  An algorithm to compute Connes spectral distance, adaptable to the
Hilbert-Schmidt operatorial formulation of non-commutative quantum mechanics,
was developed earlier by introducing the appropriate spectral triple and used
to compute infinitesimal distances in the Moyal plane, revealing a deep
connection between geometry and statistics. In this paper, using the same
algorithm, the Connes spectral distance has been calculated in the
Hilbert-Schmidt operatorial formulation for the fuzzy sphere whose spatial
coordinates satisfy the $su(2)$ algebra. This has been computed for both the
discrete, as well as for the Perelemov's $SU(2)$ coherent state. Here also, we
get a connection between geometry and statistics which is shown by computing
the infinitesimal distance between mixed states on the quantum Hilbert space of
a particular fuzzy sphere, indexed by $n\in\mathbb{Z}/2$.
