Graduation is a mathematical process that inputs an array of rates requiring smoothing and outputs an equal-sized array of smoothed rates. Methods of graduation include graphically fitting a curve to input rates or solving for the parameters of a parametric formula. There are two common situations in which graduation is used for table development –
• When modelling is not used to develop rates, arrays of observed rates are graduated. Even the largest, most credible studies produce observed rates that are not sufficiently smooth.
• When modelling is used to develop rates, but those rates require smoothing, arrays of modelled rates are graduated. When modelling is used to develop rates and those rates are sufficiently smooth, there is no need for Graduation.
Source - Society of Actuaries