Let β>1 be a non-integer. First we show that Lebesgue almost every number has a β-expansion of a given frequency if and only if Lebesgue almost every number has infinitely many β-expansions of the same given frequency. Then we deduce that Lebesgue almost every number has infinitely many balanced β-expansions, where an infinite sequence on the finite alphabet {0,1,…,m} is called balanced if the frequency of the digit k is equal to the frequency of the digit m−k for all k∈{0,1,…,m}. Finally we consider variable frequency and prove that for every pseudo-golden ratio β∈(1,2), there exists a constant c=c(β)>0 such that for any p∈[12−c,12+c], Lebesgue almost every x has infinitely many β-expansions with frequency of zeros equal to p.