The theoretical dependence of the mean and standard deviation of ADC values on signal-to-noise ratio (SNR) was derived and compared to measured values in porous phantoms and the lungs of human subjects using diffusion-weighted hyperpolarized helium-3 MRI. For SNR values below 15, mean ADC values were highly SNR-dependent due to a combination of noise and choice of noise thresholding. Above SNR values of 15 and for mean ADC values within ranges relevant for evaluating lung disease (<0.6 cm2/s), the mean ADC was largely independent of SNR. The standard deviation, by contrast, was highly dependent on SNR over a much larger range, but this dependence was well predicted by theory, suggesting the histogram of ADC values might be corrected for these stochastic processes to more accurately evaluate disease using restricted diffusion measures in the lungs.