A data driver having a positive-polarity reference voltage generation circuit, a positive-polarity decoder, a first amplifier that outputs a positive-polarity gray scale voltage, a negative-polarity reference voltage generation circuit that generates a plurality of negative-polarity reference voltages, a negative-polarity decoder that outputs first to nth negative-polarity reference voltages from among the negative-polarity reference voltages, a negative-polarity amplifier that receives the selected first to nth negative-polarity reference voltages and outputs a negative-polarity gray scale voltage, and an output switch circuit that switches and controls whether to directly connect the first output terminal and the second output terminal to first and second data lines, respectively, or to cross-connect the first output terminal and the second output terminal to the second data line and the first data line, respectively, based on a control signal.