How to obtain the transfer function of this sensor?
If this was the actual calibration,
RH' = \$\frac {V_{OUT}  (5.00V/V_{SUPPLY}) - 0.826V}{0.315}\$
So for Vsupply = 5.1V, Vout = 0.83V
RH' = (0.83V*(5V/5.1V) - 0.826V)/0.315 = 2.5%  (assuming temperature is 25°C)
However you should also correct for temperature
RH = \$\frac {RH'}{1.0546 – 0.00216T}\$
where T is the temperature in °C