Pass an array of numbers into a method that's overloaded
The code produces the right output, which is good.  It has some problems, though.

The average() functions

As @ChrisW points out, the two average() functions you defined are not being used.  Since your inputs are doubles, you only need one of them: the double average(double[] array) function.

The average() functions are currently buggy:


total = 0, so of course they will each always return 0.  Copy the summation code from main() to fix that.
The int version uses integer arithmetic, so division rounds the result to an integer (towards 0).  In general, the average of a set of integers is not an integer.  You should use double to store the total, even in the integer version.  (You did it correctly in main().)


In case you're wondering, if you want to be able to handle integral and floating-point input arrays, you do need to write out both the int[] and double[] versions explicitly.

main()

If you open a Scanner, it's good etiquette to close it.  The idiom for doing that since Java 7 is to use a try-with-resources block:

try (Scanner input = new Scanner(System.in)) {
    …
}


Avoid declaring and defining variables avg and total until you need them.

The average array is poorly named.  It's an array of ten user input numbers, not an array of ten averages.

You hard-coded 10 twice.  The first for-loop should be more like the second, which uses average.length.

The average only needs to be computed once, not ten times.  Pull the division operation out of the loop.

Of all the comments in the class, the only one worth keeping is // enter 10 numbers to average.  All of the others are redundant noise.