Both of those values are plausible.
Measure a brand new "1.5 V" alkaline battery. I usually get between 1.56 and 1.58V on several meters.
However, Wikipedia says:
The effective zero-load voltage of a non discharged alkaline battery, however, varies from 1.50 to 1.65 V, depending on the purity of the manganese dioxide used and the contents of zinc oxide in the electrolyte.