In a method for encoding and an encoder statistical information is generated and said statistical information (LSB=F(MSB) about the reconstruction values to be used during reconstruction (sometimes called “inverse quantization”) is added to the encoded data signal. The encoded data signal comprises data information providing information on the relation between parts of the original input data removed during quantization and the quantized data. The decoder and decoding method use the information data during reconstruction. This enables reconstruction values to be used during reconstruction that can adapt to the input data statistics thereby improving data reconstruction and reducing the quantization error. The reconstruction at the decoder is guided by information data which is gathered at the encoder, this information data being derived from determining statistical information on the removed parts of the input data in relation to the after quantization remaining quantized data.