On average, how many eggs a year does a laying hen lay?

"The typical interval between eggs laid is about 25 hours, so a hen that lays an egg every day will lay a bit later each day."

This is slightly less than one a day, and work out to about 350 a year. However, "Hens don't usually lay eggs in the dark, so once a hen's laying cycle reaches dusk time, she will usually not lay till the following morning." This means that the answer will depend on the hours of daylight and how they vary at the exact location where the hen is housed. It will act to reduce the annual production, but the amount is indeterminate.

http://www.backyardchickens.com/a/interesting-facts-about-chicken-eggs

"Some hen breeds can produce over 300 eggs per year, with 'the highest authenticated rate of egg laying being 371 eggs in 364 days'[26]". The note is a reference to the Guinness Book of Records.

https://en.wikipedia.org/wiki/Chicken#cite_note-26

The average varies with the age of the hen. They average around 307 eggs pa over the first 52 weeks of laying. Over the 52 weeks from age 49 wks to age 100 wks they average around 171 eggs pa.

Isabrown is a breed of commercial egg layers. Their husbandry manual for chicken farmers has their hens coming into lay at 18 weeks of age and peaking in weeks 27 and 28 at 95% production (6.65 eggs pwk), which ties-in with the 25hr cycle mentioned above in backyardchickens.com

age in wks   eggs

18 to 60    250 = avge 5.81 eggs pw for those 43 wks
18 to 72    313 = avge 5.69 eggs pw for those 55 wks
18 to100   351 = avge 4.23 eggs pw for those 83 wks


(summary of egg production numbers by weeks is on page 3 [the above table], page 47 has a detailed table week by week for the first 80 wks, and there's a graph of egg production as hens come into lay on page 17)