The dependence of the Shannon entropy (SE) of a speckle pattern on the degree of polarization (DoP) of the pattern is investigated both experimentally and numerically. The superposition of two uncorrelated speckle patterns with polarization diversity is utilized to control the DoP of the superposed speckle pattern, and the SE of the pattern is estimated from the determined probability density function of intensity of the pattern. The SE is observed to be increasing quadratically with the DoP of the speckle pattern. The experimental observations are supported by the numerical studies. As the change of the SE indicates a change in the randomness of the intensity distribution, the variation of the standard deviation of intensity with the DoP is also investigated. Moreover, a linear relation between the SE and the standard deviation of intensity of a speckle pattern is also established. (C) 2021 Optical Society of America