This paper deals with the effect of bit change errors on the linear complexity of finite sequences. Though a change in a single bit can cause a large change in linear complexity, it is shown that on the average the change will be small even when many bits, e.g. 10 % are changed. General bijections and k-fold mappings on the set of sequences of length n are studied and tight bounds are found on the average difference in linear complexity between a sequence and its image. It is also shown that any mapping, on sequences of length n that take most sequences to images of low linear complexity must take many sequences to images that are far away from them in Hamming distance.