Approximate computing is a technique to tradeoff accuracy and hardware cost. It increases energy efficiency that leverages application-level tolerance to few errors in many applications including image processing, multimedia, machine learning and wireless communication. Truncated adders, as the most conventional approximate architectures, compute the addition of most significant bits, and produce small errors with high probabilities. In prior art, the adders have been analyzed considering uniformly distributed input data. However, in digital signal processing, the data has a distribution which can be considered as Gaussian distribution characterized by a mean value and standard deviation. This paper studies the effects of input data distribution on small-error approximate adders. We will show that the effects of Gaussian distribution can be modeled for the approximate adder architectures.