1973 AMC 12 Question 5

Of the following five statements, $\mathrm{I}$ to $\mathrm{V},$ about the binary operation of averaging (arithmetic mean),

$\mathrm{I}.$ Averaging is associative

$\mathrm{II}.$ Averaging is commutative

$\mathrm{III}.$ Averaging distributes over addition

$\mathrm{IV}.$ Addition distributes over averaging

$\mathrm{V}.$ Averaging has an identity element

those which are always true are