sprague: Sprague Index (Multipliers)

In heaping: Correction of Heaping on Individual Level

Sprague Index (Multipliers)

Description

The Sprague method uses multipliers to estimate population counts for each single year of age from 5-year interval data. This is useful for creating smooth single-year age distributions from grouped census data.

Usage

sprague(x)

Arguments

x	numeric vector of population counts in five-year age intervals. Must have exactly 17 elements corresponding to age groups 0-4, 5-9, ..., 75-79, 80+.

Details

Disaggregate 5-year age group counts into single-year ages using Sprague multipliers.

The input must be population counts for 17 five-year age groups: 0-4, 5-9, 10-14, 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69, 70-74, 75-79, and 80+.

The Sprague multipliers are applied differently depending on the position of the age group:

• Lowest groups (0-4): Uses only following age groups

• Low groups (5-9): Uses mostly following age groups

• Normal groups (10-74): Uses symmetric weighting

• High groups (75-79): Uses mostly preceding age groups

• Highest groups (80+): Returned as-is (open-ended)

The total population is preserved: sum of output equals sum of input.

Value

A named numeric vector with 81 elements: single-year population counts for ages 0, 1, 2, ..., 79, and the 80+ group.

Author(s)

Matthias Templ

References

Calot, G. and Sardon, J.-P. (1998). Methodology for the calculation of Eurostat's demographic indicators. Detailed report by the European Demographic Observatory.

Sprague, T. B. (1880). Explanation of a new formula for interpolation. Journal of the Institute of Actuaries, 22, 270-285.

See Also

whipple for measuring age heaping.

Examples

# Example from World Bank data
x <- data.frame(
  age = as.factor(c(
    "0-4", "5-9", "10-14", "15-19", "20-24",
    "25-29", "30-34", "35-39", "40-44", "45-49",
    "50-54", "55-59", "60-64", "65-69", "70-74", "75-79", "80+"
  )),
  pop = c(
    1971990, 2095820, 2157190, 2094110, 2116580,
    2003840, 1785690, 1502990, 1214170, 796934,
    627551, 530305, 488014, 364498, 259029, 158047, 125941
  )
)

# Apply Sprague multipliers
s <- sprague(x$pop)
head(s, 20)  # First 20 single-year ages

# Verify population is preserved
all.equal(sum(s), sum(x$pop))

heaping documentation built on Feb. 10, 2026, 1:08 a.m.