Low frequency sounds have better dispersion because they have a long wavelength that allows them to bend or diffract around objects. If the wavelength is 2 metres (~170 Hertz), you can imagine that an object which is 1/2 metre wide would not pose much of an obstruction for the sound wave.
In an indoor situation, a speaker generating a low frequency sound of wavelength 2 metres would be about 1/2 wave in a typical room (assume 4 metre wide room. We would not be able to detect the source location because of the long wavelength. It would be termed omnidirectional (good dispersion). However high frequency sound would beam out in a straight line from the tweeter and would be easily blocked by objects. The dispersion is poor relative to the low frequency sound.
In outdoor noise propagation, air absorption is very high at high frequencies (-7 dB/100 metres and higher)depending on the frequency, and only (0.1 dB/100) metres for the lower frequencies. Therefore a low frequency sound wave can travel much greater distances before air attenuation becomes significant, while higher frequency sound is significantly attenuated in a short distance. This can also be intrepreted as better dispersion.