I need to calculate minimum and mean distance between a point dataset of households and several business types (grocery, etc.) on other layers. Point distance is inadequate for me because I want to know the average distance between a house and *all* of a given business type within a search radius, as well as the distance to the closest one.
You can accomplish this by stringing together a few geoprocessing tools. First use Select Layer By Attribute to select all of the business of your desired type. Next you can use the Generate Near Table (Analysis) tool with your house point as input and your selected businesses as the Near Features. Uncheck the option towards the bottom to "Find only closest feature". Now you have the distance from your house to all of the selected businesses. Just look in the table, sorted by NEAR_DIST to see which business is the closest, and you can run Summary Statistics (Analysis) to determine what is the average/MEAN distance.
If you want to do this process for your home and many types in your business layer you will need to set up a model to iterate based on unique values in a field. You can search for "Iterate Field Values" in the ModelBuilder documentation to learn more.