A data encoding apparatus includes a memory storing computer-readable instructions; and one or more processors configured to execute the computer-readable instruction such that the one or more processors are configured to, receive first video data in a macroblock unit, determine a first rounding offset value using the first video data, create second video data by applying the first rounding offset value to the first video data, determine a second rounding offset value, which is different from the first rounding offset value, using the second video data, and create a quantized coefficient by applying the second rounding offset value to the first video data.