Illegal use of aggregates or non-group column in target list

I'd like to return an average for one item in my database grouped by
another item. For example,

The table looks like this:
=================
CREATE TABLE data_table (
    subject                           text,
    arm                               char,
    target                            int4,          -- end of primary
key
    reaction_time                float4
);
CREATE UNIQUE INDEX pkdata_table ON data_table (subject, arm, target);


The command I'd like to use is something like:
================================
select target, avg(reaction_time) from data_table;

and I'd like this command to return:

target    |      avg
=============
   1        |     301.3
   2        |     311.45
   3        |     299.1
   4        |     300.8


However, this statement just gives me the error: Illegal use of
aggregates or non-group column in target list.

So apparently I can only return either one or the other but not the two
together. Is there a way to get the output I want in SQL?

Thanks.
-Tony