Linear Interpolation
Dating a Banjo

The Fairbanks and Cole musical instrument company manufactrued banjos in Boston from 1872 until 1884. They produced a total of about 15,000 banjos. The serial number on my banjo is 6,264. We can approximate the year that my banjo was made by using linear interpolation. A total of 15000 banjos were made in 12 years(1884 - 1872). The average number of banjos produced per year was 15,000/12, or 1,250. We will assume that after year 1, approximately 1,250 banjos had been produced, after year two, twice that number, or 2500. After year 4 there about 5000 would have been produced (1,250 * 4). After year 5, 6,250. This is very close to the serial number on my banjo, so it is likely that my banjo was produced in 1877 (1872 + 5 years).

More generally, you would divide the serial number of your banjo by 1250(the average number of banjos produced each year) to find the number of years beyond 1872 that your banjo was produced, then add this number of years to 1872. So for my banjo we would have:

Date of Banjo = 1872 + (SerialNumber/1250)

Date of Banjo = 1872 + (6264/1250)

Date of Banjo = 1872 + 5.0032 = 1877 (Rounded to nearest year)

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