The use of averaging has long been known to reduce noise in statistically independent systems that exhibit similar levels of stochastic fluctuation. This concept of averaging is general and applies to a wide variety of physical and man-made phenomena such as particle motion, shot noise, atomic clock stability, measurement uncertainty reduction, and methods of signal processing. Despite its prevalence in use for reducing statistical uncertainty, such averaging techniques so far remain comparatively undeveloped for application to light. We demonstrate here a method for averaging the frequency uncertainty of identical laser systems as a means to narrow the spectral linewidth of the resulting radiation. We experimentally achieve a reduction of frequency fluctuations from 40 Hz to 28 Hz by averaging two separate laser systems each locked to a fiber resonator. Only a single seed laser is necessary here as acousto-optic modulation is used to enable independent control of the second path. This technique of frequency averaging provides an effective solution to overcome the linewidth constraints of a single laser alone, particularly when limited by fundamental noise sources such as thermal noise, irrespective of the spectral shape of noise.