Randomly changing numbers

this is my first post here. I come from an art background and am an extremely interesting in intersecting both art and programming. I am currently working on a project where I wish to alter numbers from a list by adding a +1 or -1 to that number to a few (lets say 500) randomly selected numbers out of thousands of numbers. I am familiar with the random number generator, however unsure what my next step to alter current numbers would be. Thanks.

These are a few of the numbers I wish to edit:

-0.588700 -0.394800 2.730300 -0.491500 -0.284200 2.716800 -0.629800 -0.231300 2.574700 -0.588700 -0.394800 2.730300 -0.629800 -0.231300 2.574700 -0.711400 -0.404200 2.647700 -0.491500 -0.284200 2.716800 -0.359600 -0.120500 2.692200 -0.513300 -0.040000 2.517700 -0.491500 -0.284200 2.716800 -0.513300 -0.040000 2.517700 -0.629800 -0.231300 2.574700 -0.359600 -0.120500 2.692200 -0.213300 0.069200 2.663800 -0.375400 0.168200 2.469000 -0.359600 -0.120500 2.692200 -0.375400 0.168200 2.469000 -0.513300 -0.040000 2.517700 -0.213300 0.069200 2.663800 -0.057400 0.270200 2.639300 -0.219000 0.379800 2.436900 -0.213300 0.069200 2.663800 -0.219000 0.379800 2.436900 -0.375400 0.168200 2.469000