We used archival very long baseline interferometry (VLBI) data of active galactic nuclei (AGN) observed from 1.4GHz to 86GHz to measure the angular size of VLBI radio cores in 8959 AGNs. We analysed their sky distributions, frequency dependencies and created the most densely sampled and complete to date distribution map of large-scale scattering properties of the interstellar medium in our Galaxy. Significant angular broadening of the measured AGN core sizes is detected for the sources seen through the Galactic plane, and this effect is especially strong at low frequencies (e.g., at 2GHz). The scattering screens containing electron density fluctuations of hot plasma are mainly concentrated in the Galactic plane and manifest clumpy distribution. The region of the strongest scattering is the Galactic centre, where the Galactic bar and the compact radio source Sagittarius A* are located. We have also found the enhancement of scattering strength in regions of the Cygnus constellation, supernova remnants Taurus A, Vela, W78 and Cassiopeia A, and the Orion Nebula. Using multi-frequency observational data of AGN core sizes, we separated the contribution of the intrinsic and scattered sizes to the measured angular diameter for 1411 sources. For the sources observed through the Galactic plane, the contribution of the scattered size component is systematically larger than for those seen outside the Galactic plane. The derived power-law scattering indices are found to be in good agreement with theoretical predictions for the diffractive-dominated scattering of radio emission in a hot plasma with Gaussian distribution of density inhomogeneities.