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It can be continuous or discrete:
If you're only talking about whole numbers of years (integers) then it's discrete. If you can include parts of years (for example "I've been studying for 4 and a third years") then it's continuous.
"...4 and a third years" is not in itself discrete or continuous as a number on its own does not have this property. It's the act of breaking down the year into sub-sections (of which there are an infinite number) that makes the SCALE "years of education" continuous.
To clarify: if you're breaking a scale up into a number of sub-sections that you can count (eg. even if you specify half-years as a measure it is still discrete, as there are only 2 half-years for every year). If you're not specifying the accuracy of the measure then it's continuous as you can say 4.5, 4.6 and you can always go more accurate (4.5158956398365 for example).
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