Rounded Ages in a Written Register: A Digit-Preference Bound on the Error in Mean Age and Dependency Counts

People who do not know their exact age, and some who do, report ages ending in 0 or 5. A register full of such rounded ages shows spikes at every multiple of five, and every statistic computed from it inherits some error. This paper computes how much, from a stated model register: 100,000 people with a stated true age distribution (mean age 32.7351 years, 28.93 percent under 15, 13.34 percent aged 65 and over), in which a stated fraction h of people whose true age is not a multiple of five report the nearest multiple of five instead. The Whipple-style digit-preference index computed from the model rises from 99.98 with no heaping to 259.99 when 40 percent of ages are heaped and 420.00 when 80 percent are heaped. The headline result is a division of labour between two statistics. Mean age is barely harmed: even at 80 percent heaping its error is only −0.0582 years, because rounding moves roughly as many people up as down. Dependency counts are harmed more, because the cut-offs at 15 and 65 are themselves multiples of five and attract more people from below than from above in a declining age distribution: at 40 percent heaping the share under 15 is understated by 1.336 percentage points, the share 65 and over overstated by 0.628 points, and the dependency ratio understated by 2.101 points. Fitting the errors against the index gives a registrar's bound that needs only the index: the dependency-ratio error is at most about 0.0133 percentage points per point of the index above 100, the under-15 share error at most about 0.0084 per point, and the mean-age error at most about 0.00018 years per point — so an index of 200 guarantees a mean-age error below 0.018 years while permitting a dependency-ratio error of about 1.304 points. A simple correction — spreading each five-year group's total evenly across its five ages — removes the dependency error almost entirely in this model (residual −0.118 points at every heaping level) but does not help mean age, and at low heaping it makes the mean-age error worse than doing nothing (0.0366 years against −0.0073 years at 10 percent heaping). All figures are computed from the stated model; no register was examined. SIMULATED, NOT MEASURED.