Hello Olga - There's the easy way, and the longer way. The easiest approach is use the data enrichment analysis tools, which can be accessed in ArcGIS Online or ArcGIS Pro.
Enrich Layer—ArcGIS Online Help | ArcGIS
Enrich Layer—Help | ArcGIS Desktop
Both clients use the same methodology of data apportionment to calculate the average value when the input boundaries don't match the enriching layer.
Data apportionment—ArcGIS REST API: GeoEnrichment Service | ArcGIS for Developers
If you only have access to ArcMap, you can use a similar approach, but it would be more of a manual process.
Adam Z