In genealogy, the inferred birth year is my conventional term for a calculated estimate of the year someone was born, usually from a census or other record that reports an age, an approximate age, or an age range. There are two main cases, when an age in years is provided, and when only a range is provided.
Many records note the age of a person. So, the inferred year is what I call the subtracted year, which is the date of the record minus the age. I notate this with a superscript minus sign (-), although in tables I may for convenience omit it when it is understood. E.g., if a marriage record in 1905 says the groom is 33, then the inferred year of birth is 1872-. The notation emphasizes that the actual birth year could be the previous one, so that in this case the groom (if the record is accurate) might be born in either 1871 or 1872.
In a few cases the person's birthday is known somehow without their year of birth being certain. In that case, I may be able to use the month and day of the record to infer a specific year, rather than one of two.
An even more minor edge case is a record dated December 31.
Many types of records only provide an age range. The most common are the American federal censuses from 1790 to 1840, where a count is provided for the number of people of several genders and age ranges. E.g., the 1840 census for a household might say 1 male and 2 females aged 10 through 14, 1 female aged 30 through 39, and 1 male aged 40 through 49.
With age ranges, I'll provide an inferred birth year range that reflects all the years they might be born. Unlike above, where “1871–1872” would be more unwieldy than a conventional meaning of “1872”, it's perfectly convenient to increase the range by a year. So in the above example I'd say 1 male born 1790–1800, 1 female born 1800–1810, and 1 male and 2 females born 1825–1830. Note that the oldest male and female have overlapping years, in that both could be born in 1800.
See early census buckets.
In a table, I conventionally use parentheses around dates that are not inferred the same way as the other dates in the column, for example if that particular date can be calculated more exactly. This allows estimated and precise dates to be conveniently compared.
More generally, a parenthesized entry means that value’s derivation differs from others in the table.
In some cases, more details are provided. If an age in years, months, and days is given, usually the (supposed) exact birth date can be calculated.
For infants, an age in months is sometimes provided on records, allowing a more accurate number.
In the 1900 census, the year and month of birth is asked for on the form.
Rarely, a primary record will actually say “about 50”ref or the like, in which case we too can only estimate.