Use this interpolation method to disaggregate or estimate values only when the grouped observations and coefficient layout match the method's required age ordering.

Grouped totals

Successive five-year group totals.

Target group

One-based position of the target group among the listed groups; must have one group on each side.

Single year

Single year within the target group, from 1 (first year) to 5 (last).

Multipliers

Three multipliers applied over the target group and its neighbours.

Interpolated value

Interpolated single-year value obtained from the multipliers.

Interpolation creates model-based values rather than new observations. Edge groups, abrupt cohort changes, sparse counts, and coefficients intended for a different grouping scheme can produce implausible results.

Compare the interpolated series with a simpler linear allocation and inspect whether totals are preserved. When single-year observations exist, prefer them over values reconstructed from grouped data.

• Beers Interpolation Lookup

  Look up the interior Beers oscillatory interpolation multipliers (ordinary or modified fifth-difference form) for one single year of an age group and apply them to the grouped total and its four neighbouring groups.

• Sprague Multipliers Osculatory Lookup

  Look up the Sprague fifth-order osculatory interpolation multipliers for one single year of an age group and apply them to the grouped total and its four neighbouring groups.

• Ever-Married by Age Interpolation Calculator

  Linearly interpolate the proportion ever married at a target age from group values placed at five-year-group midpoints, holding the endpoint groups constant outside their midpoints.