Sort JavaScript Array With Both Strings and Numbers into a numbers only array and a string only array

I have an array containing the following data:

var arr = [30, "Chad", 400, 700, "Brian", "Zander", "Allen", 43, 50]

I want to sort this array into an array containing just the numbers (from lowest to highest) and another array containing just the strings (in alphabetical order).

I assume I would use a for loop combined with an if/else statement but am not sure of the syntax. Any help would be appreciated.