discusses the issue of expressing the uncertainty associated with as a whole; that is, the simultaneous estimation of at every value of x.