Suppose that one wishes to express the mean and the variance of the weight in kilograms 1pound = 0.45359kg. Weight observations were taken on a scale that had constant bias of +6

Question

Z=0.45359(X-6)

Answer 1

If you mean the bias was in lb, then that also has to be converted to kg. Variance is a square measurement (weight²), but the standard deviation would also need to be converted to kg.

If the stats are: mean±sd = (6+x)±y then 6lb=(2.72154+x)±0.45359y where you need to replace x and y by amounts in pounds. That’s my interpretation of your question.