A method and apparatus to quantize/dequantize frequency amplitude data and a method and apparatus to audio encode/decode using the method and apparatus to quantize/dequantize the frequency amplitude data. The method includes calculating and quantizing power of frequency amplitudes for each of a plurality of bands constituting an audio frame, normalizing frequency amplitude data for each of the bands using the quantized power, and quantizing a first one of even-numbered or odd-numbered data among the normalized frequency amplitude data. The method may further include interpolating frequency amplitude data that corresponds to a second one of the even-numbered or odd-numbered frequency amplitude that is not quantized from among the normalized frequency amplitude data using the quantized first one of the even-numbered or odd-numbered data, and quantizing an interpolation error corresponding to a difference between the second frequency amplitude data that is not quantized and the interpolated frequency amplitude data.