  We show that the noncommutative central limit theorem of Speicher can be
adapted to produce the Gaussian statistics associated to Coxeter groups of type
B, in the sense of Bo\.zejko, Ejsmont, and Hasebe. Specifically, we show how
type B Gaussian statistics naturally arise in systems of 'mixed spins',
providing a new application of Speicher's argument and paving the way for the
transfer of known results from the bosonic/fermionic settings to such broader
contexts.
