How is it that we have a single phase two wire ungrounded secondaries off a transformer and it's not grounded anywhere in the windings primary or secondary but when you take a meter to one of the secondarys and to ground you get half voltage how's that possible with no reference to ground

either something "is" grounded or you are a getting a false reading from a digital meter.
How about a more detailed description of the transformer, applied voltage, the type of metering equipment, the measured voltage....etc.