  We develop theory for fluctuations in atom number and spin within
finite-sized cells of a spinor Bose-Einstein condensate. This theory provides a
model of measurements that can be performed in current experiments using finite
resolution in situ imaging. We develop analytic results for quantum and
thermodynamic limits of the fluctuations and apply our theory to the four
equilibrium phases of a spin-1 condensate. We then validate these limits and
examine the behaviour over a wide parameter regime using numerical calculations
specialised to the case of a spinor condensate confined to be
quasi-two-dimensional (quasi-2D).
