Split an array based on value - powershell

Question

This is my first question here, so sorry if I make any mistakes posting this.
I'm trying to split an array based on its values. Basically I want to create two arrays whose values are as close to the average as possible. I managed to do this with this code:
function Sum($v) {
[Linq.Enumerable]::Sum([int64[]]$v)
}
$arr = 0..9 | % {get-random -min 1 -max 10}
"ARRAY:" + $arr
"SUM: " + (sum $arr)
"AVG: " + (sum $arr)/2
# start of the code that matters
$wavg = (sum $arr)/2
foreach ($i in (0..($arr.Count-1))) {
$wavg -= $arr[$i]
if ($wavg -le 0) {
$i-=(-$wavg -gt $arr[$i]/2);break
}
}
"SPLIT INDEX: " + $i
"ARR1: " + $arr[0..$i] + " (" + $(sum $arr[0..$i]) + ")"
"ARR2: " + $arr[($i+1)..$arr.Count] + " (" + $(sum $arr[($i+1)..$arr.Count]) + ")"
The reason my foreach is structured this way is because in my actual code the values are in an index hash and are accessed as $index[$arr[$i]].
This means that the resulting two arrays could be of unequal size (it would be easy if I could just split the array in half). Sample output of my code to demonstrate this:
ARRAY: 5 3 6 3 2 3 6 3 1 3
SUM: 35
AVG: 17.5
SPLIT INDEX: 3
ARR1: 5 3 6 3 (17)
ARR2: 2 3 6 3 1 3 (18)
The code works as is, but I feel it could be done in a more elegant and speedier way. Because I need to execute this code a few thousand times in my script I want it to be as fast as possible.