The precision of a radiocarbon date tells how narrow the range of dates is.
There are two main factors which determine the precision of a radiocarbon date.
In Accelerator Mass Spectrometry (AMS), for example, the number of radiocarbon atoms in a stream of atoms coming from the sample is counted.
Thus there are statistical counting uncertainties proportional to the square root of the number of atoms counted.
Older samples have a lower concentration of radiocarbon, but they can be (and often are) counted for longer periods of time to compensate for this lower concentration.
By counting longer, the counting uncertainty in a radiocarbon measurement on a very old sample can be the same as that on a young sample.
The other 4 members are acting as Yoochun's classmates.
Jaejoong is a transferred student who have lost his parents when he was young and was brought up in an orphanage.
Once the radiocarbon concentration in a sample has been measured, the sample's age in "radiocarbon years" is determined mathematically.
The radiocarbon age must then be calibrated to determine the sample's age in calendar years.
Radiocarbon dates are certainly not precise to within a year or two, but they are generally precise to within a few hundred years or better.
This means radiocarbon's precision is generally sufficient to choose between alternate chronologies which differ by a hundred years or more.
This, in fact, is the most significant factor contributing to loss of precision in radiocarbon dates today.