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A superconducting quantum interference device and Faraday rotation technique are used to study dipolar interacting nanoparticles embedded in a polystyrene matrix. Magnetization isotherms are measured for three cylindrically shaped samples of constant diameter but various heights. Detailed analysis of the isotherms supports Tsallis' conjecture of a magnetic equation of state that involves temperature and magnetic field variables scaled by the logarithm of the number of magnetic nanoparticles. This unusual scaling of thermodynamic variables, which are conventionally considered to be intensive, originates from the nonextensivity of the Gibbs free energy in three-dimensional dipolar interacting particle ensembles. Our experimental evidence for nonextensivity is based on the data collapse of various isotherms that require scaling of the field variable in accordance with Tsallis' equation of state.