APL, 8 5 bytes

+/∊+⍨

This is a monadic function train that accepts an array and returns a boolean (0/1 in APL). It uses the same algorithm as xnor's Python 3 answer.

Explanation:

   +⍨  ⍝ Double the input (+⍨x is the same as x+x)
  ∊    ⍝ Test the membership of
+/     ⍝ The sum of the input

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Saved 3 bytes thanks to Dennis!

APL, 8 5 bytes

+/∊+⍨

This is a monadic function train that accepts an array and returns a boolean (0/1 in APL). It uses the same algorithm as xnor's Python 3 answer.

Explanation:

   +⍨  ⍝ Double the input (+⍨x is the same as x+x)
  ∊    ⍝ Test the membership of
+/     ⍝ The sum of the input

Try it online

Saved 3 bytes thanks to Dennis!

APL, 8 bytes

⊢∊⍨2÷⍨+/

This is a monadic function train that accepts an array and returns a boolean (0/1 in APL). It uses the same algorithm as xnor's Python 3 answer.

Explanation:

       +/  ⍝ Sum the input
    2÷⍨    ⍝ Divide by 2
⊢∊⍨       ⍝ Test for membership

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APL, 8 5 bytes

+/∊+⍨

This is a monadic function train that accepts an array and returns a boolean (0/1 in APL). It uses the same algorithm as xnor's Python 3 answer.

Explanation:

   +⍨  ⍝ Double the input (+⍨x is the same as x+x)
  ∊    ⍝ Test the membership of
+/     ⍝ The sum of the input

Try it online

Saved 3 bytes thanks to Dennis!