Preparing data for making an ErrorListPlot

If your errors input has the form :

errorList = {1, 2, 1, 3, 1, 2}

Then do :

Thread[{dataVector, Errorbar /@ errorList}]  

(* {  
 {{0, 979}, Errorbar[1]},
 {{2, 146}, Errorbar[2]},
 {{4, 141}, Errorbar[1]},
 {{6, 157}, Errorbar[3]},
 {{10, 187}, Errorbar[1]},
 {{20, 274}, Errorbar[2]}
 } *)

You can do all the manipulation in one line if you wish:

ErrorListPlot@MapThread[{{#1, #2}, ErrorBar[#2-uncY@#2 ]} &, {x, y}]

I accidentally discovered that you can use convenient notation PlusMinus(±) for horizontal and vertical axes

ypm = Thread[y ± uncY]

ErrorListPlot[Thread[{x, ypm}]]

In your case you can use even more simple method as mentioned here:

ErrorListPlot[Thread[{x, y, uncY}]] 

Unfortunately, these nice options are still undocumented.