When some ionic compounds dissolve, not all of their bonds dissociate. what kind of conductivity would you expect such a solution to have?

A solution of an ionic compound that does not totally split in solution will nearly continually have electrical conductivity lower than that for a solution of the same concentration of a compound in which all the ionic bonds do dissociate in the solvent. As opposed to a strong electrolyte which totally dissociates into detached ions or a non-electrolyte which doesn't detach at all.